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Aqueous Solutions containing Amino-acids and PeptidesPart 3.-The Osmotic Coefficient at the Freezing Temperature of the Solutions ofAqueous Systems containing Glycine and some Alkali Metal Chlorides and someTetra-alkylammonium BromidesBY TERENCE H. LILLEY* AND R. P. SCOTT?Chemistry Department, The University, SheEeld S3 7HFReceived 14th April, 1975The freezing temperature method has been used to determine the osmotic coefficients of aqueoussolutions containing the single solutes tetramethylammonium, tetraethylammonium, tetra-n-propylammonium and tetra-n-butylammonium bromides. The results obtained are compared withthose of other tetra-alkylammonium halides. The same experimental technique has been used toinvestigate binary solute aqueous systems containing glycine and LiCI, KCI, CsCl and the tetra-alkylammonium bromides above. The results obtained are discussed from the viewpoints of theKirkwood approach to systems containing ions and amino-acids and the McMillan-Mayer treatmentof solutions.Thermodynamic aspects of the interaction of amino-acids and small peptides withsalts have been of interest for some years.I Most of the systems which have beeninvestigated in the past have contained mono-atomic ions of comparatively smallIn this paper we present an investigation of the interaction of glycinewith several salts including some of a type more complex than those previouslystudied.The work is an extension of our earlier investigations on systems containingnon-ionic solutes and mixtures of ionic and non-ionic s01utes.~ The terminologyused is similar to that used previo~sly.~EXPERIMENTALThe apparatus used to determine freezing temperatures was similar to that used byBrown and Prue." In the present experiments we wished to cover a rather larger molalityrange than these workers and preliminary experiments indicated that the size of the tankcontaining the ice-water external thermostatting was important.It would seem that thefreezing-temperature assembly should be well removed ( > 40 cm) from the edges of the tankand that the assembly should be completely immersed below the surface of the thermostattingbath. The freezing temperature assembly consisted of twin commercial Dewar flasks ofdepth 20 cm and internal diameter 6 cm which had been re-evacuated to 0.01 N m-2.TheDewars were held 4cm apart in an aluminium frame. The multijunction thermocouplewith the associated stirring and sampling devices was fixed to bungs. It was necessary toseal the bung-Dewar interfaces and several materials were tried, the most satisfactorybeing Apiezon Q compound. Stirring of the contents of each Dewar was by means of astream of pre-cooled White Spot nitrogen. The nitrogen was cooled by passage througha series of Dreschel bottles, these being immersed in the thermostat tank. Stirring insideeach Dewar was by means of a gas-jet circulator." The nitrogen flow rate was monitoredand continuously adjusted to 500 cm3 min-'. The effect of dissolved nitrogen on thet present address : Chemical Defence Establishment, Porton Down, Salisbury.19198 AQUEOUS SOLUTIONS OF AMINO-ACIDSobserved freezing point depressions l2 was well within our experimental error.The tempera-ture difference between the contents of the two Dewar vessels was obtained from a 22 junc-tion copper-constantan thermocouple. Construction was from 36 s.w.g. copper and con-stantan wire (supplied by Saxonia Electrical Wire Co. Ltd.) and junctions were soft-solderedand insulated from one another by sheaths of PTFE tubing. The completed thermocouplewas put into a glass frame l3 and the ends of the thermo-element were immersed in liquidparaffin. This ensured ready heat flow between the junctions and the solutions and reducedconsiderably the response time of the thermo-element. The measuring circuit was similar tothat used earlier.1o* l 1 The molalities of the solutions were monitored using conductancemeasurements.Samples of solution were transferred from the Dewar vessel to a conductancecell immersed in the thermostat bath.MATERIALSThe purification of water l4 and CsCl l5 have been given earlier. LiCl (K & K Labora-tories Ltd., purity 99.65 %) was dissolved in a minimum of water and the solution filtered.Most of the water was removed by heating at 420 K in a stream of HCl. This residue wasdried over P205 for 3 days and then fused in an atmosphere of HCl. Chloride analysisof the Fused material gave the purity as 99.9k0.1 %. NaCl and KCl were of Ultrar reagentgrade and were dried at 473 K before use. Tetramethylammonium bromide (Me4NBr)(B.D.H.Laboratory reagent) was recrystallised twice from a 1 : 1 mixture of methanol andethanol, tetraethylammonium bromide (Et,NBr) (Eastman Kodak) was recrystallised threetimes from a 1 : 3 mixture of methanol and ethyl acetate, tetra-n-propylammonium bromide(Pr,NBr) (Eastman Kodak) was recrystallised from acetone and tetra-n-butylammoniumbromide (Bu4NBr) (Eastman Kodak) was recrystallised from a 20: 1 mixture of ethylacetate and diethyl ether. All salts were dried in vacuo at 333 K for some days before use.Glycine (B.D.H. AnalaR) was twice recrystallised from a 1 : 1 methanol+ water mixture anddried in uacuo at 293 K.In each series of measurements the molalities of the solutions were determined from apreliminary calibration of the conductance cell.The calibration was performed by measur-ing the conductances of solutions of known molality over the molality range from whichsamples were to be taken. All solutions were prepared by mass and buoyancy correctionsapplied.The thermoelement was calibrated by using data 12* l6 on aqueous NaCl and KClsolutions. The original data for each system in the molality range 0.02-0.6 mol kg-l werereanalysed and the freezing temperatures fitted by a least-squares method to an equation ofthe form8 = bom+blm~+b2m2+b3m~fb4m3 (1)where 0 is the freezing temperature depression, bi is a coefficient and rn is the formal molalityof the salt. The agreement between experimentally observed l6 values and those calculatedfrom the smoothed data was within 2x K.Freezing temperature experiments wereperformed on aqueous NaCl and aqueous KCl solutions between molalities of 0.05-0.5mol kg-l. Most of the measurements were made on NaCl solutions. The molalities weredetermined from appropriate conductance measurements and the corresponding freezingtemperature depressions from eqn (1) with appropriate coefficients. The freezing temperaturedepression was related to the thermoelement e.m.f. ( E ) by8 = aE+bE2.The parameters obtained were a = 1.201 54x K V2.The mean difference between smoothed and experimental freezing temperatures was 5 xK. A further check on the thermoelement calibration was obtained when the aqueous CsClsystem was investigated.' The maximum difference between the results obtained by us andthose obtained by Lange I7 was 6 xThe apparatus worked well for aqueous solutions having a total molality of up to 1 molkg-I but above this molality instability in the thermoelement e.m.f. was apparent.K V-I and b = 4.853 xKT.H. LILLEY AND R. P . SCOTT 199TABLE 1 .-FREEZING TEMPERATURE DEPRESSIONS OF AQUEOUS SOLUTIONS AS A FUNCTION OFMZ/rnol kg-10.020 0480.033 0760.039 9930.050 3120.059 2730.064 8700.070 1240.092 5200.125 270.183 770.306 640.376 750.443 870.476 820.016 9520.032 4420.053 1800.071 1070.091 7680.119 990.193 150.258 680.311 94SALT MOLALITYO/K 4’az/mol kg- 1Me4NBr Et4NBr0.071 3 0.024 5680.115 0 0.039 0440.138 1 0.056 1740.172 8 0.075 9310.202 9 0.103 190.221 5 0.125 730.237 7 0.147 270.309 6 0.197 000.414 9 0.238 340.593 2 0.294 380.957 4 0.343 671.159 0 Bu4NBr1.350 1 0.013 4411.447 7 0.019 783Pr4NBr 0.029 4590.060 3 0.036 9210.112 9 0.042 2730.181 1 0.049 2330.238 4 0.060 0920.303 3 0.072 6500.389 9 0.080 9670.607 8 0.087 3120.785 9 0.096 4850.943 9 0.103 28B/K0.087 30.136 20.192 50.256 10.341 90.411 30.476 00.621 90.741 30.900 21.035 70.048 30.070 90.102 90.128 30.145 60.168 60.203 90.244 70.271 60.291 40.320 60.342 2TABLE 2.-FREEZING TEMPERATURE DEPRESSIONS FOR AQUEOUS SOLUTIONS OF GLYCINE+ SALTLiCly = 0.682 66KCly = 0.315 170.262 21 0.471 90.342 22 0.658 10.519 46 0.915 50.594 70 1.042 70.667 48 1.164 20.795 55 1.375 50.844 20 1.453 5y = 0.500 360.278 18 0.495 50.334 11 0.595 10.396 66 0.702 10.518 21 0.911 40.617 32 1.080 10.695 24 1.211 10.847 70 1.470 10.901 45 1.557 7y = 0.337 020.261 04 0.464 20.348 71 0.619 00.495 53 0.872 30.593 78 1.042 30.204 95 0.361 90.327 66 0.571 00.411 68 0.712 10.538 47 0.922 00.654 79 1.115 20.744 26 1.261 10.803 15 1.356 7y = 0.515 450.214 07 0.383 10.348 94 0.613 30.500 67 0.867 70.546 08 0.944 80.645 55 1.108 20.714 32 1.122 00.907 68 1.533 2y = 0.653 250.201 21 0.360 60.226 90 0.405 60.549 6 0.310 190.409 41 0.719 60.568 98 0.987 200 AQUEOUS SOLUTIONS OF AMINO-ACIDSTABLE 2.--continued1.126 8 0.700 83 1.206 61.339 5 0.868 55 1.476 31.474 61.568 40.642 700.765 580.843 140.897 85CSCly = 0.502 900.363 20 0.636 50.466 87 0.808 90.562 12 0.967 40.626 35 1.072 20.755 72 1.282 70.904 61 1.522 7y = 0.318 590.173 99 0.307 50.306 46 0.530 90.409 70 0.702 60.508 18 0.863 70.600 06 1.013 80.713 47 1.196 20.838 10 1.395 2Me4NBry = 0.307 980.130 42 0.233 70.237 91 0.415 70.370 00 0.635 20.449 23 0.765 70.533 03 0.902 60.661 93 1.111 10.744 87 1.245 70.853 08 1.420 6y = 0.664 860.113 36 0.208 10.166 47 0.303 00.249 98 0.405 10.348 95 0.623 60.432 13 0.768 10.525 71 0.929 10.672 27 1.180 10.786 69 1.374 30.896 56 1.558 9y = 0.679 610.067 16 0.124 30.125 55 0.231 10.149 03 0.274 90.185 70 0.341 80.246 86 0.452 40.298 12 0.546 00.346 82 0.634 5Bu4NBrEt4NBry = 0.354 190.169 02 0.298 30.302 15 0.526 00.383 62 0.662 40.491 07 0.841 50.606 73 1.035 10.747 45 1.268 40.875 77 1.479 0y = 0.590 980.164 95 0.297 80.260 16 0.467 10.425 00 0.756 00.531 66 0.944 60.648 24 1.146 80.738 47 1.303 00.815 51 1.436 9Pr,NBry = 0.332 380.192 82 0.339 90.277 08 0.484 20.432 68 0.749 90.541 53 0.939 10.666 46 1.154 50.778 22 1.351 00.869 70 1 SO9 0y = 0.616 060.217 68 0.392 80.381 72 0.689 00.516 89 0.931 50.638 08 1.149 50.763 06 1.374 70.859 79 1.549 9y = 0.504 620.044 23 0.080 80.074 02 0.134 80.135 12 0.245 30.175 70 0.317 90.217 02 0.392 70.264 36 0.477 80.308 25 0.557 50.323 07 0.583 20.373 00 0.673 90.377 54 0.681 3y is the solute fraction of glycine in the solutionsT.H . LILLEY AND R . P . SCOTT 201RESULTSThe freezing temperature depressions obtained for the solutions containing onlytetra-alkylammonium bromides are given in table 1 and those for binary solutemixtures are given in table 2. The molality range over which measurements couldbe made for the aqueous Bu,NBr system was restricted because of the precipitationof a hydrated species.DISCUSSIONTHE SYSTEMS CONTAINING H,O+TETRA-ALKYLAMMONIUM BROMIDEThe osmotic coefficients l9 of these systems were initially fitted by a least squaresprocedure to an extended Guggenheim 2o equation.where is defined l 5 asThe data for the Bu,NBr system were fitted to a truncated form of eqn (3) with onlythe first term on the right-hand side being retained.The values obtained for theparameters p, y and 6 are listed in table 3.The regressed quantity wasm(+ - @=I> = pm2 +- ym3 + 6m4 (3)+el = 1 -(+)am*o(m+). (4)TABLE 3 .-PARAMETERS FOR EQN (3) OBTAINED FOR THE AQUEOUS TETRA-ALKYLAMMONIUMBROMIDE SYSTEMS*Me4NBr -0.259 86+0.010 21 0.333 62k0.054 37 -0.201 48k0.071 39Et,NBr -0.315 56k0.022 63 0.159 81k0.175 94 0.230 17k0.330 99salt B/rnol-l kg y/mol-2 kg2 6/mol-3 kg3(-0.233 31 0.072 80 -0.321 80)tPr4NBr -0.460 11+0.010 13 0.996 58+0.085 06 -1.027 36k0.174 29Bu4NBr - 0.301 97+ 0.006 77(-0.830 45 1.437 03 1.593 50)$* The parameters in the above table are given to five significant figures, although the standarddeviation on the parameters indicates that it is meaningless to quote these to this precision.Thefigures have been retained in this table to enable these to be used to regenerate the smoothed data.t At 298.15 K, from a reanalysis of data in ref. (23).1 Data for this system were obtained using eqn (3).All of the osmotic coefficients are obtained at the freezing temperature of thesolution under investigation. It has been shown I g b that when 8 < 1 K the correc-tion required to bring the osmotic coefficients from the freezing temperature of thesolutions to the freezing temperature of the pure solvent is less than the uncertaintyin the cryoscopic constant. The osmotic coefficients at the freezing temperature ofthe solutions were taken as reasonable approximations to those at 273.15 K.Withinthis approximation the mean ionic activity coefficients at this temperature werecalculated via the Gibbs-Duhem equation and the parameters given in table 3.In table 4 are listed smoothed values of the osmotic and activity coefficients at roundedvalues of salt molality.for several aqueoustetra-alkylammonium chlorides and iodides were re-analysed using eqn (3). (Thedata were available over the molality range 0-0.1 mol kg-l and consequently atruncated form of eqn (3) containing only the first term on the right-hand side wasused.) The values of the parameters obtained are given in table 5. Prue et aZ.22have also re-analysed Lange's 21 data and the agreement of the parameters given inThe freezing temperature depression data obtained by Lang202 AQUEOUS SOLUTIONS OF A M I N O - A C I D Stable 5 with those obtained by Prue 2 2 is good with the exception of the Pr,NClsystem.This discrepancy probably arises from differences in the data analysisprocedures, since for this system the quantity (q5-4e1) scatters about zero.TABLE 4.-sMOOTHED VALUES OF THE OShlOTIC COEFFICIENT AND THE LOGARITHM OF THE MEANIONIC ACTIVITY COEFFICIENT FOR AQUEOUS SOLUTIONS OF TETRA-ALKYLAMMONIUM BROMIDESAT 273.15 KMe4NBr Et4NBr PrrNBr Bu4NBrmlmolkg-1 4 -hY+ d --In?J+ d -hY+ d - h y +0.020.040.060.080.100.120.160.200.240.280.320.360.400.440.480.951 20.932 80.919 20.908 10.898 50.890 10.875 70.863 70.853 50.844 70.837 00.830 20.824 10.818 60.813 50.150 40.208 70.252 20.288 10.319 20.346 90.394 90.435 90.471 90.504 00.532 90.559 30.583 60.606 20.627 20.950 00.930 30.915 30.902 70.891 60.881 60.861 40.849 10.836 10.825 00.815 50.152 80.213 50.259 70.298 40.332 40.363 00.417 10.464 00.505 70.543 00.576 40.947 40.925 80.909 40.895 90.884 30.874 20.857 30.843 60.832 30.822 50.813 70.158 1 0.950 2 0.152 30.223 2 0.930 6 0.212 80.2729 0.915 5 0.25900.314 4 0.902 7 0.297 90.350 4 0.891 2 0.332 40.382 50.438 00.485 10.526 00.562 30.595 3TABLE 5.-THE p PARAMETERS OBTAINED FOR THE AQUEOUS TETRA-ALKYLAMMONIUM HALIDESYSTEMScationlanionp/mol-1 kgc1- 21 Br- I- 21Me4N+ - 0.03 - 0.26 - 0.40Et,N+ 0.02 - 0.32 - 0.36Pr4N+ 0.1 1 - 0.46 - 0.78Bu~N+ 0.45 - 0.30 - 1.49The aqueous Et,NBr and Bu4NBr systems have been investigated at 298.15 Kby K u , ~ ~ using concentration cells.These data were re-analysed and regressed toeqn (3). The parameters obtained are included in table 3. A precise comparisonbetween the present results and those of Ku 2 3 is not possible because of the lackof appropriate enthalpy data but use of the limited data available 24 reproduces thequalitative features observed between the results obtained at 298.15 K and those atthe freezing temperature.The osmotic coefficients of the aqueous tetra-alkylammonium bromide systemsobtained here seem to fit into the general pattern observed for other aqueous tetra-alkylammonium halide systems.It is not appropriate to discuss this behaviour anyfurther here since an explanation of the properties of solutions containing only tetra-alkylammonium salts is not the object of the present work and such systems havebeen extensively discussed elsewhere.2SYSTEMS CONTAINING H,~+ELECTROLYTE+GLYCINEThe thermodynamic treatment for systems containing solvent + electrolyte + non-electrolyte is fairly straightforward and a simple extension of the earlier appr~ach.~The method used is given in the AppendixT. H . LILLEY AND R. P. SCOTT 203The application of eqn (A20) to the present systems requires a knowledge of theosmotic coefficients of the single solute systems glycine and each salt, at the freezingtemperature of the solutions.Scatchard et aL2 have used the freezing temperaturemethod to investigate the aqueous glycine system and in this work the osmoticcoefficient was represented as a parametric equation in the molality of glycine. Thevalue used for the cryoscopic constant differs a little from the presently acceptedvalue l 5 and so these data were re-analysed using the currently accepted value.Scatchard et ai.16 have also determined the osmotic coefficients of the aqueous systemscontaining LiCl, NaCl and KCl. The analysis of the latter two systems was referredto earlier. The LiCl system was re-analysed in the same manner as were the experi-mental results obtained by us for the CsCl l5 system and the systems containingtetra-alkylammonium bromides. The coefficients determined from this re-analysisare given in table 6.The reasons we prefer to use this method of data analysis arebecause :(a) the experimentally measured quantity is regressed,(b) the osmotic coefficients for the various solutions are determined over a rangeof temperatures and therefore different Debye-Huckel parameters should beused for each molality.The osmotic coefficients of the aqueous binary mixtures presented in table 2 wereanalysed by a least squares method using an equation of the form [see eqn (A20)]@B4(mix) - 2m4(E) - rniq5(i> - 3ct6m3 I2mi f D, = Dmmi i- Em2mi i- Fmm:. ( 5 )The coefficients in eqn (5) are related to those in eqn (A20) by[We attempted to use both expanded and truncated forms of eqn ( 5 ) but statisticalconsiderations indicated that the form finally used was adequate for the data obtained.]The value used for the dielectric increment 6 was 22.6 kg mo1-1.26 The resultsobtained from the analysis for the systems investigated are given in table 7.TABLE 6.-PARAMETERS FOR EQN (1) OBTAINED FOR AQUEOUS SINGLE ELECTROLYTE SOLUTIONSsalt bo/K kg rno1-I bl/K kgQ mol-% b2/K kgz mol-2 b3/K kgq mol-9 b4/K kg3 mol-3LiClNaClKClCsClMe4NBrEt4NBrPr4NBrB u ~ N B ~3.702 78 - 1.333 79 3.050 12 - 3.057 04 1.566 523.698 03 - 1.129 45 1.626 70 - 1.251 30 0.452 703.664 19 -0.810 43 0.235 35 0.609 16 0.441 103.613 78 -0.251 53 -2.355 16 4.481 98 -2.496 673.646 89 -0.719 19 -1.446 58 2.466 62 - 1.086 003.655 22 0.050 41 - 6.818 03 12.956 14 - 7.943 013.820 37 -2.290 44 2.658 74 -2.857 58 1.642 333.867 27 -2.575 37 2.656 94 - -Scatchard et ai.,3 Joseph and Phang and Steele have investigated the aqueoussystem glycine + NaCl at approximately the same temperatures as those covered bythe present study.The experimental results obtained by these workers are not incomplete agreement with one another ti but do fit into the general pattern of theresults presented in table 7.The behaviour of aqueous solutions containing amino-acids and peptides andelectrolytes have been discussed several times.'* 3-8* 27* 28 Some of these authors 5 204 AQUEOUS SOLUTIONS OF AMINO-ACIDShave assumed that the thermodynamic observations arise solely from ion-dipole inter-actions and may be described using the Kirkwood 279 28 approach.In such approachesthe dipole moment of the amino-acid is calculated and compared with the experi-mentally determined value. It can be shown that the Kirkwood 2 7 9 28 B coefficientmay be equated to our term 2 ( g M i + g X i ) . In table 8 we present calculated values of(gMi+gxi) using appropriate values of the molar volume for glycine 29 together withionic radii.30 We have used Robinson and Stokes’ 31 estimate for the ionic radii ofthe tetra-alkylammonium ions. Owing to the uncertainty of the dipole moment ofglycine in aqueous solutions we used the two extreme values 7* 26 estimated for this.Table 8 also includes the experimentally observed coefficients and it is apparent thatfor the larger ions particularly, the Kirkwood approach is inadequate.TABLE 7.-vALUES OF THE PARAMETERS D, E AND F FOR EQN (6) FOR VARIOUS AQUEOUS SOLU-TIONS CONTAINING GLYCINE AND AN ELECTROLYTEelectrolyte D/kg mol-1 Elkg2 mol-2 F/kg* mol-2LiCl - 0.3 1 5 + 0 -020 - 1 .OlO+ 0.056 -0.057+0.032KCl - 0.436+ 0.015 - 0.8 1 1 0.052 0.036+0.023CSCl -0.437+0.013 - 0.879+ 0.049 0.163+0.023Me4NBr - 0.043+0.024 - 0.987k 0.072 0.028 + 0.03 1Et4NBr 0.088+0.019 - 0.884f 0.054 0.122k0.345Pr4NBr 0.413+ 0.021 - 0.550f 0.059 - 0.182+ 0.23 1Bu,NBr 0.735+ 0.050 - 2.968+ 0.402 - 0.006+ 0.238TABLE 8 .-VALUES OF (&i+ &~)NE PREDICTED FROM THE KIRKWOOD ELECTROSTATICMODEL 279 28 AND THOSE OBTAINED EXPERIMENTALLYmodel using a value model using a value ofelectrolyte of 13.5 debye of 16.7 debye experimentalLiCl -0.171KCI -0.162CSCl -0.158Me4NBr -0.135Et4NBr -0.130Pr4NBr -0.125Bu4NBr - 0.121+ d d m o l kg-l-0.315- 0.294- 0.284- 0.240-0.230- 0.220-0.213-0.158- 0.21 8-0.219- 0.0220.0440.2070.3 68If the charge on the ions of the component electrolyte becomes zero, then theKirkwood method 279 28 predicts that the solutions should behave ideally.It isknown 32 however from the behaviour of systems containing only non-electrolytesthat this is not so. We assume that we may write the experimentally observed( g M i + g x i ) coefficient as the sum of two parts, an “ electrostatic ” part described bythe Kirkwood model and a “ non-electrostatic ” part described by the McMillan-Mayer 33 treatmentIf eqn (21) of ref. (9) is generalised to consider a three solute component system we get( g M i + g X i ) = (gMi+gXi)K+ (gMi+gXI)NE* (7)We stress that eqn (8) deals only with the non-dipole-ion interactions (as calculatedfrom Kirkwood’s 27* 2 8 approach) between the ions and the non-electrolyte. Thevalues of (gMl +gX& which would be obtained assuming all solute-solute interactionswere of the “ hard-sphere ” type may be estimated from knowledge of the partiaT.H. LILLEY AND R. P. SCOTT 205molar volumes of the salts 34 and the partial molar volume of g l y ~ i n e , ~ ~ all at infinitedilution. In fig. 1 we give a comparison of the determined values of (gMi+gXJNEand the values expected for " hard-sphere " interactions. There is, of course, someuncertainty in the former quantities because of the uncertainty in the dipole momentof glycine.o'6d IM%2X B 0.2 +n20 0I4[ ( r ~ + + YX -)/2]/1 O-'OmFIG.1 .-The nonelectrostatic contribution to the interaction parameter for the systems studied.The solid line represents " hard sphere " behavi~ur.~ 0, 16.7 debye ; ., 13.5 debye.Within experimental error it appears that for all of the systems investigated,(gMi +gXJNE is zero or attractive when compared with the " hard-sphere " prediction.A similar conclusion was reached earlier for systems containing only non-electrolyticsolute species.APPENDIXThe formalism used earlier may be applied to systems containing electrolytes if somemodifications are made. For simplicity we consider only systems in which the electrolyteis of the 1 : 1 charge type.The Gibbs function G(E) of a solution containing only the elec-trolytic solute MX may be written as 35G(E) = G~-22RTm$(E)+~~~~+2mRTlnmy+(E) (A0where the terminology is as before, but the parenthetical E stresses that only electrolyte ispresent in the solution. If ideality is defined on the mold scale then the excess Gibbs functionisGeX(E) = G(E)- Gid(E)= 2RTm( 1 - $(E)+ lny +(E)).The corresponding expressions for the systems solvent + non-electrolyte and solvent +electrolyte+ non-electrolyte areGex(i) = RT'i( 1 - &i)+ Inyi(i))GeX(mix) = RT(w[l -~(mix)]+2rnlny*(mix)+ milnyj(mix)).(A3)(A4)Before proceeding further, we assume that the excess Gibbs function of such systems asthose considered may be written as the sum of two parts, one part arising from electrostaticinteractions between ions in solutions and the other part arising from interactions whichare similar to those which occur in non-electrolytic solutions.If the electrostatic interactio206 AQUEOUS SOLUTIONS OF AMINO-ACIDSbetween ions may be described in terms of the Dzbye-Huckel approach, then the electro-static contribution to the Gibbs function is given by 36(A51Since Gel --+ 0 as Cmk --+ 0, the electrolyte in an electrolyte+ non-electrolyte mixture must beconsidered in terms of a " solvent " consisting of a solution of the solvent, plus the non-electrolyte i at molality mi. The chemical potential of the salt MX can then be defined asGel = - (RT/3)Cnkz,~~'S((3/2)(1+ rC'a)-l- +o(lc'a)).kp M x = + 2 ~ ~ l n m y (soln)withand consequentlywhere ,ukx is the conventional standard chemical potential of MX,If we consider the situation when mi + 0 as m + 0 thenP2;'ln = (PMX- 2RTlnm),-+(),u;ioln = / i ~ ~ + 2 ~ ~ 1 n y* m = 0 )PhX = (PMX-2RT1n m)92?-+oa2R r(gM i + Qx Jmmi - 6RT(gMii + gxiihm; - 6RT(g~,i gxx i C 2gMyIxi)m2mi * * (A1 3)If we make the simplifying approximation that eqn (A5) may be written as 37(A1 4)and that the molality of the electrolyte with respect to the pure solvent component and thesolution containing the non-electrolyte are the same, thenGel = - (RT/~)C~~Z~Z,~K'SUsing eqn (A14), together with the definitions of IC' and S 36K r 2 = 8nLpSx( 1 /2)mkz$kS = e2/4moD,kTDsoln = Ds+6mand expressing the relative permittivity of the solution as 38we haveGel (mix) - Gel (E) = R T( 8 np L)+ (e2 /4n~, k T D a ) ~ m ~ m / D, . (A 17)Since &c'S = eqn (A17) becomeT.H . LILLEY AND R. P. SCOTT 207We thank S.R.C. for the award of a Research Studentship to R. P. S .C. C. Briggs, T. H. Lilley, J. Rutherford and S . Woodhead, J. Solution Chem., 1974, 3, 649.This paper gives reference to earlier work.G. Scatchard and S. S . Prentiss, J. Amer. Chem. SOC., 1934, 56, 807.G. Scatchard and S. S. Prentiss, J. Amer. Chem. SOC., 1934, 56, 2314.R. M. Roberts and J. G. Kirkwood, J. Amer. Chem. SOC., 1941, 64, 1373.S. Phang and B. J. Steele, J. Chem. Thermodynamics, 1974, 6, 537.E. E. Schrier and R. A. Robinson, J. Biol. Chem., 1971, 264, 1971.E.E. Schrier and R. A. Robinson, J . Solution Chern., 1974, 3,493.T. H. Lilley and R. P. Scott, submitted to J.C.S. Faraday I, 1975, 71, 184.lo P. G. M. Brown and J. E. Prue, Proc. Roy. SOC. A, 1955,232,320.P. G . M. Brown, Thesis (Reading, 1955).l2 G. Scatchard, P. T. Jones and S. S. Prentiss, J. Arner. Chem. SOC., 1932, 54,2676.l3 R. P. Scott, Thesis (Sheffield, 1974).l4 C. C. Briggs, R. Charlton and T. H. Lilley, J. Chem. Thermodynamics, 1973, 5, 445.l5 T. H. Lilley and R. P. Scott, J. Chem. Thermodynamics, 1974, 6, 1015.l6 G. Scatchard and S. S . Prentiss, J. Amer. Chem. SOC., 1933,55,4355.l7 J. Lange, 2. phys. Chem., l936,177A, 193.l 8 R. McMullan and G. A. Jeffrey, J. Chem. Phys., 1959,31, 1231.l 9 (a) The transformation of freezing temperatures to osmotic coefficients is discussed in ref.(15) and by (6) G. N. Lewis and M. Randall, Thermodynamics, ed. K. S. Pitzer and L. Brewer(McGraw-Hill, New York, revised edn., 1961), p. 407.4N. R. Joseph, J. Biol. Chem., 1935, 111,489.’O E. A. Guggenheim, Phil. Mag., 1935, 19,588.21 J. Lange, 2. phys. Chem., l934,168A, 147.22 J. E. Prue, A. J. Read and G. Romeo, Trans. Faraday SOC., 1971, 67,420.23 J. C. Ku, Thesis (Pittsburgh, 1971).24 S. Lindenbaum, J. Phys. Chert., 1966, 70,814.2 5 see e.g. (a) W-Y. Wen and J. H. Hung, J. Phys. Chem., 1970,74, 170. (6) J. E. Desnoyers andC . Jolicceur, in Modern Advances in Electrochemistry, ed. J. O’M. Bockris and B. E. Conway(Butterworth, London, 1968), vol. 5, chap. 1.26 J. T. Edsall and J. Wyman, Biophysical Chemistry (Academic Press, New York, 1958), vol. 1,p. 372.27 J. G. Kirkwood, Chem. Rev., 1939, 24, 233.28 J. G. Kirkwood, in Proteins, Amino-acids and Peptides, ed. E. J. Cohn and J. T. Edsall (Rhein-hold, New York, 1943) chap. 12. *’ H. J. V. Tyrrell and M. Kennerley, J. Chem. SOC. A, 1968,2724.30 R. A. Robinson and R. H. Stokes, Electrolyte Solutions (Butterworth, London, 1965), p. 461.31 ref. (30), p. 125.32 see ref. (9) for a discussion and earlier references.33 W. G. McMillan and J. E. Mayer, J. Chem. Phys., 1945,13,276.34 F. J. Miller0 in Water and Aqueous Solutions, Thermodynamics and Transport Processes, ed.35 H. L. Friedman, Ionic Solution Theory (Wiley, New York, 1962), pp. 194-195.36 E. A. Guggenheim, Thermodynamics (North Holland, Amsterdam, 1967), p. 285.37 H. L. Friedman, Ionic SoZution Theory (Wiley, New York, 1962), p. 281.38 J. T. Edsall and J. Wyman, Biophysical Chemistry (Academic Press, New York, 1958), vol. 1,R. A. Horne (Wiley, New York, 1972), p. 569.p. 367.(PAPER 5/709

ISSN:0300-9599    

DOI:10.1039/F19767200197

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

Flame Photometric Determinations of Diffusion CoefficientsPart 5.-Results for Calcium Hydroxide, Strontium Hydroxide,Barium Hydroxide and CopperBY ANTHONY F. ASHTON? AND ALLAN N. HAYHURST*$Department of Chemical Engineering, University of CambridgePenibroke Street, CambridgeReceived 6th May, 1975Diffusion coefficients are measured for trace quantities of the additives Ca, Sr, Ba and Cu in theburnt gases of flames of H2, 0, and N2 over the temperature range 1900-2520K. The alkalineearth metals exist in these flames chiefly as the dihydroxides, whereas with copper the dominantspecies is free atoms. The measured diffusion coefficients are interpreted in terms of two intermole-cular potential functions to describe interactions between the diffusing and flame species, which areHz, H20 and N2.It is concluded that the Lennard-Jones function is preferable here to a purelyrepulsive inverse power one. Values of the Lennard-Jones parameters are presented together withthe constants characterising purely repulsive forces. In addition, two mixing rules are investigatedfor describing the overall diffusivity of a tracer in a multicomponent mixture in terms of a set ofbinary diffusion coefficients.Very few measurements have been made of gas phase diffusion coefficients attemperatures above 1OOOK. The work reported below applies further the pointsource technique,lm4 whereby trace quantities of a substance which colours a flameare added at a single point to flames (temperature range 1900-2520 K), in which thereis a good approximation to piston and laminar flow, i.e., a flat velocity profile. So farthe method has been used for atoms of the alkali metals 5 9 and also nitric oxidemolecules,’ all diffusing in effectively zero concentrations in the burnt gases of flamesof H, and 0, diluted with N2.The tracer is continuously added from one point inthe reaction zone on the flame axis. Downstream of this in the burnt gas region,where the temperature, velocity and composition are not varying significantly, theadditive diffuses radially away from the axis. The rate of this process is followed byobservations of the intensity of the radiation emitted by those tracer species remainingnear the flame axis at various points along its length.This paper is concerned with copper and the alkaline earth metals Ca, Sr and Badiffusing through the burnt gases of these flames, which are primarily comprised ofH,, N2 and H,O.With the alkaline earth metals the dominant species is the di-hydroxide.** g In addition though the oxide, monohydroxide and free metal atomsare present, but in much smaller amounts. All these alkaline earth metal compoundshave concentrations which appear to be coupled to one another through the followingreactions being equilibrated :9M+H,O +H+MOHMOH + H20 $- H + M(OH),MfOH +H+MO.f present address : Scientific Control Systems, Ltd., 49-57, Berners Street, London, W.1.$ present address : Dept. of Chemical Engineering and Fuel Technology, The University of Shef-field, Mappin Street, Sheffield.20A .F . ASHTON AND A. N. HAYHURST 209These processes also relate the concentrations of the various species of an alkalineearth metal M to those otherwise in the flame gases, in which additional reactions,such as H, +OH + H,O+H, are equilibrated.'O The equilibrium constants ofprocesses (1)-(111) have been derived 7* l1 and show that the oxide is always presentin negligible quantities. Otherwise, for Ca and Sr in a flame at about 2000 K, between90 and 95 % of the metal exists as the dihydroxide at equilibrium, with most of theremainder as the monohydroxide and less than 1 % as free metal atoms. For Baat this temperature about 80 % exists as M(OH),, 20 % as MOH and again less than1 % as M. In each case the ratio of dihydroxide to monohydroxide increases withflame temperature.For example, some 95 % of Ba in a flame at 2400 K is presentas the dihydroxide, while the fraction of metal atoms is still less than 1 %. Thealkaline earth metals show a certain amount of ionization (less than 3 % the totalamount added) in flames.l'-' This is seen below not to affect the diffusion of whatis effectively the dihydroxide. The existence of the balanced equilibria (1)-(111) enablesvariations in the concentration of the dihydroxides to be monitored with observationsof the metal atom's resonance lines.Copper on the other hand exists predominantly as free atoms in these hydrogenflames. It does form l6 small amounts of CuH and CuO, along with minute amountsof CuOH, but these compounds always comprise less than 5 % of the total metal.Copper has a fairly high ionization potential (7.68 eV) and does not ionize appre-ciably l7 in these systems.Flames containing Cu give a strong green emission, dueto electronically excited CuOH molecules.16 It has been demonstrated l8 that theseare formed by Cu+OH+X + CuOM*+X, where X is any third body. This greenemission, whose intensity is proportional to the concentrations of Cu atoms and OHradicals, was used here to monitor the diffusion of Cu atoms.EXPERIMENTALThe apparatus and eight flames studied have been fully described a l r e a d ~ . ~ Briefly, theburner was made from hypodermic tubes, with the one at the centre having its own gassupplies, identical to that of the 270 surrounding tubes. However, one of the metals (Ca,Sr, Ba or Cu) was added to the supplies to the central tube as an aerosol of an aqueoussolution (the nitrate for Cu and chloride for the alkaline earth metals).The amount ofadditive in a flame was very low, being less than 1 in lo8 by volume. Otherwise, the flameswere circular (diam. ~ 2 0 mrn), burnt vertically and with a flat reaction zone about 1 mmfrom the burner face. Initially all the additive was confined to the reaction zone and lessthan 0.25mm of the axis. Radial diffusion occurred downstream in the burnt gases, thecentral region of which was free from edge effects, such as entrainment of air, for up toaround 30 mm from the reaction zone.Light emitted by the additive at right angles to the flame axis was focussed into a mono-chromator.In effect light was taken from a region corresponding to a rectangular box,whose length was the overall diameter of the flame, whose height along the axis of the systemwas fixed at 4 mm and whose width (Ay) was usually 1 mm. The emission intensity fromthis well defined volume at a particular height above the burner face will be denoted by I ;it is proportional to the number of additive molecules in this imaginary box, because effectsof self-absorption are negligible. For every determination of I , one of I. was made. Thisis the intensity from the same height of flame, but with the width about the flame's axisincreased until I no longer became larger. In practice this amounted to a change in thewidth of flame observed from 1 to around 8mm.The quantity Illo corresponds to thefraction of diffusing species, which, after having been in the flame for a narrow range of times,have not moved more than a certain distance away from the axis in the direction orthogonalto the line of observation and the flame axis. The alkaline earth metals were monitoredusing the atomic resonance lines at 422.7,460.7 and 533.6 nm for Ca, Sr and Ba, respectively.The resonance lines for Cu lie in the ultraviolet at 327.4 and 324.7 nm and beyond the cut-of210 DIFFUSION COEFFICIENTSfor the glass optics. Instead the green CuOH bands were used over the region 535-555 nm,where a slight maximum at 545 nm was found when using low resolving power. Since thewidth of the monochromator’s entrance slit was used to control both the width of flameobserved and the spectral band width, a correction l9 was made to cater for the differentspectral ranges used when measuring I and Io.In addition, corrections for slight backgroundemissions were made. The fact that the CuOH emission is proportional l8 to the concentra-tion of OH radicals does not affect the determination of I / I o , since [OH] is everywhere thesame at a particular distance from the reaction zone and independent of the width of flameobserved here.THEORYPreviously derived theory indicates that Z/Zo measured at a distance z along theflame axis from the point of injection of additive is related to D, the effective co-efficient of diffusion, byHere Vis the velocity of motion of the burnt gases ; D refers to the overall transportof additive and for the alkaline earth metals, where possibly two species M(OH), andMOH are important, we haveD M ( O H ) 2 and D M O H are the diffusion coeacients of M(OH), and MOH, respectively,in the burnt gases.C#I is the ratio of concentrations [MOH]/[M(OH),]. It was seenabove that 4 is close to zero, being always in the range 0 < C#I < 0.25, so that D isclose to DMM(oH)z. Barium is the alkaline earth metal for which 4 is greatest, but here,because of its large atomic weight, we have DMoH z DM(OH)2. In this case D becomesclose to DMCOHl2 almost irrespective of the magnitude of 4, so that another reason isavailable for taking D to equal DM(OH)z for Ba. With copper we obtain by a similarargument, since compound formation is negligible, D referring to free atoms of themetal diffusing in the burnt gases of each flame.Eqn (1) should give a straight lineplot for (AyI0/I), against z, provided D is not a function of z, which it could wellbe if 6 is appreciable.( A Y Z ~ / I ) ~ = 4nBz/V. (1)D = (DM(OH)z + @&od/(1+ 4). (2)RESULTSSome experimental plots of (AYZ~/Z)~ against axial distance from the reaction zoneare shown in fig. 1 for the alkaline earth metals. In each case they are seen to begood stright lines, which indicates the constancy of D and also confirms eqn (1).All these plots of (AyZo/I)2 extrapolate to zero at around 1 mm upstream of the reac-tion zone. This arises 5-7 from the additive not being added from a true point sourceTABLE 1 .-MEASURED EFFECTIVE DIFFUSION COEFFICIENTS OVER A RANGE OF FLAME TEMPERA-TURES104~/m* s-1flame temp/K25202480232022802120210019201900Ca5.25.854.64.853.94.03.13.2Sr4.755.353.954.23.23.72.72.75Ba4.95.054.04.252.93.22.62.45cu7.58.56.36.55.55.54.54.A .F . ASHTON A N D A . N . HAYHURST 21 1in the reaction zone, but a slightly extended one, which, nevertheless, far into the burntgases corresponds to a virtual point source just upstream of the reaction zone. Theobscrved slopes have been taken to equal (4nD/V), as indicated by eqn (l), therebyenabling D to be obtained using previously measured values of V. The results aregiven below in table 1, where errors in each value of D are 8 %.Copper also gavegood straight line plots, similar to those of fig. 1, in each of the eight flames ; thevalues of D are also included in table 1.1086N 5 - -. N - tzl$ 4I,c120A30 10 20 30axial distance from reaction zone/mmFIG. 1.-Experimental plots of (AyIo/1)2 against distance along a flame axis from its reaction zonefor the alkaline earth metals in various flames (see table 1 for their temperatures).DISCUSSIONThe measured diffusion coefficients D will be discussed on the basis that they referto one species X diffusing in trace quantities through the multi-component mixture offlame gases. In this case D is given by the reciprocal mixing rule 20* 2 1D-' = C xi/DXi1where xi is the mole fraction of any flame species i other than X, the one diffusing.Dxi is the binary diffusion coefficient for a mixture of X and i alone.As an alter-native to eqn (3) the linear mixing ruleD = 1 xiDXit(4)will be tested below. This appears to be of some use where only atomic species areinvolved as with Na or K. According to Chapinan-Ensl<og theory 2 2 the binarydiffusion coefficient for species X and i is given byDxi = 3(kT)2j16 P,uQXi ( 5 )correct to 1 or 2 %. Here P is the pressure in atm, T the temperature and p is th2 12 DIFFUSION COEFFICIENTSreduced mass of species X and i. QXl is a collision integral and is a function of T.In addition, it depends on the form of the potential function for X and i. If aLennard-Jones (12 : 6) function is assumed for the intermolecular potential energy,we haveaXi = (nkT/2p)t~2Rgiwhere Q is the Lennard-Jones collision diameter.is a reduced collision integraland is tabulated 22 as a function of the reduced temperature T* = kT/E, where E isthe depth of the potential well for the Lennard-Jones function. At high temperatures(T* > 3) Q& is approximated well by the expression 1.12/(T*)' 16. The effective valuesof Q and E for a mixture of X and i are averages of the Lennard-Jones parameters,oXx and oii, etc., for the pure components according to :0 = +(a,,+aii); E2 = EXXEii. (7)As an alternative to the Lennard-Jones (12 : 6) potential function, the purely repulsiveinverse power oneCD = A/?' (8)has been used to describe the potential energy @ of species X and i in terms of theirseparation Y.In eqn (8) A and n are constants. Expressions are available 2 2 * 23for calculating a binary diffusion coefficient given the appropriate values of A and n.In addition collision integrals can be computed from A and rz, as well as d, an effectiverigid sphere collision diameter 2 3 for expression (8).The two potential functions are now taken, together with the two mixing rules (3)and (4), to ascertain which combination best fits the measured values of D for theeight flames in table 1. This is done by minimising the standard deviationbetween the experimental D and Dth which is that computed from the above theo-retical considerations for each flame j . The best fit then enables corresponding valuesof Q and E or A , d and n to be deduced.Table 2 lists the results of fitting the experimental data to the theoretical expres-sions derived from Chapman-Enskog theory, when using the Lennard-Jones potentialfunction.For this the Lennard-Jones parameters, crii and E i i , for the major flamespecies H2, N2 and H20, were taken to be those used previo~sly.~-~ In every caseexcept for Sr the reciprocal mixing rule gives the better fit. In fact, the linear mixingrule failed to give a minimum standard deviation in the case of copper, in that thestandard deviation decreased steadily as Elk was lowered. Even so, the reciprocalmixing rule is still the better for Cu, since for Elk = 1 the standard deviation was justover 5 %, compared with a minimum of 3 % for the reciprocal rule.This failureto produce a well-defined minimum in the standard deviation has already been notedfor Rb and Cs, where no minimum was found for either mixing rule. The fitting ofthese theoretical models to the data is poorer than usual for Ba. This may reflectthe fact that Ba exists in a flame less completely as the dihydroxide than do Ca or Sr,so that the assumption of only one diffusing species might be less correct. The impor-tance of the monohydroxide is greatest at low temperatures and may possibly be thereason why the value of D in table 1 is lower for flame F6 than A6.The Lennard-Jones parameters, cXx and cXX, are given in table 2. No markedtrends in the E values are found, but Q increases from Cu to Ca, Sr and Ba, as mightbe expected from the relative sizes of the species involved.No other measurementA. F. ASHTON A N D A . N. HAYHURST 213of these quantities appear to have been made. However, compared with the para-meters for molecules which are of similar physical size,22 such as SnCl, (a = 4 . 5 4 ~m, Elk = 1550 K) and CS2 (a = 4 . 4 4 ~ 10-lo m, Elk = 488 K) for example,the values derived here for the alkaline earth metals appear quite acceptable. Also,the parameters for Cu are very similar to those derived for K atoms (a = 2.77 x 10-l'm, Elk = 840 K) and Hg atoms 22 (a = 2.9 x 10-lo m, Elk = 851 K).TABLE ?,.--DERIVED VALUES OF LENNARD-JONES PARAMETERS AND MINIMUM STANDARDDEVIATIONS USING EACH MIXING RULEreciprocal mixing rule linear mixing rulespecies 1010 a/m (&/k)/K s.d.1010 a/m (&/k)/K s.d.Ca(OH)2 3.90 730 0.034 4.32 620 0.052Sr(OH)2 4.14 845 0.052 4.57 750 0.049Ba(OH)2 4.26 845 0.084 4.66 860 0.092c u 2.76 845 0.030We now discuss the results given in table 1 in terms of the inverse power potentialfunction (8) where attractive forces between colliding species are ignored. Somepreference for this type of function has been noted already for Li, Rb and Cs diffus-ing in these flames. Again different values of A have been assumed for interactionsof the tracer with the three principal flame species, but to minimise the number offitting parameters to four, one value of n was used for each metal. In each case theminimum standard deviations are given in table 3, together with values of A, n and d,the effective collision diameter based on a rigid sphere as discussed above.We firstcompare the reciprocal and linear mixing rules from the information given in table 3.The standard deviations quoted there indicate that there is little to choose betweenthe two mixing rules. However, looking at the derived parameters, it is seen that forTABLE 3.-DERIVED VALUES OF A , d, n AND MINIMUM DEVIATION FOR EACH MIXING RULEreciprocal rule linzar rule __--__-_------_--- _ _ - ~ _ ~ - - -binary pair A/(Jmn) lOlod/m n s.d. A/(Jmn) lOlod/m n s.d.5.1 x 10-582 . 6 ~ 10-581.2 x 10-763 . 9 ~ 10-77. 4 . 4 ~ 10-761.1 x 10-574 . 7 ~ 10-596.3 x 10-582.6 x 10-1341 . 9 ~ 10-1353.5 x 10-1448.6 x lo-''3.33.7 42.73.63.0 64.02.0 43.53.02.4 120.5-5.2 x 10-5810.1 x 10-587.5 x 10-588 .9 ~ 10-582 . 4 ~ 10-1310.043 2 . 4 ~ 10-1359.1 x 10-1324 . o ~ 10-1341.1 x 104330.026 8.3 x0.028 7.1 x0.026 3 . 2 ~3.33.7 4 0.0273.93.63.6 4 0.0303.85.22.4 12 0.0434.73.12.5 12 0.0293.4Ca both rules give similar values of A , d and n except where H, is involved. Thereciprocal rule gives d a magnitude for Ca(OH), and H, which is more in line with dfor Ca(OH), with N2 and H,O than is the case with the linear mixing rule. Thevalues of d for Ca are in fact very similar to those for caesium,6 which exists to a largeextent as CsOH in flames. With Sr the reciprocal rule gives a negative value for A.This anomaly is probably a consequence of the inaccuracy of the experimental dataand the fitting procedure employed.Also the reciprocal rule gives a larger cross2 14 DIFFUSION COEFFICIENTSsection d for collisions with N, than H,O, which is (rather unexpectedly) true for Cuand Ba as well as Sr. The linear rule on the other hand consistently gives a very largevalue of d for all interactions involving H,. The derived parameters for Ba are some-what inconsistent compared with those for Ca and Sr and again the relative inaccuracyof the data is probably the main cause. The minimum standard deviations obtainedwith Ba are noticeably higher than those for the other additives in table 3, which isthe same as with the Lennard-Jones potential (see table 2) and probably arises fromBa existing to a small extent as the monohydroxide as well as the dihydroxide.ForCu the values of A with N, and H,O are independent of mixing rule (as with Ca)but A for Cu and H, is anomalously small with the reciprocal rule. It would appearthat the fittifig procedure is compensating for the higher experimental values of D inF flames (see table 1) by deriving erroneous parameters for interactions involving H,when the reciprocal rule is used. This comment probably applies to other metalstoo, particularly Sr.The inconsistencies just noted in A and dfor the purely repulsive potential functionmust be compared with the more self-consistent Lennard-Jones parameters in table 2.Furthermore, the standard deviations in table 3 for the repulsive function, which hadfour fitting parameters, are not drastically better than those in table 2 relating to theLennard-Jones function, for which oiily two fitting parameters were employed.Certainly the Lennard-Jones potential function is the easier to use in practice, parti-cularly for predicting diffusion coefficients in totally different situations.One diffi-culty already noted with the purely repulsive function is that a minimum of fouradjustable parameters appears necessary and the measurements of D made here arepossibly not accurate enough to yield values of all of them with any degree of confi-dence. There thus appears to be a clear preference for the Lennard-Jones potentialfunction here, which is the opposite to that for the alkali metals.6 As for the twomixing rules, the reciprocal one (3) is the better when used with the Lennard-Jonesfunction, except possibly for Sr (see table 2), but the choice is not so clear with thepurely repulsive function.So far the linear rule has appeared preferable only withNa and K in these systems.6 Finally the values of n in table 3 are all in the range 4-12,but without any obvious trends appearing. Again their accuracy is difficult to assessbut cannot be very large. This derives from the fact that with the repulsive potentialfunction a binary diffusion coefficient is proportional to temperature raised to thepower ( 3 / 2 +2/n), so that for n being say 4 and 12 gives a Dxi proportional to T2 andT5I3, respectively. Even so, all the values for n so far obtained for the alkali metals,nitric oxide and the additives here have all been between 4 and 12.Of course n = 12is that used in the Lennard-Jones function.We thank the Central Electricity Generating Board for financial support.R. M. Fristrom and A. A. Westenberg, Flame Structure (McGraw-Hill, New York, 1965)p. 263.13. A. Wilson, Phil. Mag., 1912, 24, 118.R. E. Walker and A. A. Westenberg, J, Chem. Phys., 1958, 29, 1139.A. F. Ashton and A. N. Hayhurst, Trans. Faraday SOC., 1970, 66, 824.A. F. Ashton and A. N. Hayhurst, Trans. Faraday SOC., 1970, 66, 833.A. F. Ashton and A. N. Hayhurst, J.C.S. Faraday I, 1973, 69, 652. ’ A. F. Ashton and A. N. Hayhurst, Trans. Faraday Soc., 1971, 67, 2348.T. M. Sugden and K. Schofield, Trans. Faraday Sac., 1966, 62, 566.D. H. Cotton and D. R. Jenkins, Trans. Faruday SOC., 1968, 64, 2988.J. A. Dean and T. C . Rains (Marcel Dekker, New York, 19691, vol. 1, p. 151.lo D. R. Jenkins and T. M. Sugden, Flame Emission and Atomic Absorption Spectrometry ed.,l 1 A. N. Hayhurst and D. B. Kittelson, Proc. Ro,v. Soc. A, 1974, 338, 175A. F . ASHTON A N D A . N. HAYHURST 215l 2 K. Schofield and T. M. Sugden, 10th Int. Syinp. Combustion (The Combustion Institute, Pitts-l3 D. E. Jensen, Combustion and Flame, 1968, 12,261.l 4 R. Kelly and P. J. Padley, Trans. Faraday Soc., 1969, 65, 355.l5 A. N. Hayhurst and D. B. Kittelson, Proc. Roy. SOC. A , 1974, 338, 155.l6 E. M. Bulewicz and T. M. Sugden, Trans. Faraday SOC., 1956, 52, 1475, 1481.burgh, 1965), p. 589.N. R. Telford, Ph.D. Thesis (Cambridge University, 1969).R. W. Reid and T. M. Sugden, Disc. Faraday SOC., 1962,33, 213.l9 A. F. Ashton, Plz. D. Thesis (Cambridge University, 1970).2o D. F. Fairbanks and C. R. Wilke, Znd. Eng. Chem., 1950, 42,471.21 R. E. Walker, N. Dehaas and A. A. Westenberg, J. Chem. Phys., 1960, 32, 1314.22 J. 0. Hirschfelder, C . F. Curtis and R. B. Bird, Molecular Theory of Gases and Liquids (Wiley,23 J. 0. Hirschfelder and M. A. Eliason, Ann. N. Y. Acad. Sci., 1957, 67, 451.New York, 1954).(PAPER 5/851

ISSN:0300-9599    

DOI:10.1039/F19767200208

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

Protein HydrationNuclear Magnetic Resonance Relaxation Studies of the State of Water inNative Bovine Serum Albumin SolutionsBY JOHN OAKESUnilever Research Port Sunlight Laboratory, Port Sunlight,Wirral, Merseyside L62 4XNReceived 8th May, 1975N.m.r. relaxation times have been measured for protein and water protons in aqueous solutionof native bovine serum albumin (BSA), as a function of protein concentration and temperature.Estimates of protein hydration were obtained from n.m.r. studies on frozen protein solutions.Unambiguous evidence is obtained that most of the water in native BSA solutions has a mobilityequal to that of pure water at the same temperature. This exchanges rapidly with a small fractionof water which is bound largely to polar groups of the protein amino acid side chains and which hasan average mobility about a hundred-fold lower than that in pure water.The marked increase inwater proton relaxation rates and in the rigidity of the protein chains observed at high (>lo %)BSA concentrations is attributed to association of protein molecules. It is shown that the increasein relaxation rates results from an increase in protein hydration on association due to (i) a reversibleunfolding of the protein molecule which exposes new sites, and (ii) bridging of water moleculesbetween adjacent protein molecules.There has been much interest in the state of water in biological systems.'. It isgenerally believed that the properties of the water are largely determined by macro-molecules, particularly cellular protein^,^ rather than lipids or other small moleculespresent in these systems.Two theories have been put forward to explain the proper-ties of water but the evidence for both is mostly indirect and inconclusive. Oneviewpoint is that water exists in the form of polarised multilayers hundreds of watermolecules t h i ~ k . ~ - ~ The term " polarised multilayers " has not been defined preciselybut it usually refers to water polarised between protein molecules or surfaces, whichis more structured than pure water, i.e. has properties intermediate between those ofpure water and ice. The other point of view 1 ' is that the influence of proteins onthe properties of water molecules is short range; most of the water has properties ofpure water and a small fraction is tightly associated with the protein.It is essential to study the properties of water in relatively simple systems, e.g.solutions, suspensions and gels of biological macromolecules, to provide a basis forunderstanding water in living systems.In this work, solutions of the native protein,bovine serum albumin, (BSA), have been investigated by n.m.r. spectroscopy. In afollowing paper, a similar study is made of colloidal suspensions and gels of thermallydenatured BSA. Previous n.m.r. studies have shown that the bulk of water indispersions of well-characterised polystyrene lattices has a mobility similar to that ofpure water, since the surfaces have little effect on the water proton relaxation times,T1 and T2. In other disperse systems, e.g.polysaccharide gels, 9-11 mesomorphicphases,* biological cells and tissues,12 T2 < TI so that unambiguous analysis is notpossible unless the bound water concentration or relaxation times are determined.It has been argued that the small changes observed in the average self diffusion co-21J. OAKES 21 7efficient of water molecules in certain systems indicate that a major portion of watermolecules are not in a modified state ; however, the same measurements have alsobeen shown to be consistent with the multilayer rn0de1.l~Measurements have been made of relaxation times, T I , T2, for both the water andprotein protons in solutions of native BSA as a function of protein concentration andof temperature. The results were analysed using a procedure similar to that recentlyused for agarose gels ; l4 measurements are made of the concentration of bound waterand it is ascertained whether or not the remaining water has an average mobility thesame as that in pure water.EXPERIMENTALBovine serum albumin (crystalline puriss) was used as received from Koch Light.Waterwas de-ionised and distilled from alkaline permanganate. Solutions (pH = 5.6) were pre-pared by placing a known weight of BSA on the surface of a known weight of water at neutralpH and allowing solution to take place. Clear yellow viscous solutions or gels were obtainedat high protein concentrations (> 40 %). Measurements were made on undegassed samplesand, to avoid ageing effects, i.e. disulphide interchange,15 within 48 h of sample preparation.Relaxation time measurements were made using a Bruker B-KR 322s variable frequencypulse spectrometer operating at 60 MHz.The temperature of the sample was varied, andcontrolled to within 1 K at a given temperature, using the Bruker variable temperature controlunit. Spin-lattice relaxation times were measured by recording the initial height of the signaldecay after the final 90" pulse in a 90"-~-90" pulse sequence as the pulse spacing z was varied.Spin-spin relaxation times were measured by the Carr-Purcell method, employing the Gill-Meiboom modification. A pulse distance of 2 0 0 p was used for measurements of T2 andtypical pulse widths were around 2 p for a 90" pulse. Spin-spin relaxation times shorterthan about 1 ms were measured from the free induction decay (FID) following a single 90"pulse, measuring the time taken for the FID to reach e-l times its original height.Spin-spin relaxation decay curves for protein protons, measured in D20, consisted of twocomponents, but spin-lattice relaxation recovery curves were single exponentials.The signalfor HDO (-25 % of signal in 20 % BSA sample), which contained contributions fromexchangeable protein protons and from protein moisture content, was clearly resolved fromthat arising from protein protons for T2 measurements but was not resolved in TI measure-ments. Relaxation decay and recovery curves for water protons, both in solution and infrozen samples, exhibited single phase behaviour (i.e., only one water component) for allcompositions of protein.Like the HDO signal, the water proton signal was clearly resolvedfrom the protein proton signals for T2 measurements. Relaxation recovery curves for proteinprotons and water protons could not be resolved, except at high protein concentrations or infrozen samples, because of either the low intensity of the protein signal and/or the similarityof spin-lattice relaxation times.* Where separate FIDs could be observed for proteinand water protons, e.g., in frozen samples, the spin-lattice relaxation times for (bound) waterprotons were measured directly. Relaxation times were reproducible to 3-4 % when singlephase relaxation behaviour was observed but to about 10 % when two phase or multiphasebehaviour was detected.Measurements of the intensity of the unfrozen water signal were made by comparing theinitial height of the unfrozen water proton FID with that from a native protein solution,correcting for the Boltzmann factor by comparison with the FPD height of the correspondingprotein signal.Pure water when frozen did not give a detectable n.m.r. signal indicatingthat the signal from ice decays in a time short compared with the dead time of the instrument( - 5 ,us). After correcting for the Boltzmann factor and loss in signal intensity arising fromfreezing of HDO, it was found that the protein signal did not change in intensity upon freezingand further lowering of the temperature. Intensity and relaxation measurements on frozensamples were independent of the freezing method provided cooling was fairly rapid, e.g.,inserting sample in probe set at 253 K, or chilling in liquid nitrogen.The results were not so* The observation of different spin-lattice relaxation time values for protein and water protonsindicates that spin diffusion between protein and water protons is not as important as is often supposed218 N.M.R. STUDIES OF PROTEIN HYDRATIONreproducible if the samples were cooled slowly from room temperature, when hysteresis andsupercooling effects could be observed. When frozen samples were thawed, relaxation timesof both protein and water protons returned to those obtained before freezing.RESULTSRelaxation rates, Ti- I, TF for water protons as a function of BSA concentrationat temperatures 275, 294 and 318 K are shown in fig.1 and 2. The plots are linearup to about 10 % BSA but above this concentration there is a marked increase inrelaxation rates, particularly T z l, indicating a cooperative effect * of adjacent proteinmolecules on surrounding water. Studies, using both internal and external referencesshowed that there were no water proton chemical shifts with change in protein con-centration. The protein protons gave two T2 values of approximately equal intensitybut only one TI was observed which is measured as an average with that from HDO[SSAllwt. %FIG. 1.-The variation of the water proton spin-spin relaxation rate, Ti', with concentration of nativeBSA at 275 K (x), 294 K (0) and 318 K (0). In the insert Ti' at 294 K is shown over a wideconcentration range.protons.The protein relaxation times varied between 87 and 300 pus and 1.08 and1.93 ms for T2 and between 240 and 400 ms for TI over the temperature range 278-318 K. Above 25 % BSA the protein proton T2 values varied with protein concen-tration ; for a 64 % BSA gel at 296 K, 75 % of the signal had a T2 of 21.7 ,us and25 % a T2 of - 1 ms, compared with relaxation times of 150 ,us and 1.08 ms, of equalintensity, for a 25 % solution. At intermediate concentrations, complex multiphasebehaviour was detected, the overall relaxation time becoming shorter with increasingprotein Concentration, particularly above 40 % BSAJ . OAKES 219I I I I I i 0 5 10 IS 20 25[BSAIIwt. %FIG. 2.-The variation of the water proton spin-lattice relaxation rate, Ti1, with concentration ofnative BSA at 275 K (x), 294 K (0) and 318 K (8).In the insert T;' at 294 K is shown over awide concentration range.2 8 0 26 0 24 0 2 2 0 2 0 0TIKFIG. 3.-The intensity of the water proton signal remaining in a frozen 20 % BSA sample, as a func-tion of temperature. The intensity is quoted as % of total water signal, i.e., solution signal. Mea-surements were difficult to make below 200 K, since the residual water proton T2 became similar tothat of the protein protons (fig. 5)220 N.M.R. STUDIES OF PROTEIN HYDRATIONOn freezing native BSA solutions most of the water signal was lost, due to forma-tion of ice, but there remained a residual signal of low intensity. The intensity ofthis signal as a function of temperature for a typical sample is shown in fig.3. Infig. 4, the intensity of the non freezable water signal, i.e. residual signal below 253 K,is plotted against protein concentration. The percentage of the total water signalremaining unfrozen increases exponentially above 25 % BSA, equalling 10 % at 30 %BSA and reaching as high as 50 % around 60 % BSA. Spin-lattice and spin-spinrelaxation times for water protons in frozen samples as a function of temperature andconcentration are shown in fig. 5. Spin-spin and spin-lattice relaxation times of theprotein are - 10 ps and 200 ms, respectively, and remain approximately constant overthe temperature range studied (from 273 to 223 K). Clearly, " unfrozen " water hasmuch greater mobility than ice or the protein.[BSA]/wt.%FIG. 4.-Dependence of the intensity of non-freezable water on protein concentration.It has been reported l 6 that the short T2 for water protoiis in certain systems, e.g.glass beads, is determined by local magnetic field inhomogeneities. To check this inthe present systems, water proton relaxation times were measured for a solutioncontaining 33 % native BSA at frequencies 20 MHz, 40 MHz, 60 MHz and 90 MHz.No changes were observed in T2, or even T,, over this frequency range indicating thatsusceptibility effects are not important.DISCUSSIONNATIVE PROTEIN SOLUTIONSThe overall effect of adding native protein to water is to increase the relaxationrates, TT', TT', of water protons. For an isotropic system, e.g.pure water, theinolecular mobility of water molecules can be described in terms of a single correlationtime and T, z T2 over the temperature range of the present experiments. Deviationsfrom this behaviour can occur if there are anisotropic motions, local magnetic fieldinhomogeneities, exchange of water molecules between different environments or ifthere is a distribution of correlation times.The net increase in relaxation rates of water in the presence of native BSA couldbe due either to an overall decrease in water molecular mobility, i.e., due to long rangesurface effects, or to binding of a small amount of water to the protein, which exchangesrapidly with bulk water. In native BSA solutions T2 is less than TI (fig. 1 and 2).If the water motion is isotropic, the first alternative can be rejected for dilute (0-10 %I .OAKES 22 1protein solutions since the observed Tl/T2 ratios could arise only from very muchshorter relaxation times than those found as an average for the whole system. If asmall fraction of water molecules exist in a bound state which exchange with, and havea much greater relaxation rate than, bulk water then the average relaxation rate willbe given* by 14* l7(1)hc(1-hc) q l = ~ (TIb+rb)-'+TL1100v) Eh'.ICIOOC2 100h" .10263K 243K273K 253K 233K223K 213K 203KI I 1 1 I 1 I II I I I 7 I I I I3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.21 0 3 ~ 1 ~FIG. 5.-Variation of relaxation timzs, T I , T2, of mobile water protons in frozen BSA samples withternpzrature.T2 is concentration dependent and plots are shown for 25 % (O), 20 % (0) and 10 %( x ) protein samples.where c is the protein concentration (mass of solute per mass of solvent), Iz is theamount of water hydrated by unit mass of protein, q, is the lifetime of a water (proton)molecule in the bound phase and subscripts b and a refer to the bound and bulk states,respectively. A similar equation applies for T2.* In general this equation has to be modified to include contributions from exchangeable proteinprotons. Although exchange of labile protein protons and water protons makes a substantial con-tribution to the overall relaxation rate for suspensions of thermally d enatured protein,' measure-ments of T2 as a function of pulse separation show that the effect is practically negligible for nativeprotein solutions.An explanation is given in the following paper.222 N . M . R . STUDIES OF PROTEIN HYDRATIONThe relaxation rates of water protons in native BSA solutions are dominated bythe first term of eqn (1) at high concentration (fig. 1 and 2). Since Zb is expected todecrease with increasing temperature, the effect of temperature on the observed relaxa-tion rates TC', TT' can be explained by T b 4 Tb, T b -g T2b, which we already knowsince the magnetisation recovery and decay curves are single exponentials, and byassuming TIb, T 2 b are on the high temperature side of the TI minimum l8 (which isclear from fig. 5).If the observed relaxation rates are plotted against hc/(l -hc), then if the simpletwo-state model holds, TI,, T2, obtained from the intercepts should equal T,, T2 forpure water and the gradients should yield values of Tlb, T2b.It is generally agreedthat native BSA is hydrated to an extent of 16-20 % as a lower limit and values ashigh as about 40 % have been s~ggested.'~~ 2o [Hydrated water or bound water isusually defined as water in the vicinity of the protein whose properties are quiteTABLE NUMBERS OF POLAR GROUPS ON AMINO ACID SIDE CHAINS OF BSA AND ESTIMATESOF POLAR GROUP HYDRATIONpo!ar groupscarboxyl groups, CO;(glutamic, aspartic acids)basic groups(a) amino groups, NH;(b) guanidine groups(c) imidazole groupshydroxy groups(a) aliphatic(serine, threonine)(b) aromatic(tyrosine)amides, CONHz(asparagine, glutamine)other groupstryptophan NHcysteine SH(1 ysine)(arginine)(histidine)polar groupconc. /mmol(g BSA)-1 *0.900.840.350.230.770.260.630.07hydrationnumber233-51-1-2-j-121-2117HzO bound/g tg BSAF 10.0320.0460.19-0.320.004-0.0080.0140.0090.01 3-0.0230.001* Calculated from amino acid analysis data.38 t Estimated values.binding free energy,AG/kcal mol-1-2.26 22- 1.76 22-- 1.10 -+ -1.80 2 2-t Studies of simple poly-peptides 27 and substituted wool samples 21 have shown that 1 water molecule is bound to kachbackbone peptide group.However, there is evidence 22* 27 that completely amorphous proteins maybind 2 water molecules per peptide group and this is supported by studies of simple substitutedamide~.~'different from those of bulk water in that system.Difficulties are that (i) a sharpboundary between bound and bulk water is unrealistic and (ii) some properties maybe affected more than others so that different techniques may give different values ofhydration.] Theoretical estimates of BSA hydration were made from the numbersof polar groups on amino acid side chains per gram BSA and from polar group waterbinding capacities (table 1). A number of attempts have been made to estimate thf . OAKES 223number of water molecules bound per polar group 4 3 21-24 but the best evidence comesfrom adsorption isotherms of water on wool samples in which various protein func-tional groups were selectively blocked.21 Some of these hydration numbers havebeen confirmed elsewhere using other method~.~~-~O The calculation in table 1 showsthat 14-16 % water should exist bound to the protein side chain polar groups.(Similar calculations have been remarkably successful in explaining the experimentalbinding isotherms for water on lysozyme, ribonuclease and chymotrypsinogen 31 atlow humidities.)II I I I I I I I0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08hc/( 1 - hc)FIG.6.-Graph of water proton spin-spin relaxation rate against hc/(l-hc) at 275 K (0), 294 K( x , A) and 318 K El. The dashed curve is a plot using a constant value of h = 0.16 for all proteinconcentrations. Other plots were made using the following concentration dependent values of lz,obtained from fig.4, h = 0.16, 0.17, 0.18, 0.20 and 0.22 for BSA concentrations 0-10 %, 15 %,17.5 %, 20 % and 25 %, respectively. Values of Tzb obtained from the gradients are 6.25 ms,9.2 ms and 12.5 ms for temperatures 275 K, 294 K and 318 K, respectively.Plots of observed relaxation rates against hc/(l -hc) are linear up to about 10 %BSA, giving intercepts Ti-:, T;: approximately equal to TF T2 for pure water usinga constant value of h between the extremes of 0.16 and 0.4 (a typical example forh = 0.16 is shown in fig. 6). The deviation from linearity that occurs in more con-centrated solutions where there is association of protein molecules can arise from(i) breakdown of the simple two state model, i.e., Tl,' # TIHIO, TF: # TzHIo, (ii:change in h with protein concentration, (iii) change (increase) in Tci,', TTi' with proteinconcentration224 N .M . R . STUDIES OF PROTEIN HYDRATIONFROZEN SOLUTIONS OF THE NATIVE PROTEINThe low intensity, mobile water signals observed at temperatures below the freezingpoint of aqueous solutions of the native protein arise from water molecules that areunable to participate in the formation of an ice-lattice, i.e., are associated with theprotein in some way.24, 32 The non-freezable water, observed in frozen solutions ofneutral BSA at temperatures below 253 K (fig. 3), is attributed to water bound to theprotein (primary hydration sphere water). There was no evidence for irreversiblestructural changes, e.g., denaturation or aggregation, in native BSA, or even thermallydenatured' BSA, upon freezing.It is unlikely that the water is trapped in pores,unless these are of molecular dimensions, since water in pores of thermally denaturedprotein gels (average pore size - 300 A) freezes.' Residual signals detected in frozensolutions of simple acids, bases, amino acids and polypeptides 34 have beenexplained in terms of the known phase diagrams of some of the systems studied.These systems differ from frozen globular protein systems in that a gradual decreasein signal intensity is observed with decrease in temperature until the signal finallydisappears at a temperature characteristic of the solute under investigation. Binaryphase behaviour could, in part, be responsible for the decrease in residual signalintensity in frozen neutral BSA solutions between 273 and 253 K (fig.3).Clearly, the amount of water bound to BSA can be obtained from fig. 4. Thisincreases with protein concentration, h varying from 0.16 for 0-12.5 % BSA to 0.22at 25 % BSA. At higher protein concentrations, h increases exponentially, reaching0.5 at about 60 % BSA. At the lower protein concentrations (0-12.5 %) the degreeof hydration (0.16) is in good agreement with the lower limit obtained using othertechniques and with theoretical estimates. It is lower than that obtained for salt-containing BSA solutions possibly for the following reasons : (i) salt itself can giveresidual signals, (ii) the salt-protein-water mixture is a complex ternary phase systemand (iii) salt can denature the protein ; in addition, the spin echo method of measure-ment is simpler and more reliable than the broad line method.The hydration results are consistent with the view 35 that water soluble globularproteins, such as BSA, contain a large portion of their polar groups at the proteinsurface with many peptide groups and apolar groups buried in the protein interior,out of contact with the aqueous environment.It is fairly certain 21* 2 2 , 27* 30 thatbackbone peptide groups are hydrated in fibrous and random coil proteins since, asa rule, these proteins hydrate to a larger extent than globular protein^.^ Peptidegroups in globular proteins are less accessible to water because of intramolecularhydrogen bonding but the observation that hydration depends upon protein helicalcontent,22 leaves little doubt that, even in globular proteins, there is at least somepeptide hydration.Although the major part of bound water appears to be associatedwith individual polar groups of amino acid side chains, nevertheless, if the individualpolar groups are spaced less than 3 apart, there may be interaction between adjacentbound water molecules to produce cooperative hydration ~tructures.~~ In addition,water may be contained in channels or pores formed between protein chains andsufficiently small, i.e. of molecular dimensions, that no bulk water structure may exist ;this water will consist of both tightly bound hydrated water and less tightly bounddisordered water which, presumably, is unable to freeze at 273 K.The decrease inthe intensity of the residual signal in frozen solutions between 273 and 253 K (fig. 3)may, in part, arise from water in such pores, water bound to counterions, or fromwater molecules situated at the interface between the ice-lattice and the protein surfaceor hydrated protein surface. This will consist of (i) water molecules adjacent orweakly bound to exposed apolar, peptide or other polar groups on the protein surfaceJ . OAKES 225(ii) water molecules weakly bound to the protein or ice surface by hydrogen bondingto hydrated water molecules or ice and (iii) a layer of intermediate disordered watermolecules.STATE OF WATERPlots of observed relaxation times against hc/( 1 - hc) using the experimentallydetermined values of h are linear up to 30 % BSA (fig. 6 and 7).A fit is not observedabove 30 % BSA since the condition hc Q (1 -hc) is no longer satisfied. Values ofT,,, TZa estimated from the intercepts equal TI, T2 from pure water at the appropriatetemperature and, furthermore, values of TI,,, T2,, which are about a hundred-foldlower (fig. 6 and 7) are similar to values of T,, T2 from unfrozen water between 271and 253 K (fig. 5).* The Tl/T2 ratio for bound water at 223 K is > 100, indicatingthat the water molecular motion is not isotropic and describable by a single correlationtime. Probably many different protein hydration sites exist. A corresponding dis-tribution of water molecular motions and relaxation times will exist, with the observedrelaxation rates being a weighted average over the whole sites.Clearly, the water proton relaxation rates observed both in dilute and in concen-trated protein solutions can be understood in terms of a two state model, with rapidexchange occurring between the two environments.Most of the water has a mobilityequal to that of pure water and there exists a small fraction of bound water molecules,of which there are many types, which has a mobility of about a hundredfold lower.Any model invoking the existence of layers of water molecules having either aniso-tropic motion or reduced mobility and hundreds of angstroms thick can be rejected.?The decrease in protein spin-spin relaxation times shows that the protein chainsbecome more rigid with increasing protein concentration.(On plasticisation ofnylon, peptide chains in the amorphous regions become more mobile due to hydra-tion of polar sites, followed by formation of capillary or interstitial water.30) Thiseffect, like the effect of high protein concentrations on the water proton relaxationrates is attributed to association of protein molecules. The formation of a clear gelat BSA concentrations above about 60 % (corresponding to 10 water molecules perprotein amino acid residue) is consistent with association. The increase in proteinhydration that occurs on association is explained by a reversible conformational changein the protein which exposes new hydration sites, e.g., backbone peptide bonds, andby bridging of water molecules between either exposed sites or hydrated water on* It has been pointed out that hydration numbers measured from frozen samples are not neces-sarily suitable measurements of hydration in solution.20 This work shows that hydration numbersobtained from frozen solutions of neutral BSA are good estimates of hydration in solution and,furthermore, estimated relaxation times of bound water in solution are similar to those measuredin frozen samples.Also, account need not be taken of water that freezes between 273 and 253 K since (i) the effectof protein on the average relaxation rate of water will be dominated by its effect on water in theprimary hydration sphere and (ii) this water consists of both ordered and disordered water, so thatthe average properties may not be that much different from bulk water.(A similar drop off in residualwater intensity between 273 and 223 K observed in stratum corneum 37 is apparently due to waterhaving similar properties to bulk water.) Similarly any variation in bound water relaxation times withBSA concentration must be small up to 30 % BSA but T2b almost certainly decreases above thisconcentration due to decreased protein chain mobility. t It has been argued that it may be misleading to draw conclusions about the state of water incells from knowledge of protein solution^.^ It was suggested that proteins in cells may have morebackbone peptide groups exposed to water and that juxtaposed peptide surfaces can polarise multi-layers of water hundreds of molecules thick. The present studies for native BSA, both at high andlow concentrations, thermally denatured BSA and results for nylon hydration 30 show that thisargument is difficult to accept and is best ignored until there is evidence to support it.T--226 N .M . R . STUDIES OF PROTEIN HYDRATIONadjacent protein molecules. The small increase in the spin-spin relaxation time ofnon freezable or bound water (fig. 5) with protein concentration may result fromadditional water molecules being less tightly bound.0.01 0.02 0.03 0.04 0 . 0 5 0.06 0.07 0.08 0.09 0.10h c / ( l - hc)FIG. 7.-Graph of water proton spin-lattice relaxation rates against hc/(l -hc) at 275 K (x), 294 K(0) and 318 K (a) using varying values of h of fig. 6. Values of T1b obtained from the gradientsare 13.9 ms, 21.8 ins and 30.5 ms at temperatures 275 K, 294 K and 318 K, respectively.I thank several members of this laboratory for helpful discussions, in particularN. G.Pryce and E. G. Smith.Physicochemical State of Ions and Water in Living Tissues and Model Systems, ed. C. F. Hazle-wood, Ann. N.Y. Acad. Sci., 1973, 204.J. Clifford, in Water-A Comprehensive Treatise, ed. F. Franks (Plenum, New York, 1974),vol. V, chap. 2.G. N. Ling, Biophys. J., 1973, 13, 807.G. N. Ling, in Water and Aqueous Solutions, ed. R. A. Moore (Wiley, New York, 1972), p. 663.G. N. Ling, pp. 21 and 109 of ref. (1).A. Szent-Gyorgi, Bioenergetics (Academic Press, New York, 1957). ’ J. Oakes, J.C.S. Faradby I, 1976, 72,228.J. Clifford, J. Oakes and G. J. T. Tiddy, Spec.Disc. Faraduy SOC., 1970, 175.D. E. Woesnner, B. S. Snowden and Y.-C. Chiu, J. CoZloid Interface Sci., 1970, 34, 283.lo D. E. Woesnner and B. S. Snowden, J. Colloid Interface Sci., 1970, 34, 290J . OAKES 227l 1 T. F. Child and N. G. Pryce, Biopolymers, 1972, 11,409.l2 R. Cooke and R. Wien, Biophys. J., 1971, 11,1002.l 3 D. C. Chang, M. E. Rorschach, B. L. Nichols and C. F. Hazlewood, p. 434 of ref. (1).l4 W. Derbyshire and I. D. Duff, Furuduy Disc. Chem. SOC., 1973, 57, 243.l5 H. J. Nikkel and J. F. Foster, Biochemistry, 1971,10, 4479.l6 J. A. Glasel and K. H. Lee, J. Amer. Chem. SOC., 1974,96,970.D. E. Woesnner and J. R. Zimmerman, J. Phys. Chem., 1963,67,1590.A. Abragam, The Principles of Nuclear Magnetism (Clarendon, Oxford, 1961).1969), chap. 4.l 9 J. Steinhardt and J. A. Reynolds, MuZtipZe EquiZibriu in Proteins (Academic Press, New York,2o I. D. Kuntz and W. Kauzmann, Adv. Protein Chem., 1974, 28,239.21 I. C. Watt and J. D. Leeder, J. Textile Znst., 1968, 59, 353.22 M. M. Breuer, Hydrurion of Proteins, Biophysical Society Meeting, Bradford, 1968.23 M. E. Fuller and W. S. Brey, J. Biol. Chem., 1968, 243, 274.24 I. D. Kuntz, J. Amer. Chem. Soc., 1971,93, 514.25 G. Fraenkel and J. P. Kim, J. Amer. Chem. Suc., 1966,88,4203.26 M. Kennerley and H. J. V. Tyrrell, J. Chem. SOC., 1968, 607.27 E. F. Mellon, A. H. Korn and S. R. Hoover, J. Amer. Chem. SOC., 1948, 70, 3040.28 M. M. Breuer, J. Phys. Chem., 1964,68,2067.29 P. G. Assalsson, Ph.D. Thesis (Brooklyn Polytechnic Inst., 1966).30 R. Puffr and J. Sebenda, J. PoZymer Sci., 1967,16,79.31 J. D. Leeder and I. C. Watt, J. ColIoid Interface Sci., 1974, 48, 339.32 I. D. Kuntz, T. S. Brassfield, G. Law and G. Purcell, Science, 1969, 163, 1329.33 J. D. Bell, R. W. Myatt and R. E. Richards, Nature Phys. Sci., 1971, 230, 77.34 J. E. Ramirez, J. R. Cavanaugh and J. M. Purcell, J. Phys. Chem., 1974,78,807.35 G. N. Ling, in Wurer Structure at the Wuter-Polymer Interface, ed. H. H. G. Jellinek (Plenum,36 A. Ikegami, BiopoZymers, 1948, 6, 431.37 R. L. Anderson, J. M. Cassidy, J. R. Hansen and W. Yellin, BiopoZymers, 1973, 12,2789.New York, 1972), p. 4.(PAPER 5/864

ISSN:0300-9599    

DOI:10.1039/F19767200216

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

Thermally Denatured ProteinsNuclear Magnetic Resonance, Binding Isotherm and Chemical ModificationStudies of Thermally Denatured Bovine Serum AlbuminBY JOHN OARESUnilever Research Laboratory, Port Sunlight, Wirral, Merseyside L62 4XNReceived 8 th May, 1975The properties of thermal!y denatured bovine serum albumin have been investigated by n.m.r.,binding isotherm and chemical modification studies. The marked reduction observed in the proteinspin-spin relaxation times on thermal denaturation indicates that the protein chains become rigid.There was no change in the bulk water properties on thermal denaturation but a slight reductionin the amount of water bound to the protein was observed. The increase in the average water pro-ton spin-spin relaxation rate on thermal denaturation results from a decrease in the bound waterspin-spin relaxation time due to a reduction in the mobility of protein chains to which water mole-cules are bound.At temperatures higher than about 285 K, there is a contribution to the observedwater proton relaxation times from exchange between labile protein protons and water protons, whichresults in a minimum in the spin-spin relaxation time at 328 K. The native structure of bovineserum albumin is not extensively disrupted on thermal denaturation. The results are consistent witha two step mechanism for thermal denaturation, involving aggregation of initially unfolded proteinmolecules. The initial unfolding involves mainly changes in the tertiary structure rather than in thesecondary structure and aggregation results in the formation of a rigid network.The moleculesare held together by co-operative forces involving many amino acid residues and, although intermole-cular disulphide bonds do form on thermal denaturation of bovine serum albumin, chemical modifi-cation studies show that aggregation does not depend upon formation of chemical cross-links, as isoften supposed.Until a few years ago, most protein research was directed towards understandingthe properties of the native protein and the forces responsible for its structure. Manynative protein structures have now been elucidated, and it is found that the proteinsare folded into well defined, essentially rigid, three-dimensional structures. Recently,attention has been switched towards understanding the state of denatured protein,though major emphasis has been given to isolated molecules of denatured protein indilute solution rather than insoluble aggregates of denatured protein formed in moreconcentrated solutions.The aim of the work described here was to understand moreabout the properties of thermally denatured or thermally aggregated BSA. Informa-tion about changes in protein structure on thermal denaturation has been obtainedby (i) studying the effects of selective chemical modification of protein functionalgroups on thermal denaturation or on re-dissolution of thermally aggregated protein,and (ii) comparing the protein in its native and denatured states by spectroscopicstudies or by binding of small molecules.The former provides information aboutthe forces involved in aggregation whilst changes in the environment and mobility ofdifferent parts of the protein, or in the accessibility of various groups, on denaturationis obtained from the latter.Many n.m.r. studies have been made of water in gels formed by polysa~charides,~-~which gel at concentrations an order of magnitude lower than globular proteins. Theresults were analysed 2-6 assuming a two state model with rapid exchange occurringbetween bulk water molecules and those bound to macromolecules. It is known *22J . OAKES 229that the two state model holds for aqueous solutions of native BSA. A furtherobjective of the present work was to critically examine the applicability of the twostate model in suspensions and gels of thermally denatured protein and to obtain abetter understanding of mechanisms contributing to n.m.r.relaxation times in gelsystems. This should provide unambiguous evidence as to whether the bulk rheo-logical properties of thermally denatured protein dispersions and gels are partly dueto unusual properties of water in the gel or whether it is solely due to the existenceof a rigid three-dimensional macromolecular network.EXPERIMENTALThe source of BSA and the preparation of samples have been described previously.8Protein of known concentration was dissolved in water at neutral pH and heated at 74°C for1 h to denature. An opaque gel, containing bead-like aggregates with an average pore size - 300 &g-ll is obtained on thermal denaturation at concentrations of protein above about5 % but below about 0.001 % no aggregation is detected.At intermediate protein concen-trations, denatured protein exists in the form of a finely dispersed or a visco-elastic precipitate.n-Butyl and succinyl derivatives of BSA were prepared by adding the anhydride (2 g) toa 1 % BSA solution buffered to pH 8 with 2 % Na2HP04. The mixture was stirred fcr 3 hand the pH maintained between 7 and 8 by addition of 1 N NaOH. Succinic anydride andn-butyric anhydride modify the protein as follows : l 20succinic Itbutyric IIP-NH 3+ - -+ P-NH-C-CH2CH2C0 2 carboxyacylat ionanhydride 0acylation. P-NH: -+ P-NH-C-BunanhydrideUnder these conditions >90 % of the 59 free amino groups are modified.12 Two-thirds ofBSA molecules contain a sulphydryl (SH) group.These were modified by reacting 5 % BSAwith 2 % N-ethylmaleimide (NEM) at pH 7, stirring for 3 h. Modified protein was thermallydenatured in the presence of excess NEM to block SH groups that may become accessible orformed from break up of intramolecular disulphide bonds.The binding isotherm for sodium dodecyl sulphate to native and thermally denaturedBSA in phosphate buffer, pH 5.6, ionic strength 0.033 mol drr3, was determined using adodecyl sulphate ion-selective electrode described e1sewhere.l Relaxation time measure-ments were made using a Bruker B-KR 322s pulse spectrometer operating at 60 MHz. Spin-spin and spin-lattice relaxations for water protons were exponential for all protein concentra-tions.Badly prepared samples gave an additional component with relaxation times equalto pure water, indicating the presence of excess water or water not involved in the gel network.Other details of measurements are similar to those given previously.8RESULTSRelaxation rates TT ', Tc for water protons as a function of concentration ofthermally denatured BSA at 275 K are given in fig. 1. Spin-lattice relaxation ratesare similar to those obtained for the corresponding native protein solutions at allconcentrations and temperatures. Spin-spin relaxation rates are greater than incorresponding native protein solution but are independent of protein concentrationabove 45 % BSA. Thermally denatured SH-modified BSA gave TT1 values about10 % lower than dispersions and gels formed from unmodified BSA.Fig. 2 showsthe variation of the water proton TF' for a series of thermally denatured proteinsamples as a function of temperature up to 318 K. The water proton spin-spinrelaxation time for a 17 % sample was determined over a much wider temperatur230 N . M . R . STUDIES OF THERMALLY DENATURED PROTEINrange, 263-400 K and the results are shown in fig. 3. As in native protein solutions,8water proton relaxation times at 294K were independent of the frequency ofmeasurement.On thermal denaturation, the protein proton spin-spin relaxation times (50 %T2 - 150 ,us, 50 % T2 1.08 ms, native BSA at 294 K) became much shorter (75 %T2 20 ps, 25 % T2 200 pus) but the spin-lattice relaxation time remained unchangedwithin experimental error. The protein relaxation times did not show any variationwith protein concentration. The shorter T2 varied from 14 ps-20 ps and the larger T2from 74 ps-250 ps over the temperature range 278-318 K but a single temperatureindependent T2 of 10 p s was observed in frozen samples.(A single T2 of 16.7 ps wasobserved in a 25 % sample supercooled to 263 K.) Chemical modification of thesulphydryl group did not produce a measurable effect on the relaxation times.0 5 I0 15 2 0 25[thermally denatured BSA]/wt. %FIG. 1 .-Variation of water proton spin-lattice (0) and spin-spin relaxation rates ( x ) with concen-tration of thermally denatured BSA at 275 K. In the inset, Ti1 at 294 K is shown over a wideconcentration range.Measurements of hydration of thermally denatured BSA were obtained from frozenprotein solutions.8 Some supercooling was observed and on freezing most of thewater proton signal was lost.The intensity of the residual water signal varied withtemperature, as in frozen native protein solutions.8 Similarly, the amount of waterbound per protein molecule increased with protein concentration. It was estimatedthat thermally denatured BSA binds 10-15 % less water than native BSA, typicalhydration values being 0.145,0.16, 0.18 and 0.20 g water/g BSA for 0-15, 17.5,20 and25 % thermally denatured protein samples, respectively. Spin-lattice and spin-spinrelaxation times for water protons in a typical frozen denatured protein sample (20 %)as a function of temperature are shown in fig.4. Unfrozen or bound water is morJ . OAKES1000 I318K 303k'.?95K 285K 275K 243KIII I I II I 1 I I23 13.1 3.2 3.3 3.4 3.5 3.6 3.7 3.0 3.9lo3 KITFIG. 2.-Temperature dependence of the water proton spin-spin relaxation time for several thermallydenatured BSA concentrations.103K/TFIG. 3.-Variation of the water proton spin-spin relaxation time of a 17 % thermally denatured BSAsample with temperatureTIK273 263 253243 233 223 213 203I I I I I I 1 II t I I I I I I I3.6 3.8 4.0 4.2 4.4 4.6 4.0 5.0 5.21 0 3 ~ 1 ~- 6 - 5 -4 -3log ([SDS]free/mol dm-3)FIG. 5.-Binding isotherms for SDS to:native BSA ( x ) and thermally denatured BSA (a = 0.1 %BSA, @ = 1 XBSA)J . OAKES 233mobile than protons in ice or in the protein but is less mobile than water bound tonative protein.gThe binding isotherms for dodecyl sulphate to native BSA and to 0.1 and 1 %thermally denatured BSA, all at pH 5.6, ionic strength 0.033, are shown in fig.5.DISCUSSIONN . M . R . RELAXATION TIMESIn native BSA solutions the water proton relaxation rates were explained interms of rapid exchange between a small amount of water molecules tightly bound topolar groups on the surface of the protein and normal bulk water. Ti1 and TT ' aregiven by :forTT,; = h C / ( 1 - hC)(T1,2b + 7,)- -k TT,ia (1)hc Q (I-~c), Ti,2b Q T1,2*where c is the protein concentration (g BSA per g H20) ; h is the protein hydrationnumber (g H,O per g BSA) ; q, is the residence time of a water molecule at the proteinsurface and subscripts b and a refer to the bound and bulk states, respectively.On thermal denaturation, changes in the water proton relaxation times could resultfrom changes in h, (T, ,2b +zb)-l or Ti,;=.The marked decrease in the water protonT2 cannot be explained in terms of changes in h since the amount of bound waterdecreases by 10-15 %. If remained unchanged upon denaturation, then plotsof water proton relaxation rates, TC1, TF ', observed in thermally denatured BSAsuspensions against hc/( 1 - hc) should be linear and values of Ti:, 7';: obtained fromthe intercepts should equal T,, T2 for pure water at that temperature. Typical plots,i.e., at temperature 275 K, are shown in fig. 6. Clearly, water proton relaxation timesin dispersions of thermally denatured BSA can also be explained in terms of a twostate model with rapid exchange between bulk water molecules and those bound tothe macromolecule.* The measured relaxation times increase with temperature from263 to 285 K (fig. 2), hence z b Q T1,2b, so that values of Tlb, T2, can be obtainedfrom the gradients of plots shown in fig. 6. These values 13.9, 2.3 ms, respectively,are of the same order of magnitude as those for bound water obtained from frozendenatured BSA samples at 271 K (fig. 4). As in native BSA,8 the average mobilityof water molecules is reduced by about a hundred-fold on binding to the protein andis clear from the bound water Tl/T2 ratio at 223 K (fig. 4) that there are probablymany different hydration sites on the protein.T2b for water bound to thermallydenatured BSA is lower than that for water bound to native BSA (T2,, = 6.25 ms)but the corresponding spin-lattice relaxation times, Tlb, are identical. Clearly, themarked decrease in the water proton spin-spin relaxation time on thermal denaturation,and the small effect on the water proton spin-lattice relaxation time, result from changesin the bound water relaxation times. At high concentrations of denatured protein,the spin-spin relaxation rate approaches that of bound water molecules (fig. 1, inset).The decrease in the bound water relaxation time, T2b, on thermal denaturation canresult from (a) change in the environment of bound water, e.g., protein conformationalchange which replaces adjacent water protons by protein protons and (b) decrease inprotein mobility or protein segmental mobility which reduces the mobility of boundwater molecules. The observation of separate spin-lattice relaxation times for protein* Apparently, the two phase model is not entirely satisfactory in describing relaxation rates inagarose gels234 N.M.R.STUDIES OF THERMALLY DENATURED PROTEINand water protons in both native and denatured BSA samples means that spin diffusionis not so efficient, i.e., there is no strong magnetic interaction between protein andwater protons, hence change in the bound water environment is probably unimportant.On the other hand, the marked decrease in the protein spin-spin relaxation times onthermal denaturation indicates that the protein chains become much less mobile, themobility approaching that of protein chains in solids.Although the relaxationmechanisms for bound water molecules are not completely understood, the reductionin the bound water relaxation time on denaturation can be attributed largely to adecrease in protein chain mobility which reduces the net mobility of bound watermolecules.252 cc .-I I I0.025 0.05 0.075Izc/(l- hc)FIG. 6.-Graph of water proton spin-spin ( x ) and spin-lattice (0) relaxation rates against hc/(l - hc)at 275 K. Values of Tlb, Tzb obtained from the gradients are 13.9 ms, 2.30 ms, respectively.The measured water proton spin-spin relaxation time of thermally denatured BSAdispersions decreases with increasing temperature for concentrations higher than 1 %(fig.2). At higher temperatures, a minimum in T2 is observed (fig. 3) which isindependent of protein concentration above 1 % BSA and occurs at a definite tem-perature. The observed spin-spin relaxation times varied with pulse separation overthis temperature range. Clearly, an exchange process becomes important above275 K. Previous studies of native protein solutions and the present studies ofthermally denatured protein dispersions at 275 K show that exchange between boundwater molecules or protons and those in bulk water is extremely rapid, i.e., z b < Tlb,T2b. Thus the decrease in T2 above 275 K can be explained in terms of (i) proteinconformational changes or aggregation above 275 K, which reduce the rate of exJ .OAKES 235change of bound water molecules or protons with those in bulk water, or (ii) exchangebetween labile protein protons and (bound) water protons. The first alternative canbe rejected since the measured water proton spin-lattice relaxation time increases withtemperature. Thus 7 b < Tlb, and since Tlb is the same order of magnitude as T2,,(fig. 6), then z b < T2b, i.e., rapid exchange occurs. Clearly, the decrease in the waterspin-spin relaxation time with increasing temperature results from exchange betweenlabile protein protons and water protons. A similar explanation has been given l4for the decrease in T2 with increasing temperature for water adsorbed on wool keratin.For exchange between labile protein protons and water protons, then the averagerelaxation rates will be given by :Dforwhere P,, P , are the fractional concentrations of protein and water protons, respec-tively ; 2, is the residence time of a labile proton on a protein molecule ; Tl,2p representsthe spin-lattice and spin-spin relaxation times of protein protons and T, ,2w representsthe average water proton spin-lattice and spin-spin relaxation times given by eqn (1).If the first term dominates eqn (2) at concentrations above 1 % thermally de-natured BSA, then if slow exchange occurs, i.e., z, % T2,, the observed T2 willdecrease with increasing temperature since z, decreases. There will be a T2 minimumwhen z, = TZp = 20 ,us and the temperature of the T2 minimum will be concentrationindependent (fig.2 and 3). There is no effect of this exchange on the observed spin-lattice relaxation rate, since T,, x 200ms > Tlb % T2,, so that the first term ofeqn (2) is unimportant in determining the overall relaxation rate. In native BSAsolutions, the protein chain relaxation time, TZp, is much longer than in thermallydenatured BSA suspensions,* so that the first term of eqn (2) is less important. T2p issimilar to T2b in native BSA solutions so that the first term is still important but theeffect is small since the fraction of labile protons, P,, is less than the fraction of boundwater protons, Pb. This accounts for the small effect of exchange on the water protonT2 in native BSA solutions and the lack of a T2 minimum.8The marked decrease in the water proton spin-spin relaxation time upon gelationof polysaccharides, and the small effect upon the water spin-lattice relaxation time,have been attributed, at least in part, to slow exchange between bound water moleculesand bulk water,2-6 or to a " micro-space effect ".' A minimum was observed in T2with increasing temperature for agarose gels but not for the other related poly-saccharides.' Since exchange occurs between hydroxyl protons of alcohols and waterat room temprature,15 it seems that a more likely explanation for the T2 minimumis exchange of polysaccharide hydroxyl protons with water protons.Evidently,measurements of the water proton T2 can provide a measure of the relative rigiditiesof gel networks, and any subsequent aggregation, in systems where direct measure-ment is not possible, e.g., dilute gels of related macromolecules.Where there isexchange between water protons and protons of a relatively rigid macromolecule, aminimum in the water proton T2 will be observed with increasing temperature.The protein proton spin-spin relaxation times did not show any marked increaseduring the initial stages of thermal denaturation, unlike urea denaturation,l suggest-ing that if unfolding of the native structure prior to aggregation occurred, it did notinvolve extensive disruption of the secondary and tertiary structure. Similarly, themain change that occurred in the e.s.r. spectrum l6 of spin-labelled BSA upon therma236 J . OAKESdenaturation was a decrease in the intensity of the sharp spectrum, which is consistentwith protein aggregation.CHEMICAL MODIFICATION STUDIESOf the chemically modified proteins, only the SH blocked derivative thermallydenatured or aggregated upon heating to 333-353 K.The carboxyl-acylated andacylated derivatives did not aggregate, even upon heating to 373 K. Although theproduct obtained from thermal denaturation of BSA could not be re-dissolved byphysical means, that obtained from thermal denaturation of the SH modified deriva-tive was re-dissolved by sodium dodecyl sulphate (SDS), urea or increase in pH. Thisindicates that SH groups play an important part in producing insolubility of thermallyaggregated BSA. It is known that SH groups catalyze formation and break up ofdisulphide bonds and that BSA contains 17 intramolecular disulphide bonds1' Thusit is concluded that insolubility arises from formation of intermolecular disulphidebonds from intramolecular ones.This was confirmed by adding SDS to thermallydenatured BSA, to disrupt non-covalent forces, and re-dissolving with disulphidereducing or oxidising agents.Though it is often taken for granted that the mechanism of formation of aggre-gated protein is a chemical one,l the present studies show that other forces are impor-tant. Indeed, n.m.r. studies show that formation of disulphide cross-links does notproduce any further restriction in mobility of protein chains. Thermal denaturationof BSA is prevented by increasing the pH or by interaction with SDS, urea and organicsolvent mixtures (i.e., physical modification) as well as by chemical modifications withsuccinic anhydride or butyric anhydride.The various modifications affect the proteinin different ways, e.g., (i) although both succinylation and acylation expand theprotein molecule, n.m.r. studies show l9 that the secondary and tertiary structure isdisrupted to a greater extent in the succinyl derivative, and (ii) on denaturation withSDS, the unfolded product retains regions of ordered structure 2o but urea extensivelydisrupts the native structure.16 Thus, it is clear that the increased stability of theprotein in aqueous solution after modification is the result of the interplay of manydifferent forces involving many amino acid residues.Dissolution studies with SDS,urea and high pH show that these forces are similarly responsible for aggregation ofprotein molecules.BINDING ISOTHERM STUDIESThe binding isotherm for SDS to native BSA at pH 5.6 is independent of proteinconcentration. Thermally denatured BSA binds less than native BSA (fig. 5) and thebinding is concentration dependent at high binding numbers. This arises fromincreased aggregation at the higher protein concentration resulting in loss of apolarbinding sites, since binding of water molecules is concentration independent. Thedifference between isotherms for native and thermally aggregated BSA at free SDSconcentrations = mol dm-3 indicates that the initial binding sites become modi-fied on thermal denaturation.STRUCTURE OF THERMALLY DENATURED BSAThe evidence that there is an initial unfolding of the protein molecule on thermaldenaturation is as follows : (i) the marked restriction in the segmental mobility of theprotein chains on thermal denaturation is not compatible with models that involveaggregation of compact globular particles having limited points of contact ; (ii) intra-molecular disulphide bonds, which play an important role in maintaing the nativJ .OAKES 237structure, are broken on thermal denaturation and intermolecular disclphide bondsare formed ; (iii) the enhanced stability with respect to heat or urea denaturation, ofthe n-butylated derivative of BSA over native BSA itself results from increasedhydrophobic interactions, i.e., resistance to unfolding, if the decreased charge on theprotein decreases its stability.Evidence that the unfolding of the native protein is not extensive includes thefollowing : (i) there was no increase in protein proton relaxation times during thermaldenaturation, suggesting that the protein structure remains compact ; (ii) there is littlechange in the binding of water molecules or SDS molecules indicating little change inaccessibility of binding sites to the solvent ; (iii) X-ray scattering patterns producedby thermally denatured BSA are similar 21 to those of native BSA and quite unlikethose of fibrous proteins.Similarly, little changes are observed in the 0.r.d. of BSAon thermal denat~ration,~ unlike on urea denaturation, indicating little changes inprotein structure.These results indicate that much of the protein secondary structureremains intact.Clearly, the native structure of BSA is not extensively disrupted on thermal de-naturation. Though a gross over-simplification, it is convenient to regard the nativeprotein structure as consisting of folded or coiled coils. On this model, the initialstage of thermal denaturation can be considered to involve unfolding or partial un-folding mainly of the larger coils, rather than the smaller coils, e.g., helices. This isfollowed by aggregation resulting in the formation of a rigid structure held togetherby cooperative forces involving many amino acid residues. Many protein moleculesare involved in one aggregate and figures as high as 400 molecules have beensuggested 22 on thermal denaturation of 0.25 % BSA.I thank N. G. Pryce for helpful discussions.l C. Tanford, Adv. Protein Chem., 1968,23, 122.D. E. Woesnner, B. S. Snowden and Y. C. Chiu, J. Colloid Interface Sci., 1970,34,283.D. E. Woesnner and B. S. Snowden, J. Colloid Interface Sci., 1970, 34,290.T. F. Child and N. G. Pryce, Biopolymers, 1972, 11,409.T. F. Child, N. G. Pryce, M. J. Tait and S. Ablett, Chem. Comm., 1970, 1214.W. Derbyshire and I. D. Duff, Faraday Disc. Chem. Soc., 1973,57,243.J. Oakes, J.C.S. Faraday I, 1976, 72,216.R. Jaenicke, J. Polymer Sci. C, 1967, 2143.1965).' M. Aizawa, S. Suzuki, T. Suzuki and H. Toyama, Bull. Chem. SOC. Japan, 1973,46,116.lo M. Joly, A Physical Approach to the Denaturation of Proteins (Academic Press, New York,l1 M. P. Tombs, Faraday Disc. Chem. Soc., 1973, 57, 158.* G. E. Means and R. E. Feeney, ChemicalModification of Proteins (Holden-Day, San Francisco,1971).l3 B. J..Birch, D. E. Clarke, R. S . Lee and J. Oakes, Anal. Chim. Acta, 1974,70,417.l4 L. J. Lynch and K. M. Marsden, J. Colloid Interface Sci., 1973, 42, 209.l6 J. Oakes and M. C. Cafe, European J. Biochem., 1973, 36, 559.l 8 A. F. S. A. Habeeb, Biochem. Biophys. Acia, 1966, 121,21.l9 M. T. A. Evans, personal communication.2o J. Oakes, J.C.S. Faraday I, 1974, 70, 2200.21 D. P. Riley and U. W. Amdt, Proc. Roy. Soc. B, 1953, 141, 93.22 M. Nagagaki and Y . Sano, Bull. Chem. SOC. Japan, 1973,46,791.J. Oakes, J.C.S. Faraday 11, 1973, 69, 1311.R. C. Warner and M. Levy, J. Amer. Chern. SOC., 1958, 80, 5735.(PAPER 5/865

ISSN:0300-9599    

DOI:10.1039/F19767200228

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

ViscositiesBY G. P. MATTHEWS,of Oxygen and Air over a Wide Rangeof TemperaturesC . M. S. R. THOMAS, A. N. DUFTY-~ AND E. B. SMITH*Physical Chemistry Laboratory, South Parks Road, Oxford OX1 342Received 28th May, 1975Measurements have been made of the viscosities of oxygen and air relative to that of nitrogen inthe temperature range 120-1620 K using capillary flow methods over a range of gas pressures. Con-current measurements of the viscosity of argon served as a check on the methods and on the standardsof viscosity adopted. The calculation of various correction factors, which convert the measured gasflow times to accurate viscosity ratios, is discussed. A room temperature nitrogen standard, basedon the air standard of Bearden, together with standard viscosities obtained over a wide range oftemperature by Clark, Gough and Dawe, are used to obtain viscosities for each gas which are esti-mated to be accurate to f 0.5 %, rising to k 1.0 % above lo00 K and k 1.5 % below 200 K. Theviscosities are compared with those of previous workers and also with the smoothed values proposedby Maitland and Smith and by Watson.Measurements of the viscosities of the rare gases and nitrogen in recent years haverevealed large errors in earlier and have proved to be of value in the determina-tion of intermolecular forces.6-8 However, rather surprisingly little attention has beenpaid to the viscosities of oxygen and air.The early high temperature viscosity dataof Trautz et aZ.,99 lo Raw and Ellis,ll and Vasilesco l2 are believed to be seriouslyin error,13 and it has been suggested that the measurements of Johnston et all4 atlow temperatures may be rather too high.' Attempts have been made to estimatethe true viscosities at high temperatures by assuming that the errors obtained by earlierworkers for oxygen and air were of the same magnitude as those for the raregases.5 * Recently, Kestin and his co-workers 9 17* have measured the visco-sity of oxygen and air in the range 298-880 K, using an oscillating disc viscometer,and Clifford, Gray and Scott l9 have measured the viscosity ratios of oxygen tonitrogen at temperatures from 300 to 1300 K using an apparatus similar to the hightemperature capillary flow viscometer used here. The present work presents measure-ments of the viscosity of oxygen and air over the temperature range 120-1620 K.Theviscosities of nitrogen and argon were also measured concurrently over this range toprovide comparisons with previous measurements. 3*EXPERIMENTALTHE VISCOMETERSThe viscosities were measured using two capillary flow viscometers, operating in thetemperature ranges 120-330 K and 300-1620 K. These have been described in detail else-where.3* 4* 2o The viscometer sections of these apparatus consist essentially of two vessels,thermostatted at 298k0.05 K, connected by a coiled capillary tube which is enclosed eitherin a cryostat or a furnace. These sections are connected to gas handling systems and vacuumlines. The quantities measured on each apparatus were the times taken by a gas to pass fromone vessel to the other with known pressure differences across the capillary tube.The7 present address : Dunlop Oil and Marine Division, Grimsby.23G . P. MATTHEWS, C. M. S. R. THOMAS, A . N. DUFTY AND E . B . SMITH 239pressures were monitored on mercury manometers containing platinum pointers sealed intothe walls. These pointers were connected to banks of electronic timing devices, accurate toJL0.05 %, on which flow times were recorded. These times varied from 9 min for nitrogenat 124 K to 3 i h for oxygen at 1616 K. The maximum pressure drop across the capillarieswas 73.4 kN m-2 (551.0 mmHg) and the average pressures varied from 53.5 kN m-2 (401.3mmHg) to 9.7 kNm-2 (72.6 mmHg).The low temperature apparatus employed a Pyrex capillary tube 150 cm long, with aninternal diameter of 0.044 cm, surrounded by a helical heat exchanger.This was located ina fluid bath that could be thermostatted to & 0.1 K in the temperature range 120-374 K. Thewhole assembly was suspended in a large Dewar vessel containing liquid nitrogen or solidC02-alcohol as coolant. A standard platinum resistance thermometer calibrated at theNational Physics Laboratory was used to measure the temperature of the capillary tube.The high temperature apparatus required two capillaries operating over different tempera-ture ranges to minimize both the gas flow times and the various correction terms for non-Poiseuillian flow. From 293 to 880 K, a silica capillary tube of length 1.64 m and internalradius 0.22 mm was used, mounted vertically in a Gallenkamp box furnace.In the range880-1 620 K platinum+ 20 %-rhodium alloy capillary tube was employed, mounted horizon-tally in the cylindrical cavity of a Johnson-Matthey K44 furnace. The temperature of bothcapillaries was measured by calibrated thermocouples, which were independently checkedagainst standard thermometers up to 1100 K, and at the temperature of melting gold (1336 K).THE GASESThe nitrogen, argon and oxygen were supplied by the British Oxygen Company and wereof standard research grade. The air was laboratory air dried over CaC12. All four gaseswere tested for purity using a gas density balance and a inass spectrometer. These showedthat the oxygen was better than 99.5 % pure (major impurity N2), the nitrogen better than99.9 % pure (major impurity 02), the argon better than 99.5 % pure (N2 < 0.5 %, O2 <0.05 %), and that the air was of composition : N2 78+ 1 %, O2 21Ifr 1 %, Ar < 1 %,C02 < 0.1 %.The impurities give rise to uncertainties in the viscosity of argon of lessthan 0.15 %, and less than 0.08 % for the other gases.CALCULATIONThe quantities which were determin_ed experimentally were the flow times, t, correspond-ing to the measured average pressure (P) and the pressure difference across the capillary tubeat a particular temperature. Several small corrections were applied to the flow times.CURVED PIPE FLOWThe curvature of the helical capillary tubes produces an increased resistance to flow,greatest for the heavier gases at low temperatures. The correction may be expressed interms of the Dean number,21 D, given by :r3M(H,2-Pt) rD = 8q2RTcL ( E )where M is the molecular weight, q is the coefficient of viscosity, Y the capillary radius, L itslength, T, its temperature, Rh the radius of the capillary helix and Pf and Pb the mean inletand outlet pressures respectively.Runs were ignored which had Dean numbers greater than5 for the low temperature viscometer, and 3 for the high temperature apparatus, correspond-ing to corrections that were always less than 0.5 %, and usually less than 0.1 %.HAGENBACH (KINETIC ENERGY) CORRECTIONThis correction 22 never exceeded 0.04 %, since runs involving larger contributions werenot employed because of the extent of curved pipe flow effects240 VISCOSITIES OF OXYGEN A N D AIRGAS IMPERFECTIONSTwo correction terms are required here, the first depending on the temperature of the gasvessels, and the other on the temperature of the capillary tubes.4 The terms partially can-celled one another and in combination only reached 0.2 % at the lowest temperatures, andrarely exceeded 0.1 %.Second virial coefficients for the calculation of these terms weretaken from the conipilations of Dymond and Smith,23 and LeVelt Sengers, Klein andGallaher.24SLIP CORRECTIONThe times of flow were also corrected to allow for “ slip ” along the wall of the capillarytube of the layer of gas adjacent to itz5* z6 For the experiments below room temperature,the simple correction factor [ l + 6 .2 8 4 ~ lo4 (v/rP)(T,/M)*] was Although this issufficiently accurate below room temperatgre, at higher temperatures it was necessary toperform runs at many different values of P for each gas. The Poiseuille equation for gasflow through a capillary is modified by the effects of slip, giving :dn -= 7cr4(P: - P i ) [ l + = E]d t 1 6v R T, Lwhere drtldt is the flow rate (mol s-l). The slip coefficient, S, is a constant for a particulargas at a given temperature, so the effects of slip were eliminated by extrapolation to 1 / P = 0.THE RELATIVE METHODSLarge errors can be caused by small uncertainties in the precise radius of a capillary tubein an absolute viscosity calculation using eqn (2). Therefore the most accurate results incapillary flow viscometry are obtained using relative methods, in which this term cancels out.In this work, two relative methods of calculation were used, previously described asmethods A and B.27 Method B was used for comparing flow times at different temperaturesof the capillary tube, Tl and Tz, for the same or different gases.The corresponding correctedflow times, f l and t 2 , obtained for the same pressure drop are related by the equation :where To is a reference temperature (273 K) and a is the coefficient of linear expansionof the capillary material^.^. Method B calculations have been used by Clarke, Gough andDawe 3* 4, z 8 to establish the nitrogen standards used in this work. They were based on anaccurate room temperature standard :~ ~ ~ ( 2 9 3 K) = 175.7 x lo-’ kg m-l s-I.This is related to the accurate air determination of Bearden 2 9 at this temperature, who useda rotating cylinder method.The experiments described here were not primarily intended toestablish another set of standard viscosities using the method B procedure. Nevertheless,such an analysis was carried out for both nitrogen and argon for temperatures above 300 K,and the results agreed with the nitrogen standard 3, 4, z 8 and argon measurements of Daweto within the expected experimental errors.The viscosity data we report were calculated using the viscosity of nitrogen at the sametemperature as the standard (method A) as this method is more accurate once reliable stan-dards have been established. If t is the gas flow time (corrected for all effects except slip)corresponding to a pressure drop for which the average capillary tube pressure is P , and f N 2is the nitrogen flow time under identical conditions, than the integrated form of eqn (2) leads toThis equation was used to calculate the ratios of the viscosities of argon, oxygen and air tG .P. MATTHEWS, c . M. s. R. THOMAS, A. N. DUFTY AND E. B. SMITH 241that of nitrogen at the same temperature. These ratios, when used in conjunction with theappropriate nitrogen stanaard, gave the viscosities of the gases at each temperature studied.RESULTSThe flow times of oxygen relative to nitrogen were measured at 13 temperaturesin the range 124-327 K using the Pyrex capillary. On the high temperature apparatus,experiments were carried out at 5 temperatures using the silica capillary, and 5 usingthe Pt-Rh capillary.Argon was studied at 17 of these temperatures over the entirerange, and air at 20. Nitrogen was used as the standard gas.With the low temperature apparatus, measurements were carried out for threedifferent values of average pressure (F) in the capillary at each temperature. The flowtimes for the test gas at these pressures and for nitrogen under the same conditionswere formed into three ratios, and the final viscosity ratio at a particular temperaturetaken to be the average of these. To keep the flow times short, larger values of Hwere used at the higher end of the low temperature range.When using the high temperature viscometer, a large number of P values wereneeded for each gas at each temperature to correct for slip. The flow conditions werechosen to give as large a range of P values as possible without introducing the problemsof curved pipe flow.The best straight lines for the slip plots were determined by aleast squares fit. After making a full study at several temperatures, it was found thatas predicted the slip effects were very small, and the number of P values used atsubsequent temperatures was therefore reduced from 17 to 1 1. The actual experi-mental temperatures, flow time ratios and viscosities, are extensive and although notreproduced here may be obtained on request from the authors.The flow times for all three capillaries were highly reproducible, being usuallybetter than 20.2 % or 1 s, whichever was the greater.The temperatures studied witheach capillary tube were chosen in a random order, and the consistency of the resultsshowed that they were not dependent on the thermal history of the tube in use. Theagreement of the results at the overlap temperature were found to be good. Thusthe oxygen results differ by 0.02 % at the Pyrex/silica capillary tube overlap tempera-ture (290 K), and by 0.2 % at 875 K when measured by the silica and Pt-Rh tubes.The corresponding values for the air results are 0.5 and 0.05 % respectively. Theaverage standard deviations of the points from the best fitting straight lines used forthe high temperature slip calculations were 0.3 %.The main sources of error in this work were fluctuations in the temperatures ofthe capillary tubes and uncertainties in the measurement of these temperatures.Thiswas most noticeable at the extremes of the temperature range, i.e., below 200 andabove 1200 K. A consideration of these and other potential sources of error, suchas uncertainties in the measurement of time, pressure and composition, and possibleerrors in the standard of Clarke, Gough and D a ~ e , ~ . 4* 28 lead to the followingestimates of maximum uncertainty in the results : ratios 1.5 % below 200 K,k0.2 % above 250 K ; viscosities -I 1.5 % below 200 K, k0.5 % 250-1000 K,& 1.0 % above 1000 K. As a check on accuracy the viscosities of nitrogen andargon were also determined relative to the room-temperature nitrogen standard(method B).All but three of these data deviate from the nitrogen standard by lessthan 0.7 % and from the argon viscosities of Dawe by less than 0.3 %.For purposes of reference and comparison with other data, the viscosities havebeen fitted in two ranges (above and below 300 K) to curves of the type :where r,~ is the viscosity (lo-’ kg rn-l s-l) and T the temperature (K). The coefficientslnq =AlnT+B/T+C/T2+242 VISCOSITIES OF OXYGEN AND AIRof the curves for argon, air and oxygen, together with those for the nitrogen stan-dard 3 9 4 s 28 are listed in table 1. Also shown are the root mean square percentagedeviations of the experimental points (qexp) from the smoothing curves. The per-centage deviations at each temperature are shown in fig.1 and 2. In table 2, viscosi-ties derived from these equations are given. At 300 K, the values predicted by thelow temperature and high temperature smoothing curves differ slightly, and theaverage is given.TABLE 1 .-SMOOTHING COEFFICIENTSrange A B C D % r.m.s.devn.N2 < 300 0.556 994 - 72.136 11 1365.891 2.234 0.38>300 0.654944 42.582 28 - 14 190.95 1.468 0.39air < 300 0.446 487 - 124.885 5 4 138.793 3.046 0.28> 300 0.669 878 42.961 33 - 12 680.57 1.408 0.420 2 < 300 0.327 090 - 196.003 9 7 818.086 4.036 0.45>300 0.661 739 32.533 05 - 13 949.02 1.606 0.43COMPARISON WITH PREVIOUS DATAThe percentage deviations of the results of other workers from the smoothed datafor air and oxygen are shown in fig. 1 and 2. Also shown are the viscosities estimatedby Maitland and Smith and Watson.16For both oxygen and air the measurements above 300 K by early worker^,^'^^ arelower than the data given in this work.Those performed before 1930 in the range300-1 100 K (not shown here), e.g., by Williams 30 deviate by up to 6 % even nearroom temperature. The marked downward trends which occur in the data of Trautz,Zink and Vasilesco 9 9and the souces of error in these results have been the subject of considerable discus-sion.13 The early low temperature air results of Fortier 31 (140-300 K) all agree towithin 0.5 %. The smoothed data of Johnston and McCloskey l4 for both gasesbelow room temperature, which were measured using an oscillating disc, are alsoshown. These points tend to be higher than ours at the lowest temperatures, butare also observed in their measurements on the noble gasesTABLE 2.-sMOOTHED VISCOSITIES, q/107 kg m-' S-'T/K N2 (standard) air 0 21201502002503004005006007008001000120014001600170081.0100.0128.9155.0179.0223.6261.5295.7327.2356.8411.8462.8510.7556.2578.284.0103.0133.1160.5186.2232.7272.1307.8341.0372.3430.8485.1536.4585.2608.991.1111.7146.1178.2207.4261.1307.3348.9387.3423.5490.7553.0611.6667.2694.G .P . MATTHEWS, c . M. s. R . THOMAS, A . N. DUFTY AND E . B. SMITH 243nevertheless agree to within the quoted experimental errors. All the early data shownare in good agreement at room temperature, and this may be attributed to carefulstandardisation work in this region.The accurate air standard of Bearden 29 (notshown) agrees closely with our measurements as expected.-4-6,+ 4+2- * ee0t 1 1 S f I I i 1 1 i I I I ! f I !.+4+2---d 4-4For both gases, the recent measurements of Kestin and his co-workers using anoscillating disc apparatus 1 . 17* tend to be higher than ours by up to 1.2 % above600 K, and below them by about 0.5 % at room temperature. The data of Kestinand Leidenfrost,'* not shown in the diagrams, agree closely with the other data ofKestin and coworkers. The weighting of the predictions of Maitland and Smith-- + o + + +- Q +1 I I A . 1 1 I I 1 1 I I I I 1 1 I 244 VISCOSITIES OF OXYGEN AND AIRtowards Kestin’s values therefore accounts for the discrepancy between their curvesand the present experiments.The recent data of Clifford et all9 for oxygen fromroom temperature up to 1300 K used Watson’s compilation l6 as a standard ratherthan internal measurements, and these results are therefore shown both as publishedand adjusted to our nitrogen ~tandard.~. 4 s 28 It can be seen that both sets of dataare lower than ours over their entire range. The adjusted values all agree to within1.1 % of our data, whereas the published data, although closer at higher temperatures,deviates by - 1.8 % at 420 K, and by -2.1 % from Kestin’s data at this temperature.Finally, it can be seen that the predictions of Watson l6 agree to within our quotedexperimental errors over their entire ranges.In fact the agreement of the high tem-perature prediction for air is remarkable, it differing by less than 0.3 % in the range450-1650 K.G. P. M. acknowledges the receipt of an S.R.C. studentship.R. Dipippo and J. Kestin, Proc. 4th Symp. Thermophysical Properties (College Park, Maryland,1968), p. 304.F. A. Guevara, B. B. McInteer and W. E. Wageman, Phys. Fluids, 1969, 12,2493.R. A. Dawe and E. B. Smith, J. Chem. Phys., 1970,52,693.A. G. Clarke and E. B. Smith, J. Chem. Phys., 1968,48,3988.G. C. Maitland and E. B. Smith, J. Chem. Eng. Data, 1972, 17, 150.J. A. Barker, M. V. Bobetic and A. Pompe, Mol. Phys., 1971, 20, 347. ’ D. W. Gough, G. C. Maitland and E. B. Smith, klol. Phys., 1972, 24, 151.jJ A.N. Dufty, G. P. Matthews and E. B. Smith, Chem. Phys. Letters, 1974, 26, 108.M. Trautz and R. Zink, Ann. Physik., 1930, 7,427.lo M. Trautz and A. Melster, Ann. Physik., 1930, 7, 409.11 C. J. G. Raw and C. P. Ellis, J. Chem. Phys., 1958,28, 1198.l2 V. Vasilesco, Ann. Physique, 1945, 20, 137, 292.l3 e.g. H. J. M. Hanley and G. E. Childs, Science, 1968, 159, 1114.l4 H. L. Johnston and K. E. McCloskey, J. Phys. Chem., 1940,44, 1038.l5 H. J. M. Hanley and J. F. Ely, J. Phys. Chem. Ref. Data, 1973, 2, 735.l6 J. T. R. Watson, National Engineering Laboratory Report, No. 516, 1972.l7 J. H. Hellemans, J. Kestin and S. T. Ro, Physica, 1973, 65, 362.l 8 J. Kestin and W. Leidenfrost, Physica, 1959, 25, 537, 1033.l9 A. A. Clifford, P. Gray and A. C. Scott, J.C.S. Faraday I, 1975, 71, 875.2o R. A. Dawe, G. C. Maitland, M. Rigby and E. B. Smith, Trans. Faraday SOC., 1970, 66, 1955.21 W. R. Dean, Phil. Mag., 1927, 4,208; 1928, 5, 673.2 2 J. R. Partington, Advanced Treatise on Physical Chemistry (Longman, London, 1949), vol. 1,23 J. H. Dymond and E. B. Smith, The Virial Coeficients of Gases-A Criticul Compilation24J. M. H . LeVelt Sengers, M. Klein and J. S. Gallaher, Heat Division National Bureau of2 5 G. M. Freyer, Proc. Roy. SOC. A, 1966,293, 329.26 R. A. Dawe, Rev. Sci. Instr., 1973, 44, 1271.” G. C. Maitland and E. B. Smith, J.C.S. Faraday I, 1974,70,1191.28 D. W. Gough, G. P. Matthews and E. B. Smith, J. C. S. Faraday I, in press.29 J. A. Bearden, Phys. Rev., 1939, 56, 1023.30 F. A. Williams, Proc. Roy. SOC. A , 1926, 110, 141.31 A. Fortier, Thesis (University of Paris, 1937) ; quoted by V. Vasilesco in ref. (12).p. 883.(Clarendon, Oxford, 3969).Standards Report, 1971.(PAPER 5/1008

ISSN:0300-9599    

DOI:10.1039/F19767200238

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

Cross Sections for Gas Phase Ion-Ion Recombination inH30'+X- --f HX+H20 for X = C1, Br or IBY NIGEL A. BURDETT AND ALLAN N. HAYHURST*Department of Chemical Engineering and Fuel Technology,The University, Mappin Street, Sheffield S1 3JDReceiuecl3rd June, 1975Mass spectrometric measurements have been made of the concentrations of ions present in flamesof H2, O2 and N2 with trace quantities of C2HZ added, as well as one of the halogens CI, Br or I.The principal charged species found were H30+, e- and X-, where X is a halogen atom. Thehydroniuni ion is produced in the reaction zone of a flame in amounts greater than those for equili-brium at the temperature of the burnt gases. Recombination of charged species thus occurs andproceeds by two reactions ;H30++X- -+ HzO+HX (1)H30++e- -+ H+H+OH.(11)From a study of the rate of decay of H30+ for varying amounts of one of the halogens present, itproved possible to measure the ratio of the rate coefficients (kl/k2) of reactions (I) and (11). Foreach halogen k l / k z was constant over the temperature range 1810-2570 K and was 0.10+0.03 forC1, 0.07k0.02 for Br and 0.03+0.02 for I. The resulting values of kl are also independent of tem-perature and are 4.1 i- 1.6 x lo-', 2.7k 1 . 0 ~ ion-' cm3 s-' for C1, Br and I,respectively. The corresponding cross-sections (m2) are 2.1, 1.5 and 0.7 x m2. The heatsof reaction (I) are large and the products appear to be HzO and HX with the latter either electronicallyexcited or completely dissociated, but not in its ground electronic state.and 1.2k0.7 xVery few experimental studies have been made of the recombination of positiveand negative ions in the gas phase, especially at high temperatures.l This is in con-trast to the recombination of positive ions with free electrons, the rate of which hasbeen measured for a variety of ionic species over a range of conditions.For instance,work in flames has provided cross-sections for the reaction of electrons with metallicpositive ion^,^-^ as well as molecular one^,^-^ such as CaOH+, SrOH+, NO+ and H,O+.One ion-ion neutralization which has been given some attention at high temperaturesis that of an alkali metal ion A+ with a halide ion X- in A++X- + A+X, whichcan be made to occur in flames.lO- l 1The work reported below aims to measure the rate coefficient for the reaction ofH,O+ with the negative halide ions C1-, Br- and I- inA brief description of part of this study has already been given, together with apreliminary account of related work by Morley l 2 for X = Cl.The hydronium ion, H30+, is formed in the reaction zone of a flame containinga hydrocarbon by the sequence ;9 CH+O -+ CHO++e-, CHO++H,O + H30++CO.Because the species CH and 0 are present in amounts greater than those forequilibrium, so also is H,O+ in this early part of one of these flames. However,H30+ subsequently decays downstream in the burnt gas region towards an equilibriumsituation l 3 byH,O++X- -+ H,O+HX. (1)H30++e- -+ H+H+OH, (11)24246 I 0 N - I 0 N RE C 0 M BIN AT I 0 NWhen a halogen is introduced into such a system, its negative ion is formed and enablesH,O+ to disappear through another channel in (I).The work reported below mea-sures the relative rates of processes (I) and (11) by following the decay of H,O+ forvarying amounts of one of the halogens present. The kinetics of reaction (11) havealready been studied 7-99 l4 and it will be assumed here to have a recombination co-efficient k2 = 4.1 x ions-' cm3 s-l, which is constant over the temperature rangeof 1800-2600 K used in this work.EXPERIMENTALAll flames were premixed and their supplies consisted of hydrogen and oxygen withnitrogen present as a diluent. Small quantities (<+ % by vol.) of acetylene were occasionallyadded. Altogether six different flames were employed, five of which were fuel-rich and onefuel-lean.Their temperatures were measured to be in the range 1810-2570 K. Detailsare given in table 1. Each flame was burnt at atmospheric pressure in laminar flow usinga Meker-type burner. Halogens were added to a flame in controllable amounts by passinga small fraction of the nitrogen supply through a saturator containing an organic halide.This was either CHC13 or CC14 for providing chlorine, n-C3H7Br for bromine and CH31 orC2H51 for iodine. A knowledge of the gas flow and vapour pressure of the organic liquidallows the quantity of halogen in the flame to be calculated. Care has to be taken to avoidPVC tubing, because of its extensive absorption of these organic compounds.16 On enteringthe flame, these halides break down and exist in the burnt gases l6 either as molecules of thehydrogen halide, HX, or as free atoms X.If the ions X- are formed, as discussed below,they always constitute a negligible fraction (< 1 %) of the total halogen present. Hydrogenatom concentrations were measured as functions of axial distance along the five fuel-richflames using the Sr+/SrOH+ techniquee6 It was not possible to determine [HI in the fuel-leanflame, because of its low temperature.TABLE 1 .-DESCRIPTION OF FLAMES STUDIEDunburnt composition ratios equilibrium mole fractionsno. temp./K Hz 0 2 N2 [HI IH 211 2570 2.98 1 .o 1.97 1 . 4 9 ~ 1 . 9 3 ~ 10-12 2400 2.74 1 .o 2.95 5.70 x 1.28 x 10-14 1980 3.09 1 .o 4.74 3 . 0 0 ~ 1 . 3 9 ~ 10-15 1820 3.12 1 .o 5.77 1 .5 0 ~ 1.26~ 10-13 2080 3.18 1 .o 4.07 1.10~ 10-3 1 . 6 2 ~ 10-16 1810 1.49 1 .o 4.64 3 . 0 0 ~ 10-6 7.00~ 10-5Ion concentrations along the burnt gas region were measured by continuously samplinga small fraction of the flame into a quadrupole mass spectrometer, details of which have beengiven already.l79 l8 Briefly, the sample was pumped through a small hole (diam. 0.05-0.20mm) in the tip of a nickel or chromium cone and then supersonically expanded into a vacuumchamber. Here ions of one sign were focussed into a second chamber containing a massfilter, whilst neutral species were pumped away. The quadrupole filter allows only ions of achosen mass : charge ratio to pass through itself, the resulting ion current being collected,amplified and recorded.By moving the burner, it was possible to measure the concentrationof any ion as a function of axial distance along a flame. Such readings were taken at 1 mmintervals by means of a data-logger consisting of an analogue-digital converter connected toa paper tape punch.SAMPLING CONSIDER AT IONSIt is important to be able to relate both the measured ion current and the actual concen-tration of the ion in the flame. For this the sampling system must be capable of quicklyquenching all chemical reactions. The mass spectrometer was in fact calibrated l9 usinN. A . BURDETT AND A . N. HAYHURST 247the equilibrium ionization of an alkali metal, such as caesium. The relaxation time of thisionization reaction is considerably greater than the time taken by the sample to attain mole-cular flow (about 0 .5 ~ s for a nozzle of diameter 0.1 mm), so that in this case the ioncurrent is unaffected. However, certain reactions are sufficiently fast to be equilibrated atall points in a flarne and also are capable of adjusting their equilibrium position to the fallingtemperatures and pressures experienced either in the relatively cool boundary layer aroundthe sampling orifice or during the supersonic expansion. These " fast " reactions are char-acterised by having relaxation times less than the residence time in this boundary layer andcontinuum (as opposed to subsequent molecular) part of the expansion into the first vacuumchamber. As a result of one or other chemical equilibrium being rapid enough to adjust tothese falling temperatures, a measured ion current may not be indicative of a true flameconcentration.For instance, it is established that the equilibrium H30++ H20 + H30+.HzO is balanced in a flame and that H30+-H20 (as well as occasionally higher hydrates)may be formed as gases cool during sampling.18-20 Consequently, the observed ratio of[H502+]/[H30+] does not reflect its true flame value and is found to be a function of nozzlediameter and ternperature.lg* 2o Similarly, it has been shown 20-22 that chloride ions andfree electrons have concentrations in a chlorine-laden flame which are interrelated becauseof a rapid balance of HCl+e- + C1-+ H. As a result of the consequent falsification of ionabundances, measured [Cl-]/[e-] are quite different from their expected values.In this caseC1- ions are lost during sampling by reaction with hydrogen atoms, the magnitude of thedepletion being dependent on [HI and thus varying with distance along a flame.22A further complication is that the hydrate of H30+ is destroyed at a greater rate thanH30+ by collisional attenuation inside the first chamber of the mass spectrometer.lg 2oBecause of this, the observed sum [H,O+]+ [H,O,+] does not accurately reflect the true valueof [H,O+] for the flame. Work on the recombination of H30+ with free electrons showedthat this loss is approximately constant along any given flame, but is likely to vary consider-ably with nozzle diameter and temperature. A verification of this is described below.EQUILIBRIUM CONSTANTSWhen a halogen X is added to a flame containing hydrogen, it exists as free atomsand hydrogen halide molecules with the equilibrium~ p e r a t i v e .~ ~ Using standard statistical mechanical methods and the data of Herz-berg 24 and Gaydon 2 5 on the bond energies, vibration frequencies and bond lengthsfor HX and H2, it is possible to calculate K3, the equilibrium constant of (111), foreach of the three halogens. Values of K3 computed for a distance of 10 mm down-stream of the reaction zone are presented in table 2, together with the ratio, 4 =[HX]/[X] for each flame used. It is seen that chlorine is present mainly as HCl,iodine as free atoms and that bromine exists as HBr and Br in comparable amounts.The other important equilibrium lo.11* 22 for halogens in these flames isHX+H +H,+X (111)HX+e- + X-+H (IV)which produces halide ions by dissociative attachment of e- to HX in preference tothe alternative three body attachment process X+e-+M 3 X-+M, involving athird body, M. This predominance of (IV) holds even for iodine, where [HI]/[I] islow as shown in table 2. K4, the equilibrium constant of (IV) has also been calculatedby statistical mechanical methods, using data on HX from Herzberg 24 and theelectron affinities of Berry and Riemann.26 The resulting values, together with thoseof t,b = [X-]/[e-] also evaluated at a point 10 mm downstream from the reaction zone,are given in table 2 for a total halogen concentration (i.e., [HX]+[X]) of 0.2 % byvolume.For this amount of halogen, it is evident in all three cases, and especiallyfor the cooler flames, that a large fraction of the negative charge is carried by th248 I ON - I 0 N RE CO MBI N AT I 0 Nhalide ion. This iiieans that the rate of decay of H,O+ could well be significantlyaffected by the presence of halogen.TABLE 2.-vALUES OF K,,&,$ = [HX]/[X] AND $ = [X-]/[e-] FOR A POINT 10 mm DOWNEACH FLAME AND A HALOGEN CONTENT OF 0.2 % BY VOLUMEflame KdcI) fh(C1) W1) Y(CO KdBr) K4(Br) 4Br) ,u(Br) KdI) K4(I) d(l> ~ ( 1 )1 0.58 8.80 19.6 0.98 9.16 77.1 1.23 5.01 155 220 0.073 1.762 0.57 7.44 26.1 1.67 11.6 75.1 1.28 9.88 248 243 0.060 3.233 0.56 4.90 49.8 1.65 20.2 68.7 1.38 13.7 732 296 0.038 3.754 0.55 4.15 78.0 2.56 24.9 65.6 1.74 26.1 1103 316 0.039 7.495 0.55 3.03 111.0 2.92 36.5 60.3 1.68 36.9 2329 354 0.026 8.86RESULTSWhen small quantities of acetylene (<$ % by vol.) were mixed into the suppliesto the burner, the principal positive ions found in the burnt gases were H30+ and toa much smaller extent its first hydrate, with all the negative charge carried by freeelectrons.When a halogen was present too, its negative ion was detected and also[H30+] increased slightly, as a result of the extra hydrocarbon added with the halogen.Typical plots of the sum of the ion currents of H,O+ and H,O+.H,O are shown infig. 1 as a function of distance along a flame for various quantities of bromine. Itis evident from a cursory examination of the ion profiles of fig. 1 that the addition0 5 10 I 5 2 0axial distance from reaction zone/minFIG.1.-Experimental plots of I H ~ O + against axial distance along flame 2 using a chromium samplingnozzle of diameter 0.13 mm. Curves are : A no bromine added, B 4.6 x % by vol. of Br added,C 9.0 x % by vol. of Br.of even a small amount of bromine reduces the rate of decay of H,O+. Very similarobservations were made for chlorine and iodine, but one interesting feature compli-cated the situation slightly with the latter. In this case the positive ion I+ was ob-served with a concentration having a maximum value in the reaction zone and adecaying one downstream. In fact, for large quantities (>0.15 % by vol.) of iodinepresent, charge transfer reactions, such as I + H30+ + H,O + H +I+ interfered withmeasurements of [H,O+].In the work described below the ratio [I+]/[H,O+] waN. A . BURDETT A N D A . N. HAYHURST 249below 0.02 in all parts of the flame where measurements were taken. One conse-quence of this is that the charge balance ignoring [I+], i.e., [H,O+] = [I-] + [e-1, where[H,O+] includes hydrates, may be in error by up to 2 %.The observations, such as are presented in fig. 1, are interpreted as follows.H30+ ions are taken to disappear in a flame to which halogen has been added byrecombination with both electrons in (11) and halide ions in (I). The equation forthis may be written as- d[H,O+]/dt = k2[H30+][e-] + kl[H30+][X-] (1)where kl and k2 are the rate coefficients for (I) and (II), respectively. Now, becauseof the sampling falsifications mentioned earlier, the measured values of both [H30+]and [X-] are different from the true ones.To deal with this, two loss terms a and /jlare introduced to relate actual flame concentrations to those calculated from measuredion currents using the alkali metal calibration factor (see above). Denoting trueconcentrations with square brackets and measured ones as I, we have [X-] = a&-and [H,O+] = pZH30+, where I H 3 0 + includes the H30+-H,0 ion current. Thesequantities a and fi are likely to be dependent on flame temperature and the dimensionsof the sampling nozzle ; also a varies with both [HI and [HX].Since H30+, X- and e- are the principal charged species in these flames, thebalance [H,O+] = [X-] + [e-] holds.From this and the further knowledge 20-22 thatreaction (IV) is balanced at all points in a flame, a relationship between a and /jl maybe established as follows. Because K,[HX][e-] = [H][X-1, thenholds. The decay eqn (1) then becomesassuming dp/dt = 0, which is seen below to be the case. The usual recombinationplot of 1/IH30+ against time t (or axial distance) along a flame has a gradient (writtenhere as S ) which is the left hand side of eqn (2). Thus, in general, such a secondorder plot is a curve whose slope varies with time or distance. Eqn (2) gives it as- S = P(k2 + (k1 -k&) (3)where the function 2 = K,[HX]/(&[HX]+[H]) is the fraction of negative chargecarried by the halide ions at any given point in the flame.To determine S, the left hand side of eqn (2), from a profile of IH~o+, numericaldifferentiation was employed following the procedure described by Hershey et al.,27which required an initial smoothing of the data. A typical plot is shown in fig. 2giving the variation of S along the burnt gases of flame 3 (see table 1) containing nohalogen (curve A) and the same flame with 0.066 % iodine present (curve B). CurveA represents So (i.e.., S for no halogen), which is seen to be constant in the range 5-20mm from the reaction zone. This demonstrates that P is constant over this distancerange or that dp/dt = 0. The increase at smaller distances is attributable l 9 to gasvelocity changes caused by interaction of the flame with the front plate of the spec-trometer. The gentle rise downstream probably arises from air-entrainment causinga drop in the velocity of the burnt gases.These observations are in accord with thoseof Hayhurst and T e l f ~ r d , ~ who determined k2 from such measurements. Also shownin fig. 2 is the variation of 2 with axial distance (curve C) along flame 3 for 0.066 %of iodine present250 ION-ION RECOMBINATIONIf S, now represents the value for S for a halogen-laden flame, then from eqn (3)we haveSX/S, = 1 - (1 -kJkJZ. (4)This ratio S,/S, is now seen to be independent of p, for even if p were to vary alonga flame, then so long as its variation is the same with and without halogen, then Sx/S,remains unaffected. Eqn (4) also indicates that a graph of SJS, against 2 shouldbe a straight line, from whose slope the ratio kl/k2 may be derived.Two such plotsare shown in fig. 3 for flame 3 containing a range of concentrations of iodine [fig. 3(a)]c u - . - . - . - - u o0 5 10 15 2 0axial distance from reaction zonelmmFIG. 2.-Plots of S against axial distance along flame 3 for a halogen free flame (curve A) and for0.066 % by vol. of iodine added (curve B). A chromium sampling nozzle of diameter 0.16 mm wasused. Curve C shows the variation of Z along the iodine-laden flame.L - L A *o 0.5 0 0.5 1.0(4 z (b)FIG. 3.-Experimental plots of Sx/So against 2 for iodine and chromium sampling nozzles in (a) :A, 4.0 x %, orifice diameter 0.07 mm ; @,1.95 x lo-' %, diameter 0.10 mm. (6) Bromine : 0, 1.8 x %, hole diam. 0.07 mm ; A, 3.4 x% of I and orifice diameter 0.07 mm ; 0, 9.8 x%,diam.O.lOmm; 0, lSxlO-' %, diam.0.13mmN. A .BURDETT AND A . N . HAYHURST 25 1and bromine [fig. 3(b)] and also using chromium sampling nozzles of varying diameter.In each case a straight line can be fitted to the experimental observations and theintercept for 2 = 0 is SJS, = 1, as expected from eqn (1). The plots of fig. 3confirm the above interpretation and particularly the assumption that reaction (IV)is balanced,The same procedure has been used for all three halogens in the five fuel-rich flames;the resulting kllk2 values are presented in table 3. Because of the lack of informationon [HI in the fuel-lean flame, it was impossible to derive 2 along its length. Inchlorine-laden flames, however, this difficulty was overcome, because Zis approximatelyconstant in the burnt gas region. This arises from 2 = K,[HX]/(K,[HX]+[H]) inwhich [HCl], as shown above, is almost equal to the total chlorine concentration andhence nearly invariant. Also well downstream in a flame [HI is not changing signi-1.101 10 5 10[HCl]-l/(vol %)-lFIG.4.-Plot of 1 /<1- Scl/S,) against 1 /[HCI] for flame 2. Diameters of sampling nozzles (nickel)used : 0 = 0.20 mm, B ,0.06 mm, A, 0.14 mm, 0 . 0 . 1 7 mm and for chromium nozzles : a, 0.05 mm,W, 0.14 mm.ficantly, so that 2 is nearly constant. Because of these factors, plots of 1 /IH3o + againstdistance along a flame are almost straight lines l2 of slopes Scl. From eqn (2) it isapparent that S,, varies from k2P for zero chlorine (2 = 0) to klP for large [HCl] orZ = 1.The ratio of these two limiting slopes gives k l / k , directly irrespective ofnozzle orifice size. It might be noted here that this linearity of the recombinationplots for chlorine again indicates that the loss term p for H30+ is independent ofdistance along a flame. The following extrapolation procedure was used to obtainconditions for large [HCl].This predicts that a plot of 1/(1 -Sc,/So) against l/[HCl] should be linear with anintercept for 1 /[HC1] = 0 giving kl/k2. Fig. 4 shows such a plot for chlorine in flame2 for both chromium and nickel sampling nozzles of varying orifice diameters. Allthe observations are seen to fit well to a straight line. This confirms eqn (5) and alsothat Sc,/S, is independent of both nozzle diameter and sampling system.This is inspite of the loss factor P being rather different for these two types of orifice, becauseEqn (4) for X = C1 gives(1 - S’ci/So)-l = (I -kl/k2)-l( 1 + [H]/K,[HCI]). ( 5 252 ION-ION RECOMBINATIONof the much larger quantities of H,0+.H20 detected with nickel ones.2o The resultsof these extrapolations for flames 1-5 give identical k1/k2 to those obtained from thedifferentiation method described earlier (see table 3 for their values), but are achievedin a simpler manner and without the need for a knowledge of [HI as a function ofdistance down a flame.TABLE VALUES OF k l / k 2flame temp./K C1 Br I1 2570 0.10 0.0s 0.0202 2400 0.09 0.06 0.0303 2080 0.115 0.065 0.0254 1980 0.08 0.07 0.0355 1820 0.115 0.055 0.0356 1 s10 0.1 1 I -DI SCU SSIONThe tabulated kl //c2 do not appear to show any systematic temperature dependence,particularly when their associated errors are considered.For instance, each of themeasured kl/k2 for chlorine and bromine are correct to about 30 %, whereas thosefor iodine have errors of roughly 50 %. This means that any temperature variationof kl/k, over the range 1810-2570 K is masked by experimental errors. Since nosignificant change or trend is detected, we conclude that reactions (I) and (11) havevery similar dependences on temperature for the conditions employed here. Theslightly larger error with iodine arises from the measured rates of decay of H,O+being small and hence difficult to measure.Mean values of kl/k2 are given in table 4.Also quoted are kl for k2 constant and equal ion-' cm3 s-l,together with cross-sectional areas (no2) for kl = no2(8kT/np)+, an average T =2200 K and with ,u being the reduced mass of the reactants. Such an expression fork l assumes that for all three halogens, reaction (I) has zero activation energy. Theheats of reaction at absolute zero are also listed in table 4 as AEl ; these are based ona proton affinity for water l 3 of 699 kJ mol-I.to 4.1 1.0 xTABLE 4.-vALUES OF k 1 /k2, kl , CROSS SECTIONAL AREA AND HEATS OF REACTION AT ABSOLUTEZEROc1 Br Ikltk2 0.10L-0.03 0.07&0.02 0.03 rt0.02lo8 kl/ion-l cm3 s-' 4.1 1.6 2.7+ 1 .O 1.2+ 0.710" m2/m2 2.1 1.5 0.71-AEl /kJ mol-' 691 650 612-AE,/kJ 1110l-l 264 288 317For each halogen, recombination in (I) is quite strongly exothermic.Also, it isstriking that both k l and k2 appear to be independent of temperature, for over therange used here, it should be possible to detect, for example, the change by a factorof 2.4 predicted by the TS dependence of simple Thomson the0ry.l Also, the cross-sectional areas given in table 4 are all very large, being greater than that for electron-ion recombination in (11), which has no2 = 1.4 x Finally, it is seen fromtable 4 that nc2 decreases along the series C1 -+ Br -+ I. Such a trend also contrastswith simple Thomson theory,l which predicts a dependence of kl on CL), rather thanaroundm2.as exhibited in this workN. A . BURDETT A N D A . N. HAYHURST 253These results should be compared with those of Calcote and Kurzius,28 who foundthat kl for chlorine was 3 x ion-l cm3 s-l at flame temperature.Also, Morley l2using a very similar technique to ours, found that the ratio kl/k2 was 0.12f0.03 forchlorine in a flame of CH4, O2 and argon at 2570K. Both these independentmeasurements are in very satisfactory agreement with those of this work. The onlyother ion-ion recombination studied in flames l1 isK++X- -+ M+X. (V)This has cross-sections which are smaller than those of (I) by a factor of 200 forX = C1, 70 for Br and 3 for I.To comment on the above facts about reaction (I), it would be useful to knowwhether the process is one of electron or proton transfer. Here it should be notedthat Page 2 9 has correlated the rates of charge transfer for H30+ reacting with variousspecies A in : H30+ +A + H 2 0 + H +A+ with the ionization potential of A.Fromthis he concluded that the rate-determining step is the transfer of an electron from Ato H30+, irrespective of the nature of A. Thus the smaller the ionization potential(or electron affinity if A is a negative ion), the faster the reaction. This approachdoes not, however, fit the experimental results from this work, since kl is largest forC1 and smallest for I, whereas electron affinities indicate the opposite with Page'scorrelation. This is probably because the above charge transfer process with speciesA has a completely different mechanism from dissociative recombination in (I).Thus, it is likely that the important step in (I) is proton rather than electron transfer.In this case it is difficult to compare reaction (I) with (V), which clearly is an electrontransfer process.Another feature of table 4 is the large magnitude of A&.The process is suffi-ciently exothermic to remove an H atom from either of the assumed products H20or HX. Considering (I) as a proton transfer suggests that HX is initially formed carry-ing a substantial fraction of the large amount of energy released. Also, since dis-sociation of highly excited HX could be more likely than quenching, one possibilityis that the products of recombination are H20, H and X. The heats of this newreaction, i.e.,H30++X- 3 H20+H+X (VI)are listed in table 4 as A& for zero temperature.Product dissociation here is com-parable to that in reaction (11), where H20 is formed initially with a large amount ofenergy, so that it dissociates because of the relative inefficiency of quenching.13Some of the possibilities can be seen in very approximate form from fig. 5, whichis a plot of the potential energy of the H30+ . . . C1- system as a function of the separa-tion between the 0 and Cl nuclei. The curve for the two ions has been based on aminimum energy at a separation of 2 x 10-lo m. This value is a rough estimateusing an ionic radius 30 of 1.8 x 10-lo m for a Cl- ion and covalent radii 30 of 0.7and 1.0 x 10-lo m for 0 and C1 atoms, respectively. The conclusions we now arriveat are the same as if a minimum at 2.5 x 10-lo m is assumed or if bromine or iodineare considered.From fig. 5 the potential minimum for the two ions is seen to lieabove the energy of a molecule of H20 and one of HC1 (each in their ground elec-tronic states), whose interaction is expected to be largely that of two dipoles and accord-ingly fairly small. In this situation, where the two curves do not cross, the productsof reaction (I) could be ground state HC1 and H20 molecules, but only if a third bodyparticipates to lower the energy. The large cross-sections noted in table 4 wouldappear to rule out three-body processes, which are inherently slow, and thus also HC1and H,O as products in their ground states. The other possible products are first254 ION-ION RECOMBINATIONH20 and HC1 with the latter electronically excited and secondly, H20 together withatoms of H and C1, as noted above.In both cases the transition state is the same andarises from a pseudo-crossing of the ionic potential curve with that of H20 and HClin some electronically excited state, denoted as HCl*. No very strong attractiveforces are expected between H20 and HCl*, so that only a shallow minimum in theirenergy has been drawn in fig. 5. The recombination reaction (I) can now be envisagedwith a mass point moving in along the ionic curve and, as the 0 and C1 nuclei separateafter an encounter, the mass point may still move along the ionic curve (i.e., no reac-tion occurs) or initially along that for H,O and HC1*. In the latter case either theH and C1 atoms remain together or separate as depicted by the dotted line in fig.5.The probability of reaction could in principle be computed using the Landau-Zenerformula 31 or one of its modifications, but not enough information is available on theenergies of HX* for the halogens. This is unfortunate because such an approacheven in a qualitative manner ought at least to provide an explanation of why recom-bination in (I) is fastest for C1 and slowest for I.2 0 0 -&c1I0E3 ---38 400- - .& * (dE *0 aI6 0 0 -I I I I I 1 I I 10 2 4 6 ainternuclear separation x 10'o/mFIG. 5.-Approximate form of the potential energy curves for the H30+ . . . C1- system as a functionof distance between the 0 and Cl nuclei. The dotted line indicates an electronically excited HCImolecule undergoing dissociation.At these relatively high temperatures (1810-2570 K), where the number density ofmolecules is roughly 8 times smaller than at normal temperatures, no need has arisento invoke the participation of a third body in reaction (I).This contrasts with thework of Mahan et aZ.,32 who conclude that at room temperature and pressure a reac-tion such as NO++NO, + neutral products, has both bi- and ter-molecular contri-butions. The termolecular process was considered 32 to proceed by one of the ionN. A . BURDETT AND A . N. HAYHURST 255first attaching itself rapidly in equilibrium quantities to a chaperon molecule, followedby the resulting cluster reacting with the other ion. Such a scheme would be possiblehere, because of a hydrogen flame containing an appreciable amount of water,which could readily attach itself to an ion of either sign, but mostly likely to H,O+.We then might have a sequence, such asH30+ + H,O + H30+.H,0H30+*H,0 + C1- -+ neutral products.However, the high temperatures in flames do mean that an ion such as H,O+.H,O,although actually detected, is only present in a flame in minute concentrations.'*In addition, the rate of recombination by such a two-step process would be expectedto vary with temperature in a manner governed mainly by the large hydration energy 33(151 kJ mol-l) of H,O+, since the second reaction is likely to be weakly dependenton temperature.The observation made here that recombination is not very sensitiveto temperature for any of the halogens appears to rule out such a three-body scheme.This work was carried out with the support of the Procurement Executive, Ministryof Defence.J.B. Hasted, Physics of Atomic Collisions (Butterworth, London, 1964).Moscow, 1965.R. Kelly and P. J. Padley, Trans. Faraday SOC., 1969, 65, 355.D. E. Jensen and P. J. Padley, Ilth Int. Symp. Combustion (The Combustion Institute, Pitts-burgh, 1967), p. 351.A. F. Ashton and A. N. Hayhurst, Combustion and Flame, 1973, 21, 69.A. N. Hayhurst and D. B. Kittelson, Proc. Roy. SOC. A., 1974, 338, 175.R. Kelly and P. J. Padley, Trans. Faraday Soc., 1970, 66, 1127.J. A. Green and T. M. Sugden, 9th Int. Symp. Combustion (Academic Press, New York, 1963),p. 607.2A.N. Hayhurst and T. M. Sugden, 20th Z.U.P.A.C. Congress, Sy171p. Low Temp. Plasmas,' A. N. Hayhurst and N. R. Telford, J.C.S. Faraday I, 1974, 70, 1999.lo P. J. Padley, F. M. Page and T. M. Sugden, Trans. Faraday Soc., 1961, 57, 1522.l1 A. N. Hayhurst and T. M. Sugden, Trans. Faraday SOC., 1967, 63, 1375.l2 N. A. Burdett, A. N. Hayhurst and C. Morley, Chem. Phys. Letters, 1974, 25, 596.l 3 A. N. Hayhurst and N. R. Telford, J.C.S. Faraday Z, 1975, 71, 1352.l4 H. F. Calcote, S. C . Kurzius and W. J. Miller, 10th Int. Symp. Cornbustion (The Combustionl5 D. B. Kittelson, Ph.D. Thesis (Cambridge University, 1971).l6 L. F. Phillips, Ph. D. Thesis (Cambridge University, 1960).l7 A. N. Hayhurst, F. R. G. Mitchell and N. R. Telford, Znt. J. Mass Spectrom. Ion Phys., 1971, 7,l8 A. N. Hayhurst and N. R. Telford, Proc. Roy. SOC. A., 1971,322,483.l9 N. R. Telford, Ph.D. Thesis (Cambridge University, 1969).2o N. A. Burdett, Ph.D. Thesis (Cambridge University, 1974).21 N. A. Burdett and A. N. Hayhurst, Nature (Phys. Sci.), 1973, 245, 77.22 N. A. Burdett and A. N. Hayhurst, 15th Znt. Symp. Combustion (The Combustion Institute,23 L. F. Phillips and T. M. Sugden, Canad. J. Chem., 1960,38, 1804.24 G. Herzberg, Spectra of Diatomic Molecules (Van Nostrand, Princeton, 1960).25 A. G. Gaydon, Dissociation Energies and Spectra of Diatomic Molecules (Chapman and Hall,26 R. S . Berry and C. W. Riemann, J. Chem. Phys., 1963,38,1540.27 H. C. Hershey, J. L. Zakin and R. Simha, Znd. Eng. Chem. (Fundamentals), 1967, 6, 413.z* H. F. Calcote and S . C. Kurzius, Aerochem. Rep., TP 92 (Aerochem., Princeton, 1962).29 F. M. Page, Physical Chemistry of Fast Reactions, ed. B. P. Levitt (Plenum, New York, 1973),30 F. A. Cotton and G. Wilkinson, Adzmnced Inorganic Chemistry (Interscience, New York,Institute, Pittsburgh, 1965), p. 605.177.Pittsburgh, 1975), p. 979.London, 1968).p. 161.1962)256 ION-ION RECOMBINATION31 K. J. Laidler, The Chemical Kinetics of Excited States (Clarendon, Oxford, 1955), p. 31.32 B. H. Mahan and J. C. Person, J. Chem. Phys., 1964, 40, 392, 2851 ; T. S. Carlton and B. H.Mahan, J. Chem. Phys., 1964, 40,3683 ; G. A. Fisk, B. H. Mahan and E. K. Parks, J. Chem.Phys., 1967, 47, 2649.33 P. Kebarle, S . K. Searles, A. Zolla, J. Scarborough and M. Arshadi, J. Amer. Chem. SOC., 1967,89, 6393.(PAPER S/1074

ISSN:0300-9599    

DOI:10.1039/F19767200245

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

Reactions of Hydrogen Atoms in 6 mol dm-3 Sulphuric AcidPart 2.-The Transition from Activation to Diffusion ControlFREDERICK S . DAINTON, B. J. HOLT, NIGEL A. PHILIPSON AND M. J. PILLING *Physical Chemistry Laboratory, South Parks Road, OxfordReceived 13th February, 1975The relative rates of abstraction by hydrogen atoms of hydrogen and deuterium atoms frompropan-2-01 and [2H7]propan-2-ol have been studied, as a function of temperature, in 6 mol dm-3H2S04, using both y-radiation and photolysis of Fez+ as the source of H. As the temperature isdecreased the expected activation control, reflected in an Arrhenius temperature dependence, givesway to diffusion control. Similar behaviour is shown for the same reactions of deuterium atoms in6 mol dm-3 D2S04, and for the competition between propan-2-01 and Fe2+ for hydrogen atoms.Inall cases, the low temperature behaviour is inadequately described by the diffusional parametersderived in the preceding paper, and a low temperature diffusion process, with an Arrhenius tempera-ture dependence, is proposed to explain the discrepancies. From the competition studies, absoluterate parameters are obtained for the following reactions : (i) H + [2H7]propan-2-ol (abstraction ofa-D) A = (6.3 k 0.5) x 10" dm3 mo1-1 s-I, E = 20+ 2.6 kJ mol-I, (ii) H+ [2H7] propan-2-01,(abstraction of hydroxylic H) A = (2.5 & 0.6) x 10'O dm3 mol-' s-I, E = 23 +_ 3 kJ mol-I,(iii) H+Fe2+, A = (1.4k0.6)~ 10" dm3 mol-I set, E = 14+3 kJ mol-l.Reactions in solution involve the diffusive approach of the reactant molecules(A, B) to form an encounter pair (A B), followed by separation or reaction:kd kr A + B + A s B - products.The relative rates of the first order reactions of the encounter pair, diffusional separa-tion (k-J or reaction (k,) determine whether the overall process shows activation-controlled (k-d $- k,) or diffusion-controlled (k-d < k,) kinetics.l In the precedingpaper we recorded rate parameters for the two extreme types of reaction in 6 moldm-3 sulphuric acid.When k-d * k,, the reaction shows intermediate behaviour, which has beenstudied comparatively little.It has been suggested that, in low viscosity media,exothermic triplet energy transfer falls below the diffusion-controlled limit becausethe rate of back diffusion becomes comparable with the rate of energy transferbetween the encounter pair. Warrick et aL4 measured the acid-base recombinationrate constant for Bromocresol Green in water +glycerol mixtures.As the glycerolcontent increased, the reaction mechanism changed to one of diffusion control.described novel experiments which conclusively demonstrate a changeover from activation to diffusion control. He studied the competition betweenreactions (1) and (2) in y-radiolysed 6 mol dm-3 H2S04.k-dVacekH + (CH,),CHOH + H2 + (CH3)ZCOHH + (CD3)2CDOH --+ HD + (CD&COH.(1)(2)As the temperature was lowered, he found that the product ratio, [H,]/[HD], at firstincreased but then reached a maximum and decreased sharply to a value of -2 at1-9 25258 REACTIONS OF €I ATOMS IN SOLUTION77 K.The activation energy for reaction (l), El, is lower than that for reaction (2),E,, because of zero point energy differences, and the increase in [H,]/[HD] arisesfrom the increase in exp((E2 - E,)/RT} with decreasing temperature. Vacek attributedthe decrease in [H,]/[HD], found at still lower temperatures, to a change in mechanismfrom one of activation- to one of diffusion-control. Under diffusion-control therates of the two reactions should be equal since they are both governed primarily bythe diffusion of hydrogen atoms (the more mobile reactant) through the solvent.Vacek's data were limited, and precluded a full analysis, and he did not discuss theorigin of the change in mechanism. In this paper we report a more detailed investiga-tion of this competition and also of that between Fe2+ ions and propan-2-01, forhydrogen atoms, which similarly demonstrates a change over from activation- todiffusion-control.EXPERIMENTALThe dose-rate inwater at room temperature, as measured by Fricke dosimetry, was 2.7 x 10'' eV ~ m - ~ min-l,taking G(FelI1) as 15.5.Samples of 6 mol dm3 H2S04 will experience a somewhat higherdose rate.' The samples were contained in Pyrex tubes, 12 cm long, 2 em diameter, placedin a Pyrex Dewar vessel. They were degassed by the freeze-pump-thaw technique, andirradiated for 30 min.Samples were irradiated with y-rays from a 2OOO Ci cobalt-60 source.TABLE l.-Summy OF REACTIONS INVESTIGATEDkzk3H+ (CD3)2CDOH -+ HD+(CD3)2COHH+ (CD3)ZCDOH -+ Ha+ (CD3)2CDO*D+(CH3)2CHOD 2 HD+(CH,),CODk6D+ (CD3)ZCDOD 4 D2+ (CD3)2CDO*2k7H+ CH2DOH 3 H2+ CHDOHH+ CHZDOH 2 HD+ (2H20HD+CH2DOD f HD+CHDOD (9)kr iH+ Fe2++ H+ -+ H2 + Fe3+D + Fe2++ D+ -+ D2 + Fe3+k12254 nm light from a flat, spiral, low-pressure mercury lamp was used in the steady-statephotolysis experiments.The samples were contained in quartz tubes, 6 cm long, 2.5 cmdiameter, placed in a quartz Dewar vessel; they were degassed by the freeze-pump-thawtechnique, and illuminated for 30 min.In both sets of experiments, the Dewar vessels were cooled by the passage of cold, drynitrogen gas, obtained by evaporating liquid nitrogen. Temperatures in the range 77-273 Kwere used, and maintained within 4 1 K ; they were measured by means of a calibrateF. s.DAINTON, B. J . HOLT, N . A . PHILIPSON AND M. J. PILLING 259chromel/alumel thermocouple. No crystallization problems were experienced with thelarge bore sample cells.The gas produced on irradiation was collected in a small cell, and the relative amounts ofH P , HD and D2 measured using an A.E.I. MSlO mass spectrometer. The relative sensitivityof the spectrometer to masses 2,3 and 4 was found to vary and the instrument was recalibratedeach day. Initially this was effected with an equilibrium mixture of H2, HD and D2.8 Thiscalibration was then used to measure the relative yields of H2 and HD from irradiated6 rnol dm--3 H2S04/H20+ 0.1 rnol dm3 (CD3)2CDOH at room temperature. The ir-radiated samples were subsequently used as secondary calibrants.The following chemicals were used as supplied: H,SO, (B.D.H., AnalaR), D2S04(Ryan Ltd., 99.5 % D), (CH&CDOD (Merck, 99 % D), CH2DOH (B.O.C.Ltd.,),D20 (B.O.C. Ltd. 99.8 %), FeS04 (Fisons Ltd., analytical reagent grade). Solutions weremade up in triply distilled water.RESULTSy-RADIOLYSIS OF 6 mol dm-3 H2SO4The relative rates of formation of H2 and HD in y-radiolysed 6 mol dm-3 H2S04containing propan-2-01 and [2H,]propan-2-ol were measured mass-spectrometrically.Before the data could be converted into relative rate constants for abstraction fromthe secondary carbon atom, certain ancillary data were required.(i) RELATIVE G VALUES FOR ATOMIC AND MOLECULAR HYDROGENIn the y-radiolysis of 6 mol dm-3 H2S04, molecular hydrogen is formed by intra-spur reactions, and is unaffected by scavengers unless they are present in very highconcentrations.This intraspur yield of molecular hydrogen must be subtractedfrom that formed by reaction of atomic hydrogen with propan-2-01, and GH2/GH isnN -1.2 s3 - 1.4 -I i- 1.61 I- 1 . 8 1 I I I , , I +,3 4 5 6 7 8 91 0 3 ~ 1 ~FIG. 1.-Plot of Ig(k,/kz) against:l /T. The straight line is a least squares fit to the data above 167 K.required. The isotopic equivalent, GD,/GD, was measured by adding (CH3)2CHODto 6 mol dm-3 D2S04 in D20. The OD bond is sufficiently strong that no significantabstraction takes place from the oxygen atom. The alcohol concentration wasincreased until a constant ratio of G(D,)/G(HD) was obtained, indicating completescavenging of the isotropically distributed deuterium atoms, without interference ofthe spur reactions.G(D,)/G(HD) was equated to GD,/GD, giving a value of0.12+0.01 at 293 and 77 K.which is 0.15.1°GD,/GD is expected to be slightly smaller than GH2/GH260 REACTIONS OF H ATOMS I N SOLUTION(ii) RATE OF ABSTRACTION OF HYDROXY HYDROGEN ATOMSBecause of the primary isotope effect, abstraction from the alcohol oxygen atomis more likely in H2S0, than in D2S04, i.e. (k3/k2) > (k6/k5). Assuming thatGH2/GH is independent of temperature, as is the case for GD2/GD, then k3/k2 is deter-mined by measuring the relative yields of H2 and HD [G(H,)/G(HD)] formed fromy-radiolysed 6 mol dm-3 H2S04 in H20 containing 0.1 mol dm-3 (CD3)2CDOHafter correcting for the spur yield of H2 :Fig.1 shows a plot of lg(k3/k2) against 1/T. At low temperatures, the yield of H2from reaction (3) is very small, and the error in the ratio is large.k3/k2 = (G(H2)/G(HD)-G,,/GH)/{ +GH2/GH)*(iii) RELATIVE RATES OF REACTION OF HYDROGEN ATOMS WITH PROPAN-2-OLAND [ 2H7]PROPAN-2-OLThe competition between reactions (1) and (2) was studied by measuring therelative yields of H2 and HD following y-irradiation of 6 mol dm-3 HzSO4 in H20,containing propan-2-01 and [2H,]propan-2-ol at a total concentration of 0.1 mol dm-?k,/k2 was calculated from:Fig. 2 shows a plot of 1g(k,/k2) against 1/T. At selected temperatures, the relativeconcentrations of the alcohols were varied. In each case kl/k2 was independent ofkl/k2 = ([G(H2)/G(HD)-GH2/GHI/(1 + GH2/GH))([RDI/[Rw)*I(CH3)2CHoHI/[(CD,),cDOHI.1.2 r-0g21Lu22d 0.0 3 5 7 9 1 1 13 15103 KITFIG.2.-Plot of Ig(kl/k2) against 1/T, showing the change over from Arrhenius behaviour. (@>yradiolysis, (0) photolysis of Fe2+. - - - - - VTF fit for rate of diffusion, Aa = 4 x lox2 dm3 mol-'s-l, B = 667 K, To = 139 K ; - fit including an Arrhenius term in the diffusion rater Ap = 2.3 x 10' 'dm3 mol-' s-l, Ep = 20 kJ mol-'.THE RELATIVE RATES OF REACTION OF DEUTERIUM ATOMS WITHThe experiments in (iii) were repeated in 6 mol dm-3 D2S04 in D20, and k4/k5(CH3)ZCHOD AND (CD3)ZCDODdetermined from the relative yields of HD and D2 :Fig. 3 shows a plot of lg(k4/k5) against 1/T. For those temperatures at which therelative concentrations of the alcohols were varied, k4/k5 was independent ofk4/k5 = + GD2/GD) {G(D2)/G(HD)- GD,/GD)[RDl/[RHl.[(CH,),CHoDl/[(CD,)2cDODlF. S .DAINTON, B . J . HOLT, N. A. PHILIPSON AND M. J . PILLING 261(v) THE REACTIONS BETWEEN HYDROGEN ATOMS AND CH2DOH ANDDEUTERIUM ATOMS AND CH2DOD AT 77KThe rate constant ratios k,/k8 and kg/klo were determined by irradiating 6 moldm-3 H2S04 in H20 and 6 mol dm-3 D2S04 in D20 containing 0.1 mol dm-3CH2DOH (D), at 77 K. Abstraction of H or D from 0 was assumed to be un-important at these temperatures (cf. fig. 1). A value for k7/k8 of 11.1 f 1 .O wascalculated fromwhilst kg/klo = 16.4+ 1.1 was calculated from a similar equation.2Wks = W(H2)/G(HD) - G H 2 / G H W H J G H + 1)0e0.8n 25.57 0 .6M -0 -0 ee -O S 4 l 0 . 20.0 12 4 6 8 1 0 1 2103 KITFIG. 3.-Plot of lg(k4/k,) against 1/T, showing the change over from Arrhenius behaviour.PHOTOLY SISHydrogen atoms are generated on exposing iron(@ ions in acid solution to254 nm radiation: l1Fe2+ + hv + Fe3+ -k e-ea-q + H+ + H.(i) THE RELATIVE RATES OF REACTION OF HYDROGEN ATOMS WITH Fe2+AND (CD3)ZCDOHkI1/k2 was determined, as a function of temperature, by exposing 6 mol dm-3mol dm-3 FeSO, and 0.1 mol dm-3 (CD3)2CDOH, H2S04 in H20 containingto 254 nm light :where [H,] and [HD] are the yields of H2 and HD.Fig. 4 shows a plot of 1g(kl1/k2) against 1/T. Although the temperature de-pendence of kl 2/k4 was not investigated, its dependence on [Fe2+]/[(CH3)2CHOD] wasexamined.kl l/k2 = “H,I/[HDI - k3/~2)[(CD,>2CDoHI/Fe2+lFig. 5 shows the expected linear plot, at 298 K.(ii) THE TEMPERATURE DEPENDENCE OF kJk,ofFig.2 includes data for kl/k2 obtained from [H,]/[HD] ratios following photolysismol dm-3 FeS04 in 6 mol dm-3 H2S04/H20 containing (CH&CHOH an262 REACTIONS OF H ATOMS I N SOLUTION(CD,),CDOH at a total concentration of 0.1 mol dme3. The ratio was calculatedfromk l h = ([H,I/[HDI -k1 1[Fe2+l/k2[(CD,),CDOHl)x [(CD3)2CDoHl/[(CH,)2cHoHl*The correction term for H abstraction from 0 was neglected, as in this case k3/k2(-0.15) introduces a systematic error of only 2 %.0.7 r T0 . 0 13 5 7 9 I 1 13103 KITFIG. 4 . P I o t of lg(kll/kla) against 1/T, showing the change over from Arrhenius behaviour.- fit including both VTF and Arrhenius terms in the diffusion rate, and using the datafgiven in fig.2.2 A r2.cKEe 2 0.8;= 1.2’N0.4i0.0 I I l 1 I I I0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.01 0[Fe2+]/[(CH&CHOD]FIG. 5 . P l o t of [D,]/[HD] as a function of [Fe”+]/[(CH,),CHOD], from the photolysis oflo-, mol dm-3 FeS04 in 6 mol dm-3 D2S04 in DzO, at 298 K.DISCUSSIONRATE PARAMETERS I N THE ACTIVATION-CONTROLLED REGIONAt the higher temperatures (T > 200 IS) fig. 1-4 show the expected linear Arrhe-nius plots for competition between two activation controlled reactions. In the pre-ceding paper we determined the rate parameters for reaction (1) over the temperaturerange 190-280 K. These data have been used to convert the relative rate constantF .s. DAINTON, B . J . HOLT, N . A . PHILIPSON AND M . J . PILLING 263for H atom reactions, determined in the present work, into absolute values, and theseare shown in table 2. The difference in activation energies for reactions (1) and (2) is3.7k0.6 kJ mol-'. When compared with the difference in zero point energies for thesecondary C--M (C-D) stretching vibration of 4.8 kJ mol-l, this value suggests thatthe C-H (C-D) bond has been substantially broken in the transition state. The Afactor ratio (1.6kO.2) is a little higher than might be expected from Transition StateTheory?TABLE 2.-RATE PARAMETERS FOR H ATOM REACTIONSreaction A/dm3 mol-1 s-1 E/kJ mol-1H+(CD,)zCDOH -+ HD+(CD3)2CQH (6.3f0.5)~ 10" 20k2.6 (2)(3) H+(CD,),CDOH 4 Hz+(CD,)CDO (2.5k0.6)~ lolo 22&3(11) H+Fe2++Hf --+ H1+Fe3+ (1.4k0.6)~ 1O1O 14+3Since the rate constant of reaction (4) has not been determined absolutely, the rateparameters for the deuterium atom reactions cannot be evaluated. From the hightemperature section of fig.3, the rate constant ratio k4/k5 agrees, within the limits ofexperimental error, with kl/k, (fig. 2), and thus (E2 -El) = (Es -E4), and AJA2 =A4/A5, within these limits.4 6 8 10 12 14lo3 K/TFIG. 6.-Schematic plot of the temperature dependence of the component reactions in the competitionbetween reactions (1) and (2). -, kgp; -.- kFXp, . . . . . kr (o( diffusion, VTF dependence);- - - kr (p diffusion, Arrhenius dependence).The ratio of the rate constants of reactions (1) and (2) at 298 K is 6.8 +0.4, whichmay be compared with the value of 7.53-1 reported by Anbar and Meyerstein.12They also measured the ratio of abstraction of a versus p hydrogen atoms in propan-2-01, and obtained a value of 110, which justifies our limitation of the discussion toabstraction of a or hydroxylic hydrogen atoms.The rate constant for reaction (1 1) at 298 K is - 5 x lo7 dm3 mol-1 s-l, whichmay be compared with previous values in the range 1.3-2 x lo7 dm3 mol-l s-l.l3-lSA and El are both smaller than would be expected for simple H atom metathesis,involving only bond breaking and formation.Mechanisms involving an element ofelectron transfer from Fe2+ are easily formulated, and if this transfer markedlyregulates the rate, the low A and E values can be accommodated264 REACTIONS OF H ATOMS I N SOLUTIONTRANSITION FROM ACTIVATION- TO DIFFUSION-CONTROLIn the preceding paper we recorded rate parameters for both activation- anddiffusion-controlled reactions of hydrogen atoms.The data for the diffusion-controlled reactions responded most satisfactorily to a non-Arrhenius treatmentbased on the empirical VTF equation. If we presume that the hydrogen atom issignificantly more mobile than any of the reaction partners studied in this and thepreceding paper, then the rate parameters derived from the reaction between H andAg+ should adequately represent the rate constant, kd, for the diffusive approach ofH and a reactant molecule. Fig. 6 shows Arrhenius plots for reactions (1) and (2)which are linear, and also for k2, which shows the expected curvature.At hightemperatures kd is greater than the measured rate constants k, and k2, and the ratedetermining step is therefore the reaction of the encounter pair. At lower tempera-tures, kd falls below first kl and then k2, and both reactions might be expected to showdiffusion-control. In the notation of the introduction, kl is given by:The rate constant ratio iskl kFKH (k:/kvd + 1)k2 kyKD (kY/kEd+ 1)- =where KH = k?/kZd, and the superscripts H and D label the component steps in theabstraction of H and D, respectively.At high temperatures, when the reactions are activation controlled, kl = kyKH( = k&J, and k, = k!?KD( = kFxp). Thus, over the whole temperature range assumingkf = k: = kd,kl/k2 = (l / k k p + /kd)/(l / k ? ~ p + lkd), (1)where kFxp and k:xp are determined from the high temperature (Arrhenius) region offig.2. Fig. 2 also shows a plot of 1g(k1/k2), calculated from eqn (l), against 1/T.The rate parameters shown in table 2 were used for kEp and kFxp, and the VTFparameters, A = 4 x lo1' dm3 mol-l s-l, B = 667 K, To = 139 K, for kd. Thesedata accurately predict the maximum in the plot of lg(kl/k2) against 1/T, but thecalculated ratio falls to unity much more rapidly than that found experimentally.Indeed the experimental data never reach the limiting ratio of unity predicted byeqn (1). At 77 K, k1/k2 is 2.1 k 0.2, in good agreement with that previously reportedby Vacek and von Sonntag." This value is the mean of the values obtained fromy-radiolysis and photolysis and any abnormalities cannot be ascribed to radiationchemical effects.The same value for kH/k, was obtained on leaving the photolysedsolution for four days at 77 K before analysis, showing that the anomalous value doesnot result from reaction during the warm up period before removal of the gas mixture.Clearly, at low temperatures the competition is not dominated by diffusion-controlled reactions with the rate parameters determined in the previous paper.Either the rate of diffusion does not fall off as rapidly, at temperatures below 190 K,as the VTF equation predicts, or diffusion to (CH3)2CHOH is favoured over diffusionto (CD,),CDOH. In addition, reaction persists at temperatures below To ; transportof hydrogen atoms is possible at temperatures below that of zero mobility for normal,co-operative diffusion. This non-co-operative, low temperature transport mechanismcould be similar to the Grotthus mechanism for H+ and OH- diffusion in aqueousmedia. This would involve the making and breaking of covalent and hydrogenF .s. DAINTON, B . J . HOLT, N. A . PHILIPSON AND M. J . PILLING 265bonds, and effective transport of H without mass transport. The hydrogen atomsare thus carried along chains until terminated by reaction with an alcohol.Reaction at the hydroxy group would lead to a high apparent value for k1/k2:both the hydro- and deutero-compounds have OH groups, because of exchange withthe solvent. This possibility is ruled out by fig.1, which shows that reaction (3) isunimportant at 77 K. Furthermore, this mechanism would require that the apparentvalue of k4/k5 at 77 K was less than unity, since solvent exchange now substitutes Dfor H; the observed value is 3.3 +0.3. Presumably the hydrogen atom of the hydroxygroup is so strongly bound by hydrogen-bonding that it is effectively unavailable forreaction.The detailed mechanism of termination of the hydrogen atom transport chain atthe alcohol may account for the high value of k l / k z . If the final movement of thealcohol molecule into a position to react with the mobile hydrogen atom were slowerthan the movement of molecules in the chain, then the hydrogen atom could move on,and every encounter would not be reactive.Furthermore, if the adjustment wereslower still for the deutero species, because of its greater reduced mass, then (CH,),CHOH would be preferred over (CD3)2CDOH as the final reaction partner. Theinvestigation of CHzDOH at 77 K is of interest in this context. In this system,G(H,)/G(HD) is determined by the relative rates of H and D abstraction on encounter.If the alcohol could rotate freely, then H abstraction would be favoured, since thedifference in activation energies would lead to a rate constant ratio, k7/ks, of -400,and this could be further enhanced by quantum mechanical tunnelling. If themolecule were held rigidly, then k7/k8 would be unity, although the ratio might beslightly enhanced by H-atom tunnelling.The observed ratio of 1 1.1 f 1 .O arguesagainst free rotation, and suggests that at least one of the following operates: (i) ahighly hindered rotation, (ii) a preferential termination of the transport chain at H,(iii) quantum mechanical tunnelling.Quantum mechanical tunnelling has frequently been invoked to explain largeratios for H versus D abstraction at low temperatures.6*18-21 Most of these investi-gations were of radical reactions with solvent molecules, and diffusion of the reactantswas unnecessary. Quantum mechanical tunnelling could at least partly account forpreferential termination at (CH3)2CHOH and the ratio for kl/k2 of 2.1 at 77 K. Itis, however, unable to explain the deviations from the VTF plot which occur at - 190 K, where the solvent is more fluid, and where molecular motions are likely toswamp the short range movement of H atoms by tunnelling.These deviations aremost adequately explained by a breakdown of the VTF equation at lower tempera-tures, which has been reported in other systems. Ambrus et al. 22 note that, inaqueous calcium nitrate solutions, To is temperature dependent and falls as the visco-sity increases. They report that the VTF equation is only applicable, with a constantTo, over a three decade change in conductance. Bose et al. 23 have shown that, inKN03 + Ca(NO,), , the temperature dependence of the conductance changes fromVTF to Arrhenius behaviour at a temperature -30 K above the glass transitiontemperature, Tg. Tg is greater than To, and a value of 158 K has been reported forH2S04 3H20.24 It is, perhaps, significant that the experimental and calculatedrate constant ratios begin to diverge at - 180-190 K.*26 have shown thepresence of two relaxation processes in molecular glasses.The a relaxation showsnon-Arrhenius behaviour, is co-operative in nature, and is related to the highertemperature diffusional behaviour shown by hydrogen atoms and described by theVTF equation. The p relaxation shows Arrhenius behaviour, with an activationenergy of -20-50 kJ mol-I. It arises from non-co-operative rearrangements, andBy dielectric relaxation measurements, Johari and Goldstei266 REACTIONS OF H ATOMS IN SOLUTIONpersists below Tg. Such a process could, conceivably, be important in the transportof H atoms at low temperatures.As the co-operative (VTF) mass transport processslows down with increasing viscosity, the Grotthus type of mechanism discussed abovemay become important. In a non-crystalline medium, the molecular arrangement isnot optimized for the making and breaking of hydrogen and covalent bonds, andindividual molecules must rotate into position before the mechanism can operate.Although the viscosity is so high that co-operative motion is unlikely, Johari’s 25*26work suggests that a hindered rotation of individual molecules could occur with Ar-rhenius characteristics. The overall diffusional rate constant would then be of theform :Fig. 2 shows a plot of 1g(k1/k2), calculated using AB = 2.3 x lof1 dm3 mol-1 s-l andEs = 20 kJ mol-1 and the VTF parameters used above.2 With the inclusion of anArrhenius diffusion term, kl/k2 does not reach a limiting value of unity at 77 K.Fig.6 illustrates schematically why this is so. The diffusion rate falls below the activationrate for H abstraction, but remains above that for D abstraction. The latter processdoes not become diffusion-controlled, and proceeds at a slower rate than H abstrac-tion. The fit at intermediate temperatures is poor, and this may arise from a decreas-ing value for To such as that found by Ambrus et al. No attempt was made tooptimize the fit: the indirect nature of the experimental data, and the large numberof adjustable parameters would make such a fit meaningless.Fig. 3 and 5 show that the same type of behaviour is found for the competitionbetween reactions (4) and ( 5 ) and reactions (1) and (1 1) respectively.The rate para-meters are known for reactions (1) and (1 l), and fig. 5 includes the calculated tempera-ture dependence of lg(kl /kl) using eqn (2) and the diffusion parameters used in fig. 2.It was not possible to calculate lg(k,/k,), since no absolute rate data are available forD atom reactions. The form of the experimental plot in fig. 3 is similar to those infig. 2 and 5, and suggests that a similar mechanism is operative.The suggestion of the onset of an Arrhenius component in the diffusion rate istentative. The experimental evidence, derived from competitive studies in a complexsystem, is circumstantial. It is, however, sufficiently compelling to encourage directrate measurements in this low temperature region.k, = A, exp( - B(T- To)) +A, exp( - Es/RT).(2)We thank the S.R.C. for a Research Studentship to N. A. P.A. M. North, The Collision Theory of Chemical Reactions in Liquids (Methuen, London, 1964).F. S. Dainton, N. A. Philipson and M. J. Pilling, J.C.S. Faraday I, 1975, 71,2377.N. J. Turro, N. E. Schore, H-C. Steinmetzer and A. Yekta, J. Amer. Chem. Soc., 1974,96,1936.P. Warrick, J. J. Auborn and E. M. Eyring, J. Phys. Chem., 1972, 76, 1184.K. Vacek, Proc. X Czech. Annual Meeting in Radiation Chem., 1970, 2, 367.R. P. Bell, The Proton in Chemistry (Chapman and Hall, London, 1973). ’ F. S. Dainton, A. R. Gibbs and D. Smithies, J. Chem. SOC. A, 1967, 33.R. H. Fowler and E. A. Guggenheim, Statistical Zhermoydnamics (Cambridge, 1939).K. Coatsworth, E. Collinson and F. S. Dainton, Trans. Faraduy Soc., 1960, 56, 1008.lo F. S. Dainton and F. T. Jones, Radiation Res., 1962, 17, 388.l 1 P. N. Moorthy and J. J. Weiss, J. Chem. Phys., 1965, 42,3121.M. Anbar and D. Meyerstein, J. Phys. Chem., 1964,68, 3184.l3 W. G. Rothschild and A. 0. Allen, Radiation Res., 1958, 8, 101.l4 P. Riesz and E. J. Hart, J. Phys. Chem., 1959,63,858.lS H. A. Schwarz, J. Phys. Chem., 1963, 67,2827.l6 G. Czapski, J. Jortner and G. Stein, J. Phys. Chem., 1961, 65, 964.l7 K. Vacek and C. von Sonntag, Chem. Comm., 1969, 1256.l 8 A. Canapion and F. Williams, J. Amer. Chem. Soc., 1972, 94, 7633F . s. DAINTON, B . J . HOLT, N. A . PHILIPSON AND M. J . PILLING 267l9 E. D. Sprague and F. Williams, J. Amer. Chem. SOC., 1971, 93,787.2o J. T. Wang and F. Williams, J. Amer. Chem. Soc., 1972, 94, 2930.'l R. J. LeRoy, E. D. Sprague and F. Williams, J. Phys. Chem., 1972, 76, 546.22 J. H. Ambrus, C. T. Moynihan and P. B. Macedo, J. Electrochem. Soc., 1972, 119,192.23 R. Bose, R. Weiler and P. B. Macedo, Phys. Chem. Glasses, 1970, 11, 117.24 C. A. Angel1 and K. J. Rao, J. Chem. Phys., 1972,57,470.25 G. P. Johari and M. Goldstein, J. Chem. Phys., 1971, 55,4245.26 G. P. Johari, J. Chem. Phys., 1973,58, 1766.(PAPER 51302

ISSN:0300-9599    

DOI:10.1039/F19767200257

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

Atomization Energies of Gaseous AlPd and A1,PdBY DAVID L. COCKE, KARL A. GINGERICH" AND CHIN-AN CHANGDepartment of Chemistry, Texas A & M University,College Station, Texas 77843, U.S.A.Received 24th February, 1975Knudsen cell mass spectrometry has been used to investigate the gaseous equilibrium reactions(1) AlPd(g) + Al(g)+ Pd(g) and (2) AlzPd(g) + Pd(g) + 2AlPd(g). The reaction enthalpies AH:are (1) 250.6 k 12.0 kJ mol-' and (2) - 8.8 k 3.0 kJ mol-' where the second and third law procedureswere used to obtain the value for reaction (1) and the third law procedure for reaction (2). Theatomization energies derived from these reaction enthalpies are : Dz(A1Pd) = 250.6_+ 12.0 kJ mol-land DX(A1,Pd) = 492.4f 24 kJ mol-'. The corresponding standard heats of formation, AH fo,298are AlPd : 451.8 k 12.5 kJ mol-' and A12Pd : 536.45 24.3 kJ mo1-l.The bonding in these moleculesis discussed in terms of empirical models.The dissociation energies of only a few gaseous diatomic intermetallic molecules(AIM) containing aluminium are known and these are confined to compounds of theGroup IB metals. 1-4 Triatomic intermetallic molecules (A& M and AlMJ containingaluminium have only been reported with gold. In the present study, the atomizationenergies of the first diatomic and triatomic aluminium intermetallic molecules with aplatinum group metal are reported.The bond energies of these molecules are discussed in terms of the Paulingmodel of a polar bond.6EXPERIMENTALThe high temperature Knudsen cell mass spectrometer used, as well as the experimentaltechniques, have been described previ~usly.~~ Specific instrument operating conditionswere 18 eV electron energy, 1 mA emission current, 4.5 kV ion acceleration voltage and 1.9 kVat the entrance shield of the electron multiplier.A tungsten Knudsen cell with a knife edgeorifice of 0.60mm diameter was used in this vaporization study and was initially chargedwith a sample of powdered AlN and Pd and Au metals.The pertinent ions were identified by their shutterability, mle ratio, isotopic distributionand ionization efficiency curves. The appearance potentials for AIPd+ and AI2Pd+ are givenin table 1 and their low values indicate that these are parent ions.In addition the ion All was observed. The ionization efficiency curve for Al; indicateda sizable contribution from fragmentation of gaseous AI20 to the Al,+ ion intensity.Thepresence of A120(g) was due to an oxygen impurity in the commercial AlN(s) sample.Thermodynamic evaluation of the data taken on Al, supports the lower dissociationenergy 9-11 reported recently by Stearns and Kohl."The instrument was pressure calibrated by the monomer-dimer technique 8* l2 by thegaseous Au2(g) + 2Au(g) reaction which was monitored during a large part of the experi-mental investigation. The resulting calibration constants for the pertinent species are givenin table 1 along with the necessary experimental and estimated parameters.Ion intensities observed for the pertinent species are given in table 2.The experimentalion intensities at 1923 and 1961 K for AlzPd+ were measured near the limits of detection.This explains the similarity in value of the two ion intensities even though tfieoretically theyshould differ by a factor of five.26D. L. COCKE, K . A. GINGERICH AND C.-A. CHANG 269Partial pressures were obtained from the observed ion intensities given in table 2, by therelation Pi = kiliT.TABLE 1 .-SUMMARY OF EXPERIMENTAL AND ESTIMATED PARAMETERSrelative correctionappearance ionization * multiplier to maximum calibrationpotential/ cross section gains ionization constant fion eV ui Yi/YAu efficiency EI ki/atm A-1 K-1Au+ 9.22 a 5.85 1 .oo 1.32 0.750Alf 6.0k0.4 6.18 1.92 1.01 0.373Pd+ 8.2k0.4 6.07 1.05 1 .oo 2.52AlPd+ 6.2+ 0.4 9.19 1.05 1.23 2.05AI2Pd+ <9.0+ 1.0 13.82 1.05 1.23 1.36AlZ - 9.27 2.11 1.02 0.22911 Standard, ref. (13) ; b taken from ref.(14) for atomic ; molecular calculated as 0.75 times thesum of the atomic cross sections ; c taken from ref. (15) ; destimated as yA1pd = 'YAlzPd = m d ;estimated as y~~ = 1 . 1 ~ ~ 1 ; f ki = kAuuAuYAuEi/UiYlni where ni = fractional isotopic distribution.TABLE 2.-10N INTENSITIES a IN AMPERES OBSERVED FOR PERTINENT SPECIESdatasetno.12345678910111213141516171819TIK17391785182217291768183618601895189518881888188818881923192318861961197420102 7 ~ 1 +3.95 x 10-99.81 x 10-91 . 1 4 ~ 10-73.71 x 10-75 . 2 7 ~ 10-78.28 x 10-79.08 x 10-78.95 x 10-77 .9 4 ~ 10-78 . 2 2 ~ 10-77 . 9 4 ~ 10-72.91 x9.75 x1.27 x1.1ox1 . 0 6 ~1.29 x1.58 x1.76 x lo-*54Al+ b1.40 x 10-11.4ox 10-l11.23 x1 . 0 6 ~1 . 0 6 ~ 10-l14 . 3 0 ~ 10-l11.03 x 10-l12 . 8 2 ~ 10-l'l06pd+1 . 7 9 ~1.98 x lo-"2.18 x 10-l'1 . 1 9 ~ 10-l23 . 1 8 ~ 10-l27 . 5 0 ~ 10-l28.31 x1.02x lo-"27AllO6pd+ 27AlzlOaPd+8 . 1 0 ~ 10-141 . 7 7 ~ 10-133 . 3 0 ~ 10-131.28 x 10-132 . 6 0 ~ 10-139 . 6 9 ~ 10-131 . 3 0 ~1.95 x8.61 x 10-l2 1 . 7 2 ~ 10-l25 . 1 9 ~ 7 . 2 6 ~ 2 . 7 0 ~1.88 x 4.68 x 10-l22 . 2 9 ~ 10-9 5.55 x 10-12a Partial pressures in atmospheres given by Pi = kiIiT. b Corrected for fragmentation contribu-tion from A120.RESULTSThe following gaseous equilibria were used to characterize the gaseous moleculesAlPd and A12Pd :AlPd(g) + Al(g) + Pd(g)Al,Pd(g) + Pd(g) + 2AlPd(g).(1)(2)Enthalpy changes for these reactions were determined from the measured equili-brium constants, K,, by the third law method for reactions (1) and (2) and additionally,by the second law method for reaction (1) where sufficient data were available, usingthe well known relations AH: = -RTln K,-TA[(GP-H;)/T] and AH; = -Rd InKJd (117') for the third and second law methods, respectively270 ATOMIZATION OF AlPd AND A1,PdThe necessary free energy functions, - (GP - H:)/T, for Al(g) and Pd(g) were takenfrom the literature.16 Those given in table 3 for AlPd and A1,Pd were calculated bystandard statistical methods from the estimated molecular parameters given.TABLE 3.-FREE ENERGY FUNCTIONS - (@-H;)/T FOR THE GASEOUS MOLECULES AlPd ANDA12Pd AS CALCULATED FROM THE TABULATED MOLECULAR CONSTANT ESTIMATESPdmolecule AlPdpoint group CaJ"symmetry number, Q 1angle -internuclear distance r& 2.288vibrational bands v/cm-l 331 V lground electronic state 2cv2v3A/ 'A1c20290" a(AI-Pd) 2.28833211833 1' A 117001800190020002100277.23279.32281.37283.13284.93344.64347.82350.83353.72356.43* Estimated by analogy to angle in [PdCl&." b Sum of Pauling radii of Al and Pd shortened inproportion to that observed for AIAu.'* C Calculated by the Guggenheimer re1ati0n.l~ d ForAlPd(g), H:98- HE = 9.76 kJ mol-' and for Al,Pd(g), HigB- HE = 13.77 kJ mol-'.A1 Wg)The third law treatment of reaction (1) is summarized in table 4.The third lawenthalpy, AH: = 252.6+ 3.4 kJ mol-l, represents directly the dissociation energy.The second law enthalpy AH:,,, = 259.7k21.2 kJ mol-l or AH: = 244.7k21.2 kJmol-1 is in fair agreement with the third law value. The second law entropy, AS;98 =77.0 11.3 J K-l is also in agreement within experimental error with the third lawentropy AS:,, = 82.0 J K-l. A final dissociation energy, D: = 250.6f 12.0 kJmol-1 is taken as a weighted average of the second and third law values.TABLE 4.-THIRD LAW TREATMENT OF THE REACTION AlPd(g) + AI(g)+Pd(g)number TIK - log Kp J K-1 kJ mol-1data set -At(&- H00)lTI AH: I1 1739 3.157 85.13 253.22 1785 3.046 85.44 256.63 1822 2.917 85.69 257.84 1729 3.143 85.06 251.15 1768 2.868 85.33 247.96 1836 2.616 85.79 249.57 1860 2.541 85.93 250.38 1895 2.423 86.13 251.111 1888 2.463 86.09 251.515 1923 2.396 86.27 254.117 1961 2.081 86.42 247.618 1974 2.240 86.45 255.319 2010 2.174 86.53 257.6average : 252.6+ 3.4 aJkor is standard deviationD .L . COCKE, K . A . GINGERICH AND C.-A. CHANG 27 1A12Pd(g)The A12Pd molecule was observed for only two data sets and at low ion intensities,but was positively identified by its isotopic distribution. The third law enthalpy ofreaction (2) was determined as AH: = -8.8f3.0 kJ. This value in combinationwith D:(AlPd) gives the atomization energy of Al,Pd(g) as D: = 492.4 f 24 kJ mol-l.All final values have error limits that include estimated uncertainties in tempera-tures, ionization cross sections, multiplier gains and free energy functions.The standard heats of formation, of AlPd(g) and Al,Pd(g) were derivedas 451.8 & 12.5 kJ mol-1 and 536.4+ 24.3 kJ mol-l, respectively, using correspondingD;,, values of 254.02 12.0 kJ mol-I and 498.6f24.0 kJ mol-l and the literature l6standard heats of formation, AHf0.298, of Al(g) [329.3+2.1 kJ mol-l] and Pd(g)L376.6f2.1 kJ mol-l].DISCUSSIONAlPdThe Pauling model of a polar bond has been shown to be quite useful in interpret-ing and predicting the single bond strengths of diatomic as well as triatomic inter-metallic gold 21 However, recent findings 22 concerning diatomicand triatomic intermetallic molecules containing a platinum group metal have shownthat the Pauling model does not successfully predict the dissociation energies of thesemolecules, but does aid in understanding the bonding involved by predicting theexpected single bond energies.Bonding in gaseous intermetallic molecules betweena platinum group metal and a transition metal especially from the left side of thetransition metal series as well as the lanthanoid and actinoid metals has been foundto be very strong and has been interpreted by the Brewer-Engel theory 12* 22 whichpredicts mu1 t iple bonding.Applying the Pauling model to the AlPd molecule and using D;[Al,(g)] = 138.6516.0 kJmol-I, D:[Pd,(g)] = 104.6f20.9 kJmol-l; X A ~ = 1.5 and XPd = 2.3, adissociation energy D: = 183 kJ mol-1 is obtained.This value is 68 kJ lower thanthe value determined experimentally in this study. Taking the Pauling model pre-dicted value as that of an Al-Pd single bond, it can be suggested that the enhancedbond strength in this molecule is due to effective use of d electrons from Pd in theformation of a bond order larger than unity. This interpretation parallels that of theBrewer-Engel theory 12* 2 2 as applied to the gas phase. It should be mentioned thatin the condensed AlPd system 2 3 a strong negative deviation of aluminium activityfrom ideality around the stoichiometric composition of AlPd indicates exceptionallystrong Al-Pd bonding. This strong bonding is evidently carried into the gas phase.A1,PdThe atomization energy of Al,Pd(g), AH&o = 492.4+24 kJ mol-l is approxi-mately twice the dissociation energy of AlPd(g).This high value supports the sym-metric structure Al-Pd-A1 that was chosen and further suggests that the A1-Pdbonds are similar in the dimer and trimer. Evidently, palladium has sufficient delectrons to accommodate one or two aluminium atoms, or even more as was notedfor the condensed phase.This work was supported by the National Science Foundation and by the RobertA. Welch Foundation272 ATOMIZATION OF AlPd AND A12Pd' G. D. Blue and K. A. Gingerich, 16th Ann. Conf. Mass Spectrometry and AZZied Topics, ASTME-14, paper No. 129.0. M. Uy and J. Drowart, Trans. Faraday SOC., 1971, 67, 1293.K. A. Gingerich and G. D. Blue, J. Chem. Phys., 1973,59, 185.A.M. Cuthill, D. J. Fabian and S. Shu-Shou-Shen, J. Phys. Chem., 1973, 77, 2008. ' K. A. Gingerich, D. L. Cocke, H. C. Finkbeiner and C.-A. Chang, Chem. Phys. Letters, 1973,18, 102.L. Pauling, The Nature of the Chemical Bond (Cornell University Press, Ithaca, 3rd edn.,1960). ' K. A. Gingerich, J. Chem. Phys., 1968, 49, 14. * R. T. Grimley in Characterization of High Temperature Vapors, ed. J. L. Margrave (Wiley,New York, 1967).W. A. Chupka, J. Berkowitz, C. F. Giese and M. G. Inghram, J. Phys. Chem., 1958, 62, 611.The appearance potential (AP) for Alt fragment was determined in the present study as 12.6 &1.0 eV using the AP = 7.7 eV for AlzO+ as standard. This AP for the Alg fragment is lowerthan those reported by Kohl and Stearns, 15.2f0.5 and 16.2 eV.However, it does indicatethat even with the 18 eV electron energy used in the present study fragmentation of A 1 2 0 toAl: is substantial. Stearns and Kohl corrected their Al; ion intensities based on their experi-mental ratio of fragment Ali to parent A120+ (7 x loe3) at 30 eV ionizing energy. Evidencefrom the present study suggests that even at 18 eV ionizing energy, this ratio may be as highas (9 x Using this ratio and the Al, data taken in this study yields DE A12(g) = 138.6416 kJ mol-l.l 1 D. S. Ginter, M. L. Ginter and K. K. Innes, J. Astrophys., 1973, 139, 365; P. B. Zeeman,Canad. J. Phys., 1954, 32, 9.D. L. Cocke and K. A. Gingerich, J. Chem. Phys., 1974, 60, 1958 ; J. Phys. Chem., 1972, 76,2332.lo C. A. Stearns and F. J. Kohl, High Temp. Sci., 1973, 5, 113.l3 C. E. Moore, Nat. Bur. Stand. Circ., 1958, 467, 3, 186.l4 J. B. Mann, Proc. Int. Con$ Mass Spectroscopy, Kyoto, Japan (University of Tokyo Press,R. F. Pottie, D. L. Cocke and K. A. Gingerich, J. Mass Spectrom. Ion Phys., 1973, 11,41.l6 R. Hultgren, R. L. Orr and K. K. Kelly, Supplement to Selected Values of ThermodynamicProperties of Metals and AZloys [University of California, Berkeley, California, Aluminium(1968) and Palladium (1968)l.C. J. Cheetham and R. F. Barrow in Advances in High Temperature Chemistry, ed. L. Eyring(Academic Press, New York, 1967), vol. I.1970), pp. 814-819.l 7 A. F. Wells, 2. Krist, 1939, 100, 189.l9 K. M. Guggenheimer, Proc. Phys. SOC., 1946,58, 456.'OK. A. Gingerich, Chimia, 1972, 26, 619.21 K. A. Gingerich, Chem. Phys. Letters, 1972, 13, 262.22 K. A. Gingerich, High Temp. Sci., 1971, 3, 415 ; Chem. Phys. Letters, 1973, 23, 270 ; J.C.S.23 M. Ettenberg, K. L. Komarek and E. Miller, Metal Trans., 1971,2,1173.Faraday IZ, 1974, 70, 471.(PAPER 5/383

ISSN:0300-9599    

DOI:10.1039/F19767200268

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

Equation of State for all PhasesPart 1 .-Basic Isothermal EquationBY E. A. SEIBOLD~I.C.I. Ltd., Corporate Laboratory, Whitchurch Hill, Reading, BerkshireReceived 2nd April, 1975An open-ended isothermal equation of state developed from the van der Waals equation has theexcluded volume term, B, as a function of (P+ A/un). As values of (Pi- A/u") become large, the equa-tion becomes simple in form while at low pressures it is most complex. A non-linear optimizationtechnique was used to fit the equation parameters to various sets of PUT data which included thevapour, liquid and solid phases. The equation can represent the extremes of the pressure ranges ofall the isotherms investigated including some at near critical temperatures within the experimentalaccuracies.1. INTRODUCTIONThere is a need for an equation of state which is valid for the complete range ofpressures, densities and temperatures which are experimentally obtainable.Such anequation should be capable of representing both low and high pressure gases andliquids with the same parameters and within the accuracies which are at presentexperimentally possible. The range of experimental conditions is covered by thefollowing approximate values,0 < P I lo3 MPa0 < T S 1300 Kwith an accuracy of kO.01 % on pressure and volume and kO.01 K on temperature.In exceptional cases, however, the volume and temperature measurements may be upto 10 times more accurate. Ultimately it would be desirable to be able to representthe solid phase as well as the liquid and gaseous phases with the same parameters but,because of the scarcity of measurements covering such a wide range, this is not yet apressing need.However, with the available PUT measurements it has been possibleto show how the isothermal vapour-liquid equation, that is developed below, can besimply modified to produce fits in the solid phase to the same accuracy as those inthe liquid phase.Since the uses for a pure isothermal equation of state are limited, although Michels,et aZ.l13 l 2 usually represented their measurements by the use of an isothermal virialtype of equation, this paper must be regarded as a first step in an overall study toobtain a complete equation of state. This approach is necessary because it was foundthat different molecules have different temperature variations of the isothermalequation parameters.2.DEVELOPMENT OF THE ISOTHERMAL EQUATION OF STATEThe starting point, as in many other studies (such as those due to Clausius,Berthelot, Dieterici, Wohl, Keyes, Beattie and Bridgeman, Redlich and Kwong, etc.),t present address : The Old Malt House, Blewbury, Didcot, Oxfordshire OX11 9PR.27274 EQUATION OF STATEfor the development of an equation of state is from the well known van der Waalsequationwhere a and b are constants characteristic of a particular substance.these constants with the two parameters(P+a/u2)(u-b) = RT (2.1)Here we replaceA =f(T)B = f(P,v,T).Intuitively one might say that since the volume is a function of pressure and tempera-ture then the excluded volume, B, might be a function of pressure, volume and tem-perature. Alternatively, the following reasoning might be used : let B be a functionof the total pressure and the temperaturewhere the total pressure, A, is the sum of the external pressure and the internal pressureof the fluid. That is,This idea stems from the consideration of a fluid changing from a liquid state atconstant pressure and temperature to a gaseous state.The change in internal pressuremust then account for the overall change in the volume and excluded volume. Anapproximation to the internaI pressure of a fluid obtained from the van der Waalsequation is as follows,and, therefore, the total pressure is given byThis approximation to the total pressure will be used in this work.arrived at a similar conclusion in his study of liquids by consideration of the freespace between molecules, calculated from viscosity data and specific volumes, fromwhich he obtained the internal pressure of a liquid.In order to get a functional form for B the following considerations were used :when a gas or liquid or solid is subjected to steadily increasing pressures it could beargued that the volume occupied by the molecules should, in the later stages of com-pression, be of some simple relationship to the applied pressure.This statement issupported by the success of the various equations devised to represent liquids andsolids such as those due to Tait,2 M~rnaghan,~ etc. Using this reasoning, severalfactors contribute to the volume at low pressures but gradually merge and becomeone at high pressures.The excluded volume would be subject to the same effects, sothat a suitable simple expression for the B term under conditions of high total pressuremight beorwhere A, C and D are functions of temperature only.It is also well known that at low pressures, virial equations with large numbers ofterms can be devised to produce any desired accuracy of fit to a given set of PvTdata,and that such a series of virial terms can be represented by an exponential term.Therefore, the B term may be considered to be a composite function as follows,B = f(A,T) (2.4)A = P+PI. (2.5)PI = a/v2 (2.6)A = P+a/v2. (2.7)MacLeodB = C-DA (2.8)B = C - D(P+A/v2) (2.9)B = C- DA + El exp( - FIA) + E2 exp( - FzA) + 9 (2.10E.A . SEIBOLD 275where El, Fl, E2, F2, etc., are also functions of temperature only and where anynumber of exponential terms may be used. It is, of course, implied that the exponen-tial terms become negligible at very large values of A so that eqn (2.10) reverts to (2.9).The number of terms in (2.10) will depend upon the complexity of the pressure-volumemeasurements of a particular molecule and also on the accuracy of fit required.In the gaseous and liquid phases the molecules are free to move about at will andit seems reasonable to suppose that the exponent, equal to two, on the volume in theterm A/v2 will be the same in both phases. However, in the solid phase this is notthe case and the exponent should be different according to how the moleoules packin this phase.In the case of argon, X-ray diffraction studies by Eisenstein andGingrich 4* show that there are more near neighbours in the solid phase than in theliquid phase so that one could expect an increase in the value of the exponent to somequantity greater than two. Some earlier work by Gibson and Loeffler l7 suggestedthat the exponent for liquids should be larger, i.e., 2.74 for polar liquids, but thisvalue was volume-dependent. They used the Tait equation in their work and, sincetheir exponent is only empirically identified with the van der Waals exponent. theirfindings do not apply to the work reported here.The isothermal equation of state finally evolved can be considered an open-endedequation as follows,whereand n = 2 for gases and liquids.This equation is capable of representing pressure-volume conditions from very low to very high pressures, if necessary passing throughthe vapour-liquid phase boundary, with the same set of parameters. It can alsorepresent solid state conditions by altering n but this has only been tested on onesubstance.A(v- C+ DA-cEi exp(-F*A)) = RT (2.1 1)A = P+A/v" (2.12)i3. SOLUTION OF EQUATION OF STATESince eqn (2.1 1) is not explicit in P or it is necessary to employ an iterativemethod for its solution. The method used in this work uses a modified rule of" false position ".or abbreviatedThe calculation is started by first choosing two initial estimates for X, where XequalsP or v.When the correct value of X has been arrived at in the iterative calculationIn order to get a better approximation to X a linear extrapolation from the startingpointsto the point (X3,1) can be taken. When this is done we getEqn (2.11) can be writtenA = RT/(v-B) (3.1)A = t,b. (3.2)A/t,b = 1. (3.3)(XI ,(A/$) 1) and w 2 9 ("2)where n = 1. The approximation can be further improved by increasing n by unityand solving eqn (3.4) for X4, etc., until the desired accuracy is attained.In practice, this method converges very quickly and it does not matter if the initialestimates for Xare too large or too small. Four or five iterations are usually neede276 EQUATION OF STATEto attain an accuracy of 1 part in 1O1O when the initial estimates are within 90 to 110 %of the desired value.4.LEAST SQUARES FITTING AND WEIGHTING FUNCTIONSIf an equation of state is to be used for the calculation of both pressure and volume(isothermal conditions) then it is desirable to determine the parameters of the equationby minimizing the sums of squares on both. That is minimize,Nwhere W(P)n and W(u), are the weighting functions for the pressure and volume datapoints. Because of the large variation in both pressure and volume encountered inmost of the PvT data used in this study, it was found that the numerically larger datavalues were being fitted more accurately when equal weighting was employed. There-fore, in order to compensate for this effect, graduated weighting functions were usedso that, within the limits of experimental variations, approximately equal percentageerrors of fit over the range of the variables would be obtained. The weightingfunctions are of the simple form,WP>n = (1/PA2 (4.2)J V u ) n = (l/Vnl2 (4.3)where P, and vn are the experimental pressure and volume values.The fitting of eqn (2.1 1) to PUT data was carried out by using the non-linearoptimization technique developed by Powell.6 Powell’s method was chosen for thisapplication because it does not require function derivatives and has been recommendedby Box, Davies and Swann ’ as the most effective of currently available direct searchmet hods.The overall pressure and volume errors of fitting reported in this work have beendetermined using the following equation,where 8 equals P or v and N is the total number of data points.5.ISOTHERMAL FITTING RESULTSThe full capabilities of eqn (2.1 1) can best be illustrated by showing the fittingresults obtained from molecules with wide ranges of PUT measurements, preferablycovering the gas and liquid regions or on near-critical isotherms. Three moleculesout of ten investigated have been chosen for illustration. These are argon, carbondioxide and water. Plots of the percentage residuals on pressure and volume are avery efficient way of seeing how well a set of PUT measurements is represented by anequation of state; at the same time a comparison of the errors on pressure andvolume can be made. This method has been adopted here, but because of spacelimitations only a few of the plots of the most wide ranging or complex isotherms canbe shown for each compound.5(i) ARGONThe available PUT measurements for argon are extensive and cover a wide rangeOne set of measure- of conditions, consequently they are ideal for testing purposesE .A . SEIBOLD 211ments has been chosen in the region below the critical temperature and one set aboveto illustrate the capabilities of eqn (2.1 1). The set below T, is made up of results fromseveral workers obtained at slightly different temperatures because no one individualset of measurements has a wide enough range in pressure and density to be sufficientlysearching as an example. At the approximate temperature of 101 K, data due toStreet and Staveley,* Crawford and Daniels and van Witzenburg and Stryland lowere combined with some very low pressure vapour points calculated from the virialequation.The data details, equation parameters and fitting results are given in table 1.In addition, the fitting residuals which can be seen in fig. 1 show the results of fittingfrom low pressure gas through the vapour-liquid boundary, through the liquid region,through the liquid-solid boundary and into the solid region. The residuals for thesolid phase, right hand side of fig. 1, show considerable scatter, but no positive trend,and appear to be as well represented as the liquid phase.TABLE AR ARGON DATA AND FITTING RESULTS AT THE APPROXIMATE TEMPERATURE OF 101 K100.94 K ref. (8). 11 liquid PUT measurements.data errors, P = + 1.4 to 0.1 %u = kO.1 %T = kO.01 K100.76 K ref.(9). 5 liquid PUT measurements.data errors, P = kO.6 to 0.4 %u = k0.07 %T = k0.02K101.11 K ref. (10).measurements.data errors, P = k 0 . l %T = +O.Ol K1 liquid and 9 solid PUTu = +O.l %equation of state parameters.8.122 972 759 D+Ol A =El =F1 =C =Ez = -3.696 234 165 D-03Fz = 4.075 310 844 D-08D = 3.632 154 555 D- 14E3 = 2.078 906 039 D-03F3 = 3.774 016 429 D-081.346 257 582 D-042.474 203 261 D-095.266 000 933 D-04nga-ljqujd = 2.0 D+ 00holid = 2.066 176592 D+ 00100.94 K virial equation calculated values.B(T) = -0.004 561 m3 kg-l, with 10 vapour resultsfrom 1 to 10kPa.fitting results (overall values), r.m.s. Perror = f0.68 %r.m.s. vemor = k0.041 %The exponent on v in the term A/vn for the solid phase shows an increase ofapproximately 3.5 % over the value 2.0 used for the liquid and gaseous phases.Thiscan be compared with an approximate increase in density of 9 % on changing fromliquid to solid.Even though, for this first example, the individual PUT sets are at slightly differenttemperatures, the differences are small enough not to separate the residual curves toany great extent. The curves also give an indication of how well the different experi-mental results fit together. The fitting of any one individual PUT set could be easilycarried out with greater accuracy, so that the overall errors of fitting given in table 1are larger than would be obtained for each individual temperature.For the fitting at 373.15 K, two sets of measurements were combined to get themaximum spread of pressure and density.Fig. 2 shows the residuals of fitting thefirst set due to Michels, Wijker and Wijker l2 and fig. 3, which is a continuation offig. 2, shows mainly the residuals of fitting the second set due to Robertson, Bab278 EQUATION OF STATE2.0I .o0-1.0-1.00.20.10-0.1-0.1pressure/MPaFIG. 1.-Pressure and volume fitting residuals for vapour, liquid and solid argon data by Street andStaveley * (A at 100.94 ), Crawford and Daniels (0 at 100.76 K), van Witzenbug and Stryland lo( x at 101.11 K) and virial equation calculated values (0 at 100.94 K) with B(T) = -0.004 561 m3kg-’. The vapour-liquid and liquid-solid phase boundary pressures are indicated by dashed linesand the pressure scale changes at 0.01 and 1 MPa.%8 3 r( 0‘01 0.013 - O mI X 0 32 -0.01-0.0 30pressure / MPaFIG.2.-Pressure and volume fitting residuals for gaseous argon data by Michels, Wijker and Wij ker *at 373.15 K. The pressure scale changes at 65 MPa. This figure is continued in fig. 3.-O“ r 0.1 9l- ipressue/MPaFIG. 3.-Pressure and volume fitting residuals for gaseous argon data by Michels, Wijker andWijker l 2 (0), and Robertson, Babb and Scott l3 (0) at 373.15 K. This is a continuation offig. 2E. A . SEIBOLD 279and Scott,13 but some of the highest pressure results of Michels et al. are also includedto show how well they overlap. By separating the two sets of results in this way,residual scale lengths suitable to each can be used.For this temperature a very widerange in pressure and density is available. The greatest densities are nearly as greatas those in the solid phase fitted at the lower temperatures and the pressure is aboutfive times larger.The data of Robertson, Babb and Scott l3 have been slightly modified accordingto the method they suggest in order to allow for a change in the fiducial PUT valuesat 308.15 K. The fiducial values have been changed to correspond to a new tempera-ture model, details of which will be published later, which covers their 308.15 Kisotherm. Their correction equations4 w r = ~ 1 4 / ( 4 ( 1 - r ) + rdi)dcorr(P,T)/dcorr(P, 308.15 K) = d(P,T)/d(P, 308.15 K)r = (d2(P2 -P1))/(P2(d2 - 4 ) )(5.1)(5.2)(5-3)use the valuesdl = 614.73 amagats (150 MPa)dz = 715.67 amagats (250 MPa)r = 1.0.The new fiducial densities arep1 = 614.862 071 amagats (150 MPa)p2 = 714.767 460 amagats (250 MPa)with r = 0.991.New values for the di on the 308.15 K isotherm were calculatedfrom eqn (5.1) and for the other isotherms from eqn (5.2).In the fitting of these combined measurements at 373.15 K greater weight has beengiven to the Michels Wijker and Wijker l2 results because they have a high degreeof internal consistency. For example, if this isotherm is fitted without the Robertson,Babb and Scott l 3 measurements the errors in fitting arer.m.s. Per,,r = 0.005 %r.m.s. v,r,,r = 0.004 %.These results are about half as great as those given in table 2 obtained in the combinedfitting.All the Michels et aZ.l'* l 2 data from 423.15 K down to 188.15 K can befitted with r.m.s. errors 10.01 %. At 173.15 K the r.m.s. error is twice as big(0.02 %) and at 153.15 K and 150.65 K it is ten times larger (0.10 %).TABLE 2.-ARGON DATA AND FITTING RESULTS AT 373.15 K373.15 K ref. (12). 51 gasdataerrors, P = 50.01 %u = kO.01 %T = 50.01 KPUT measurements.fitting results, r.m.s. Pernor = 5 0.01 1 %r.m.s. Verro, = +0.008 %373.15 K ref. (13).data errors, P = +O.l %17 gas PuTmeasurements.v = 50.2 to 0.1 %T = 50.05Kfitting results, r.m.s. Pmor = k0.16 %r.m.s. vcrror = 50.044 "/,equation of state parameters.7.006 592 008 D+Ol A =El = 4.447 434 225 D-04Fi = 3.028 299 519 D-09C = 5.927 997 596 D- 04E2 = - 3.006 721 689 D-04Fz = 3.028 299 517 D-09D = 6.548 390 824 D- 14E3 = 7.574 340 623 D-05F3 = 1.616 976 183 D-08ngas = 2.0D+0280 EQUATION OF STATE5(ii) CARBON DIOXIDEThe residuals from fitting an isotherm at 304.197 K, which is near critical forcarbon dioxide, are shown in fig.4. The details of the PUT measurements due toMichels and Michels l4 and Michels, Michels and Wouters l 5 are given in table 3with the equation parameters obtained from the fitting. The fitting residuals on thisnear critical isotherm are 4 to 7 times larger than Michels et aZ.149 l 5 have estimated.This is due to the large swings in the specific volume residuals near the critical pressure.FIG. 4.-Pressure and volume fitting residuals for carbon dioxide at near critical conditions.Databy Michels and Michels l4 and Michels, Michels and Wouters l S at 304.197 K. The vapour pressureis indicated by a dashed line and the pressure scale changes at 11 MPa.TABLE 3 .-CARBON DIOXIDE DATA AND FJTTING RESULTS AT 304.197 K304.197 K ref. (14) and (15). 15 vapour and 8 liquid equation of state parameters.PUT measurements. A = 1.529 411 394 D+02data errors, P = +O.Ol % El = 1.582 230 743 D-03U = kO.01 % E'1 = 4.411 213 980 D-08T = kO.01 K C = 7.352 580 039 D-04E2 = -2.381 117 453 D-03F2 = 5.424 21 6 576 D- 08D = 1.361 088 578 D--13E3 = 1.063 955 769 D- 04F3 = 8.609 739 541 D-07fitting results, r.m.s. Pernor = 50.036 %r.m.s. Vernor = k0.068 %Ifga-liquid = 2.0 D+ OO5(iii) WATERThe PUT measurements for water were taken from the highly accurate results ofKell and Whalley.These results have extraordinarily accurate volume measure-ments with published errors in the range of 20 to 40 parts per million. The fittingresiduals, illustrated in fig. 5, show this to be a conservative claim. The r.m.s. Verrorobtained in fitting, given in table 4, is only 3.5 parts per million. In fact all theisotherms from 273.15 to 423.166 K for water listed by Kell and Whalley can be fittedwithin their claimed accuracy on volume. However, the fitting residuals on pressureshow fairly large swings at the low pressures, gradually becoming very small at thehigher pressures. Again, this is generally true for all their isotherms and the causewill be discussed below.The overall r.m.s. fitting error on pressure is approximatelythree times larger than the experimental errorE. A. SEIBOLD 28 1I cpressure/MPaFIG. 5.-Pressure and volume fitting residuals for liquid water data by Kell and Whalley l 6 at423.166 K. The pressure scale changes at 11 MPa.TABLE 4.-wATER DATA AND FITTING RESULTS AT 423.166 K423.166 K ref. (16). 27 liquid P~Tmeasurements.data errors, P = kO.02 %equation of state parameters.1.034 288 846 D+03 A =u = k0.002 1 to 0.0040 % 4.582 852 985 D-01T = +O.OOlK F1 = 1.262 161 735 D-08fitting results, r.m.s. Perror = k0.064 % 9.283 059 767 D-04E ' Z = -4.702 367 358 D-01F2 = 1.260 866 956 D-08D = 7.118 353 950 D- 14El =C =r.m.s. Uerror = +O.OOO 35 %ngas-ljquid = 2.0 D 006.DISCUSSIONThe effectiveness and value of an equation of state is very largely dependent uponhow good it is at fitting PvT measurements for different molecules under the variousconditions to be found in their gaseous and liquid phases at high and low pressures.The goodness of fit can only be judged by the magnitude of the residuals in fittingcompared with the errors obtained experimentally and by examination of the trendsin the plots of the residuals.The accuracy of fitting of the various sets of PUT measurements investigated inthis study are sometimes better and sometimes worse for the variables P and v thanthe claimed experimental accuracy, but the residual plots do not seem to show anyconsistent evidence of systematic deviations.The equation represents the extremesof the pressure ranges of all isotherms without a decrease in the accuracy of fitting.However, some isotherms depending upon the molecule and temperature are morecomplicated at low pressures, and thus require more exponential terms in the equationof state to represent them.There are, however, two regions where the fitting residuals are larger than expected ;these require an explanation.It was noticed that when liquids and gases were fitted it was generally found thatthe pressure errors on the low pressure liquids were larger than those on the gases orhigh pressure liquids. In order to investigate this effect plots of (r.m.s. Perror)/(r.m.s. Uerror) against P/A were kept for the PvTpoints of most of the various isothermsfitted. The plots showed that all the points, with the exception of a few very accurateresults, fell into the curved band reproduced in fig.6. This shows that the relativeerror in fitting the pressure rises quite steeply when the pressure becomes a smallfraction of the total pressure. A reason for this observation can be found by examina-tion of the equation of state (2.11) which can be rearranged as follows,P = RT/(v - B) - AJv2282 EQUATION OF STATEHere P is calculated by taking the difference between two terms and, when P is asmall fraction of the total pressure A, it is obtained by taking the difference betweentwo much larger numbers both of which are dependent on v to a great extent. There-fore, if P is to be calculated to the same accuracy to which it can be measured whenconditions of small fractional P/A apply, then v must be known to a very much greateraccuracy than P.This condition is apparent even in the very accurate measurementsof Kell and Whalley l6 for water, where there is a general random increase in thepressure residuals in going from high to low pressures. In order to satisfy their errorrequirements of 0.02 % on the pressure at low pressures, an increase in the accuracyof approximately 40 times on v would have to be obtained in order to satisfy all theirisotherms.In-’ I 0-2 10” 1PIAFIG. 6.-A band (filled with zigzag lines) which contain a series of curves obtained by plotting(r.m,s. Penor)/(r.m.s. umr) against the ratio of pressure to total pressure (P/A) for different workers’fitting results.It is not known to what extent this limitation applies to other equations of state,but probably all those based on van der Waals equation behave in a similar way.The other region where the fitting residuals are larger than expected is encounteredwhen the PUT conditions are near those of the critical state.One explanation is thatthe PUT results for near-critical conditions used in this study have been obtained onapparatus that allowed density gradients to be formed in the fluids under study becauseof the relatively large vertical dimensions of the fluid container. In addition, anotherexplanation is that some workers “ smooth ” their experimental results ; in the criticalregion this procedure could alter volume readings a great deal because of the extremesensitivity of volume to pressure.The accuracy of the fitting is also dependent upon finding a good combination ofthe various parameters in the equation of state.How good these are very largelydepends upon the starting values used in the search, the length of time devoted to thesearch and if a sufhcient number of exponential terms have been included in theequation of state. If an isotherm is to be fitted for which there is a fitting result ata nearby temperature, then the parameters for this temperature are usually adequateas starting values for the fitting search. Even if the molecules are not the same butare of similar shape such as C 0 2 and N,O then the fitting parameters from one caE.A. SEIBOLD 283be used as starting values for the other. If a completely new molecule is to be fittedit is better to start fitting the isotherms with temperatures well above the criticaltemperature. Also, when starting, it is usually easier to restrict the data to the highestpressure points without any exponential terms in the equation of state. The exponen-tial terms can then be introduced gradually as the low pressure values are added.Once a satisfactory fit has been established it is usually relatively straightforward toprogress through a series of isotherms. The time taken to complete a search dependsupon the starting values, the accuracy required for the parameters and the speed ofthe computer. In this work the search procedure was usually terminated when thevalues of the parameters changed by less than one part in lo8 for a complete searchiteration.7.CONCLUDING REMARKSFor the past 100 years or so there has been an almost universal quest for a simpletwo- or three-constant equation of state that will represent all gases and liquids.This ideal may never be realized and it is necessary, therefore, to accept that equationsof state with many parameters will have to be used if the accurate measurementsobtained from experiments are to be exploited. Also, a useful equation of state neednot necessarily be explicit in P or u since the use of a computer and an iterative methodof solution can easily be used to solve for either. One of the disadvantages with largeequations of state is in fitting them initially to the experimental data because of thedifficulty in finding suitable starting values for a search routine. The approach usedin this work, the fist stage of which is reported here, is to try and minimize thisdifficulty by fitting isothermal data first and then finding the temperature variationof these parameters.The isothermal equation of state presented here has been used to fit between 2000and 3000 isothermal data points comprising the PUT data for the molecules argon,neon, carbon dioxide, nitrous oxide, nitrogen, methane, ammonia, ethylene, water andmixtures of methane and ammonia.The PUT conditions ranged from the very lowesttemperatures (86.637 K), that is, just above the triple point of argon, to values over1200 K and pressures up to 1000 MPa (10 000 bar) and down to 1 kPa (0.01 bar).None of the results showed any consistent evidence of systematic deviations exceptfor a few, at very low pressures, where the errors were too small to justify the use ofadditional exponential terms.It seems, therefore, that the use of eqn (2.1 1) as thebasis for the development of a total equation of state, by elucidating the temperaturevariation of the equation parameters, is well justified.APPENDIX ANOMENCLATUREa = van der Waals equation constantA = equation of state parameterb = van der Waals equationexcluded volume constantB = equation of state excludedvolume termC, D, E l , F,, etc. = equation of stateparametersB(T) = second virial coefficientd = p = density in amagatsR = universal gas constantrequationT = thermodynamic temperatureV = specific volumeW(P) = weighting function on pressureW(u) = weighting function on volumeXI, X,, X,, etc.= approximate valuesdetermined in the iterativecalcuIation of P or u= parameter in density correctio284 EQUATION OF STATEN = total number of data points 8 = pressure or volume in thebeing fitted r.m.s. error calculationP = pressure 4 = sum of squares on the pressurePI = internal pressure of fluid and volume residualsPUT = pressure-volume-temperatureA = P+PI = P+A/v2 II/ = RT/(u-B)SUBSCRIPTSc = critical corr = correctedcalc = calculatedThe International System of Units (SI) is used here and, therefore, to use theequation parameters listed in the tables all PvT data must have units, pressure inpascal = Pa = N m-2, specific volume in m3 kg-l, temperature in kelvin = K.Throughout the text the word volume should be understood to mean specificvolume.In addition, the number of significant figures given in the tables is not anindication of the accuracy of the results but is necessary in order to maintain con-sistency in calculation.exp = experimentalAPPENDIX BPHYSICAL CONSTANTSMolecular weights and ice pointsargon 39.948 273.15 Kcarbon dioxide 44.010 273.16 Kwater 18.015 34 273.15 KSpecific gas constants, Pa m3 kg-l K-largon 208.129carbon dioxide 188.927water 461.532Specific volume conversion factorsargoncarbon dioxideamagat density = 1.783 56 kg m-3amagat density = 1.976 85 kg M - ~D. B. MacLeod, Trans. Faraday SOC., 1937, 33, 694.P. G. Tait, Reported Sci. Results Voyage H.M.S. Challenger, Phys. Chem., 1888,2, 1.F. D. Murnaghan, Proc. Nat. Acad. Sci., 1949, 30,244.A. Eisenstein and N. S. Gingrich, Phys. Rev., 1940,58, 307.A. Eisenstein and N. S. Gingrich, Phys. Rev., 1942, 62,261.M. J. D. Powell, Computer J., 1964, 7, 155.Ltd., Edinburgh, 1969), chap. 3, p. 31.R. K. Crawford and W. B. Daniels, J. Chem. Phys., 1969,50,3171.lo W. van Witzenburg and J. C. Stryland, Canad. J. Phys., 1968, 46, 811.l 1 A. Michels, J. M. Levelt and W. De Graaff, Physica, 1958, 24, 659.A. Michels, Hub. Wijker and H. K. Wijker, Physica, 1949, 15, 627.l 3 S. L. Robertson, S. E. Babb Jr. and G. J. Scott, J. Chem. Phys., 1969,50,2160.l4 A. Michels and C. Michels, Proc. Roy. SOC. A , 1935, 153, 201.l5 A. Michels, C. Michels and H. Wouters, Proc. Roy. SOC. A, 1935, 153, 214.l6 G, S. Kell and E. Whalley, Phil. Trans. A, 1965, 258, 565.l7 R. E. Gibson and 0. H. Loeffler, J. Amer. Chem. Soc., 1939, 61,2515.' M. J. Box, D. Davies and W. H. Swann, Non-Linear Optimization Techniques (Oliver and Boyd* W. B. Street and L. A. K. Staveley, J. Chem. Phys., 1969,50,2302.(PAPER 51606

ISSN:0300-9599    

DOI:10.1039/F19767200273

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

Radiolysis of Carboxylic CompoundsPart 2.-Radiolysis of Liquid Acetic AcidBY LJ. JOSIMOVIC,* J. TEPL+t AND 0. I. MI616Boris KidriE Institute of Nuclear Sciences,P.O. Box 522, 11001 Beograd, YugoslaviaReceived 14th April, 1975Analysis of the stable products of y radiolysis of liquid CH3COOH, carried out earlier, has beencompleted by determination of biacetyl and water yields. A transient absorption spectrum fouudduring pulse radiolysis experiments has been ascribed to the CH3C0 radical by comparison with asimilar observation for concentrated aqueous solutions of CH,COOH. Under pulse radiolysisconditions (0.5-15 h a d pulse-l) the CH2COOH radical was not observed. The yields of primaryspecies, i.e., cation and anion radicals, are estimated by applying a steady state kinetic treatment.Areaction mechanism for the radiolysis of liquid CH3COOH is proposed.Radiolysis of acetic acid in both the liquid 1-4 and solid 5 9 states has been studied.Transient species have been identified by an e.s.r. technique, following y radiolysis atlow temperature^.^^ Despite a number of investigations important features of thereaction mechanism remain unexplained, including the failure t o account for the fateof all CH,COOH radicals. Also, the established material balance is not satisfactory.In this work an attempt was made t o complete the information on the yields of stableproducts and to find, by use of pulse radiolysis measurements, the main transientspecies produced as well as to outline the reaction mechanism of y radiolysis of liquidCH,COOH.EXPERIMENTALGlacial acetic acid (AnalaR, Merck) was purified as described previously.6 Samples weredeaerated on the vacuum line using a freeze-pump thaw technique or alternatively dry argonwas bubbled through the acetic acid for about an hour.Irradiations were carried out in a 6oCo y source, and a Febetron 707 (Field Emission Corp.)was used for pulse radiolysis work.The sealed ampoules containing 5 cm3 of acetic acidwere y-irradiated at a dose rate of 5 krad min-l with doses from 4 to 30 krad for biacetyl,and up to lo4 krad for water determination. For the dose determination a Fricke dosimeter[G(Fe3+) = 15.61 was used. The pulse radiolysis set up has been described el~ewhere.~ Itsmain features are : a pulsed 450 W Xe lamp, all Suprasil silica optics and an irradiation cell,a double prism quartz monochromator OPTON MM 12, a RCA 1P 28 photomultiplier tubecoupled directly t o Tektronix 454 and 564B osilloscopes.The light passed twice through thecell and the totai light path was 5.1 cm in length. The electronic rise time of the system(build-up of the fast signal from 10 to 90 % of the maximum) was about 0.4~~. Absolutedoses of the order of 10 h a d were measured using N20-saturated ferrocyanide solution( E ~ ~ ~ = 1000 dm3 rn0l-l cm-1).8 The dose per pulse was calculated on the basis of GOH+G,, = 6.0.Water was determined by gas chromatography, with a 154 DG Perkin Elmer instrument,t Institute of Nuclear Research, Czechoslovak Academy of Sciences, Prague-Rei, Czechoslo-vakia.28286 RADIOLYSIS OF CARBOXYLIC COMPOUNDSon a column filled with Synachrom (polimer porous beads, Lachema C.S.S.R.), with heliumas the carrier gas at 120°C.Since the method had low sensitivity, and it was possible to takeonly a small quantity of the sample (a few mm3) for analysis the yield of water was determinedonly with very high absorbed doses. Under our working conditions the accuracy was& 10 %. Biacetyl was determined spectrophotometrically by the 2,7-&hydroxynaphthalenerneth~d.~ Since the test with 2-hydrazinoben~othiazole,~~ the reagent specific for aliphaticaldehydes, gave negative results, the procedure developed for formaldehyde determination inacetic acid (with an accuracy of + 5 %) was used.RESULTS AND DISCUSSIONThe yields of water and biacetyl measured after y-radiolysis of liquid acetic acidhave not been reported previously.Water was found after helium ion radiolysisand biacetyl was found in solutions of acetic acid of 1 mol dm-3 or more.12* l3 Theyields of biacetyl and water obtained here, together with the product yields publishedearlier,6* l4 are presented in table 1.TABLE PR PRODUCT YIELDS FOR THE y RADIOLYSIS OF DEAERATED ACETIC ACID AT NORMALTEMPERATUREproduct (P) an ref.5.403.900.480.220.530.451.742.20+ 0.112.00+ 0.205.08k0.25666661414this workthis workthis workThe transient absorption spectrum obtained by pulse radiolysis of liquid aceticacid is presented in fig. 1. The spectrum was unaffected by electron scavengers suchas N20 and 02.Under the same conditions at 600nm the absorption due to thesolvated electron was not observed. The observed absorption can be ascribed to theCH,CO radical. The spectrum is indentical with those obtained by pulse radiolysisof concentrated acetic acid solutions where only the CH3c0 radicals are produced bythe reaction of e& with CH3COOH.15~ l6 The yield of CH,cO (table 1) was cal-culated using the extinction coefficient of the CH3c0 radical, &260 = 940 dm3 mol-lcm-l, determined in aqueous solutions of acetic acid.16 The decay of the absorptionat 260 nm is of a second order with rate constant 2k = 1.2 x lo9 dm3 mol-1 s-l.Bearing in mind the high yield of anion radical, G(CH3COOH7) = 4.96, foundin crystalline acetic acid at 77 KY6 it seems resaonable to assume that ionization playsa significant role in the radiolysis of acetic acid at ambient temperatures :CH,COOH --+ CH,COOHt +e-.(1)Ionization in the condensed state is immediately followed by the ion-molecule reaction(2) through the hydrogen bond :The lack of dependence of G(C0J on radical scavenger concentration 3 3fast decay of the CH,COO radicalCH,COOH+ - * CH,COOH -+ CH3COOH; + CH,COi).CH3COQ 3 CH, + COz.(2)indicates(3L. JOSIMOVIC, J . TEPL+ AND 0. I. MICIC 287Also, no singlet corresponding to this radical has been found in the e.s.r. spectrumat 77 K 5 9 Reactions of the CH, radical formed lead to stable productsCH, + CH,COOH 3 CH, + CH2COOH (4)CH3+CH3 + C2H6 ( 5 )CH, +CH3C0 -+ CH,COCH3.(6)The proposed mechanism reveals that process (2) followed by decomposition ofCH,COO* is the main source of C02 and of the products formed by CH, radicalreactions. Evidence relating to the occurrence of reaction (4) and formation ofcH,COOH radical has been provided by investigation of the radiolysis of deuteratedacetic acid;2 a spectrum corresponding to this radical was found in crystallineCH,COOH.5* Similarly, according to the published data, the CH4 yield is reducedin the presence of the CH, radical scavenger, i ~ d i n e . ~ The high yield of methane(G = 3.90) compared to the small yield of ethane (G = 0.48) indicates that under ther 1 I I I250 300 350 400AlnmFIG. 1.-Transient absorption spectrum in acetic acid taken 0.5 ps after the pulse; path length 5.1cm ; dose rate 9.5 h a d pulse-'.y-radiolysis conditions, reaction (4) is more efficient than (5).In pulse radiolysisexperiments, owing to the very high dose rate the relative extents of these two reactionsare changed in favour of reaction (5) and, as a consequence, the radical cH,COOHdoes not appear in an observable concentration. The absorption maximum of thecH2COOH radical at 320 nm has not been observed at between 1 ,us and 100 p s atdoses between 0.5 and 15 krad (fig. 1). During y-radiolysis CH2COOH radicalsdisappear by recombinationgiving succinic acid with a yield G[(CH,COOH),] = 1.74.the unstable anion radical CH,COOH-which dissociates immediatelycH,COOH + tH,COOH + (CH2COOH), (7)Initial ionization is followed by the capture of thermal electrons and formation ofCH,COOH+e- 3 CH,COOH' (8)CH,COOH' -+ CH,CO+OH- (9)CH,COOH' + H+CH,COO-.(1 0288 RADIOLYSIS OF CARBOXYLIC COMPOUNDS4The species OH- and CH,COO- are probably removed by neutralization reactionsOH-+ CH,COOHZ -+ H,O + CH,COOH (1 1)CH3COO-+ CH,COOH; -+ 2CH3COOH. (12)In dilute aqueous solutions the CH,COOH molecule reacts with e& by two reac-tions [similar to (9) and (lo)] of roughly comparable However, in con-centrated solutions a decrease in G(eJ and a decrease in G(H2) as well as an increasein G(CH,cO) was found in both microsecond l6 and picosecond 2o experiments.This is consistent with the assumption that in concentrated solutions, and more soin pure CH3COOH, the electron is not hydrated and reacts mainly by reactions (8)and (9).We may therefore assume that reaction (10) is considerably less frequentthan (9) ; this is supported by the small yield of H,. Decomposition of the CH,COradical, formed in reaction (9), givesHowever, most of the CH3C0 radicals disappear by recombinationgiving biacetyl with G[(CH,CO),] = 2.20.CH,CO + CH,+CO. (1 3)CH,cO+ CH,CO -+ (CH,CO), (14)The most probable reactions of hydrogen atoms in liquid acetic acid areH+H + H, (1 5 )(16)(17)H + CH,COOH --+ H, + CH,COOHH + CH,COOH +. H, + CH3C00.Reaction (17) followed by (3) was proposed as an interpretation of the U.V. photolysisof a solution of H2S in CH,COOH at 77 K,5 where only CH, radicals were formed.The reaction scheme presented in fig.2 gives an overall view of the reaction0.53FIG. 2.-Reaction scheme for the radiolysis of acetic acid ; underlined formulae, stable products ;figures, their yields in G-unitsL. JOSIMOVIC, J. TEPL+ AND 0. I. MICIC 289mechanism of acetic acid radiolysis discussed in this paper. From it some stoichio-metric consequences may be inferred.The yield of CO, may indicate the size of the yield of positive ions, i.e.,G(CH,COOH+) = G(C0,) = 5.40, but it will be slightly high as reaction (17) alsogives CH3CO0 enchancing G(C02). The sum of the yields of C02 and CO[G(CO) = G(13) = 0.221 may be compared with the sum of the yields of CH,, C2H6and CH,COCH,, G(C02) + G(C0) = 5.62 and G(CH,) + G(CH,COCH,) +2G(C2H,)= 5.24. The difference indicates that some reactions of CH, other than those con-sidered occur to a minor extent giving an undetermined product.As the radicalCH,COOH formed in reaction (1 6) also contributes to the formation of succinic acid,G(CH,) will be less than 2G[(CH,COOH),]; in fact G(CH,) = 3.90 and 2G-[(CH,COOH),] = 3.48, therefore some other product may be missing from thisanalysis .The yield of negative ions can be given as the sum of the yields of CH,CO radicalsand H-atoms, where G(CH,CO) should be equal to the sum of the yields of CH,-COCH,, CO and (CH,CO),. G(H) cannot be expressed as the yield of molecularhydrogen as it is not known to what extent reaction (1 5) participates in H, formation ;probably not much and therefore G(H) = G(H,).G(CH,COOH-) NN G(CH3CO) + G(H,) = 5.61G(CH,COOH-) w G(CH,COCH,)+ G(C0) +2G[(CH3CO),] + G(H2) = 5.60.G(CH,COOH-) is 4.96 in crystalline acetic acid at 77 K,6 closely comparable withthe corresponding value at ambient temperature.The yield of water appears to be significantly lower (G = 2.0) than the valueexpected (G = 5.08) according to reactions (9) and (11).The most likely cause oft h s is the high absorbed doses (up to lo4 had) at which water was measured. Undersuch conditions the stable products will accumulate and water may disappear insecondary reactions. Some other products (CH,OH, C2H50H, CH,COOCH3) havebeen determined Evidently the proposed mechanism is not completebut the differences in compared yields are not serious.A. S. Newton, J.Chem. Phys., 1957, 26, 1764.G. E. Adams, J. H. Baxendale and R. D. Sedgwick, J. Phys. Chem., 1959, 63, 854.R. H. Johnsen, J. Phys. Chem., 1959, 63, 2041.P. B. Ayscough, K. Mach, J. P. Oversby and A. K. Roy, Trans. Faraday Soc., 1971, 67, 360.S. LukaE, J. Teplg and K. Vacek, J.C.S. Faraday I, 1972, 68,1337.P. Pagsberg, H. Christensen, J. Rabani, G. Nilsson, J. Fenger and S. 0. Nielsen, J. Phys. Chem.,1969, 73, 1029.F. Snell and C. Snell, Colorimetric Methods of Analysis (Van Nostrand, New York, 1955),vol. 111.' J. G. Burr, J. Phys. Chem., 1957, 61, 1451.' V. MarkoviC, Internal Report, Boris KidriE Institute of Nuclear Sciences, 1974.lo E. Sawicki and T. R. Hauser, Analyt. Chem., 1960, 32, 1434.l1 Lj. JosimoviC, Analyt. Chim. Acta, 1972, 62, 210.l3 W. M. Garrison, W. Bennet, S. Cole, H. R. Haymond and B. M. Weeks, J. Amer. Chem. SOC.,l4 Lj. JosimoviC and I. G. DraganiC, Int. J. Radiation Phys. Chem., 1973, 5, 505.l6 0. I. MiCiC and V. MarkoviC, Int. J. Radiation Phys. Chem., 1975, 7, 541.E. Hayon and J. J. Weiss, J. Chem. SOC., 1960, 5091.1955,77,2720.B. Cercek and 0. I. MiCiC, Nature (Phys. Sci.), 1972, 238, 74.E. J. Hart, J. K. Thomas and S. Gordon, Radiation Res. Suppl., 1964, 4, 74.M. Anbar, Adv. in Chem. Series, 1965, 50, 55.l9 0. I. MiCiC and V. MarkoviC, Znt. J. Radiation Phys. Chem., 1972, 4, 43.2o J. E. Aldrich, M. Bronskill, R. K. Wolf and J. W. Hunt, J. Chem. Phys., 1970, 55,530.21 S. LukaE, unpublished results.(PAPER 5/702)1-1

ISSN:0300-9599    

DOI:10.1039/F19767200285

出版商:RSC    

年代:1976

数据来源: RSC