Rate of Proton Transfer in Strong Acids and RamanLine BroadeningBY A. K. COVINGTON, M. J. TAIT* AND LORD WYNNE-JONESDept. of Physical Chemistry, School of Chemistry,University of Newcastle upon Tyne, 1Received 15th January, 1965A recent theory of Raman line broadening has been applied to measurements on perchloricand nitric acid solutions. The second-order rate constant obtained for the reaction of the per-chlorate ion with the proton is a factor of ten lower than that found for the triffuoroacetate ion.The occurrence of line broadening with increased concentration is not restricted to solutions ofacids and consequently some doubts may be raised about its interpretation in terms of the rateof proton exchange between acid and anion.Kreevoy and Mead 1 from a generalization of Heitler's methods 2 have derived anexpression for the second-order rate constant k2 for the reactionkzk iH,O+ +A-+HA+H,O,where A- is an anion species, in terms of the increase in half-width at half-height ofa Raman band of the anion or acid molecule.For slow exchange of the protonthe expression simplifies towhere c is the velocity of light, @-PI is the increased half-width of the line in wavenumbers. It is assumed that the Raman transition does not involve degrees offreedom of the acid molecule which take part in the exchange. Kreevoy and Mead 1applied the theory to measurements on trifluoroacetic acid, taking for the half-width in solutions of the sodium salt.Studies which will be reported elsewhere 3 have been made recently in theselaboratories of the dissociation of perchloric acid by the Raman method.In markeddisagreement with the results of n.m.r. measurements,4-6 perchloric acid was foundto be effectively completely dissociated up to at least 10 M. The basis of the Ramanmethod 79 8 is the determination to a very high degree of accuracy and reproducibility(0.2 %) of the integrated intensity (area under the Raman band), which is proportionalto the concentration of the exciting species. For these measurements the 931 cm-1perchlorate ion band was used. It is of interest to apply Kreevoy and Mead's theoryto results obtained during this study.k2 = 2nc (B-P1)/CH30+1,EXPERIMENTALThe measurements were obtained using 3 the Hilger and Watts E616 recording RamanSpectrometer in conjunction with a very stable Toronto arc source of design similar to thatof Jam, Mikawa and James,9 oFerated at low power (5 kW).Special attention was necessary* present address : Chemistry Department, Rensselear Polyteclmic Iqqtitutq, Troy, New York.17A . K . COVINGTON, M. J . TAIT AND WYNNE-JONES 173to achieve high quality results from the electronic circuitry and for measurements on dilutesolutions a specially developed transistorized amplifier 10 which utilizes a field-effect transistorfor impedance matching was employed with advantage.Perchloric acid solutions were prepared by weight dilution of a stock solution prepareddirectly from A.R. acid without further purification. The molarity of the stock solutionwas determined by potentiometric titration against hydrochloric acid as primary standardthrough borax as intermediate.Intercalibrated interchangeable Raman cells (60 ml) onground-glass joints permitted easy comparison of the intensities from solutions of con-centration up to 11 M in groups of three or four so that scans could be made at optimuminstrumental gains and any slight drifts in source output or amplifier gain could be corrected.RESULTS AND DISCUSSIONThe results of the half-width measurements (p> are shown in table 1. The linewidth in dilute solutions (0.3-3 M) was constant at 6.6 cin-1 and this was taken asthe value of PI. These values refer to slit widths of 0.2 mm (8 cm-1) but the valuesof p -PI were found to be independent of slit width within the experimental accuracy.The second-order rate constant kz for the reaction (1) is shown in the last column,where the perchlorate ion concentration was obtained from the integrated intensities.3The 931 cm-1 perchlorate ion peak is approximately Lorentzian in shape.Insodium perchlorate solutions the peak maximurn occurs at 940 cm-1. The corres-ponding shift in the trifluoroacetate frequency is less than half this. The peakmaximum occurs at about 920 cm-1 in some divalent perchlorates.11 The half-width was the same in 1 M sodium perchlorate as in dilute acid solutions. Hencethe same results would be obtained if following Kreevoy and Mead,l P1 was taken,as the half-width in the sodium salt. The half-width was found to be invariant inmixed sodium perchlorate + potassium chloride solutions of constant perchlorateconcentration (1 -6 M).TABLE 1 .-LINE BROADENING IN PERCHLORIC ACIDC 8-81 10-%t~[H30+] 10-1OkZ 84-03 6-9 0.3 0-6 1.46-06 7.3 0.7 1.3 2.28.36 8.0 1.4 2.6 3.210.54 9.1 2.5 4.7 4.51 1 *44 9.8 3.3 6.2 5.4mole 1.-1 cm- 1 cm-1 sec-1 1.mole-1 sec-1Measurements of the integrated intensities showed 3 that it is only in concentratedsolutions (greater than 10 M) that the concentration of perchlorate ions falls signific-antly below the stoichiometric concentration. That this is due to the formation ofperchloric acid molecules was confirmed 3 by the appearance of a new Raman bandat 974-1 174 cm-1 which is found in solutions of much higher concentration 12 andby the presence of a band in the infra-red.Representing the dissociation formallyby eqn. (1) would lead to a thermodynamic dissociation constant in excess of 103.It was concluded 3 that the appearance of perchloric acid molecules in concentratedsolutions only occurs when there are insufficient water molecules present to solvatethe proton fully as H90: as in dilute solutions.13 If this interpretation is correctthere are no, or certainly very few, perchloric acid molecules present in solutionswhere line broadening is observed.Vollmar has recently 14 studied the variation of the nitrate ion 1048 cm-1 line in anumber of nitrates with increase in concentration. Besides the broadening of theline and a shift in the frequency of the peak, there may be a non-Compensating dropin peak height causing the ratio of the integrated line intensity to the stoichiometri1 74 RAMAN LINE BROADENINGnitrate ion concentration (termed the specific intensity) to vary from a constant valueby 1-2 % for some salts.The only nitrate where no broadening was observed wasthe ammonium salt. He interpreted this as a result of the ammonium ion beingable to fit into the water structure so that it has no effect on the anion. Only if thehydronium ion behaves in the same manner to the ammonium ion is it possible tointerpret the total band broadening in terms of proton jump. Vollmar attributedband broadening in salts to cations of large hydrated radius breaking down the waterstructure thus enabling the nitrate ions to vibrate over a wider frequency range.Frequency shifts, on the other hand, were attributed indirectly to contact ion pairformation causing the release of water molecules which modifies the frequency ofvibration of the nitrate ion.It seems very likely that, in perchloric acid solutions,as the solvation of the proton changes as the solution becomes more concentrated,the changed water structure around the perchlorate ion will lead to line broadening.Krawetz in some unpublished work 15 gives results for line broadening in nitricacid at 25°C. The 1048 cm-1 band in dilute nitric acid (1 M) has a half-width of16 cm-1 which approximately doubles in width at 20 M. Some of Krawetz's resultsare shown in table 2. He found that the half-width of 1048 cm-1 line in sodiumnitrate increased from 15.3 cm-1 in 1 M solution to 16.5 cm-1 in 4-39 M solution,the increase in width with molarity being approximately the same as in acid solutions.The line broadened only slightly (0-2 cm-1) in mixed NaN03 + KC1 solutions.Selecting the value of 16.1 cm-1 the values for k2 in the third column of table 2 haveTABLE 2.-LINE BROADENING IN NITRIC ACID3.143-994-8 16.617-488.079-239-7910.3017-2417.6217-8019.4020.2420.7 121.4621.6422-492.12.63.16.17.88.79.410.412.02.863-503.914.664.975.205.105-044.930.80.80.81.31.61.71.82-12.4been obtained.The values of k2 shown in the last column were obtained from theNO 3 concentrations calculated by Krawetz from integrated intensities.The calcula-tion has not been extended to molarities higher than 10 M since other species such as(H"03)2, NO; are present 169 17 at concentrations higher than 7 My (the molaritywhere the nitrate ion comentration is a maximum) and these will contribute to theline broadening.The parallel increase in line width in nitric acid and sodium nitrate solutions maybe coincidental especially as other nitrates, with the exception of the ammonium andpotassium salts, show greater increases 14 than does sodium nitrate, and also sincethe line widths at the same concentrations of acid and sodium salt are different.New measurements of sodium perchlorate solutions have revealed that the line widthis the same as that in solutions of perchloric acid of the same concentration up to 8 M.Again this may be coincidental and due to entirely different effects as a frequencyshift is involved, but the same question arises here as for intensity measurements 3of the best reference solution to employA .K . COVINGTON, M. J . TAIT A N D WYNNE-JONES 175CONCLUSIONSThe results obtained by the application of Kreevoy and Mead’s theory 1 to threeacids at a concentration 5-6 M are summarized together with other relevant infornia-tion in table 3. The second-order rate constants for the combination reaction(eqn. (1)) range over an order of magnitude. At best, the values must be regardedas estimates only, since other factors, particularly changes in solvent structure insolution, may lead to line broadening ; at worst these factors may be entirely respons-ible for the observed broadening.TABLE 3a 10-llk2 lo-Wcl= 1 0 - 4 2 KK’ = a2c/(1 -4 1.mole-l sec-~ sec-1s toichiome tricmolarity acidperchloric 3 6-06 0-997 1980 0-22 435nitric 15 4.8 1 0.8 13 17.1 0.80 13-7trifluoroacetic 1 5.3 0.34 0.93 3.8 3.5Precise Raman studies of variations in specific intensity, of frequency shifts,as well as of line broadening, preferably coupled with parallel investigations of changesin the Raman water bands 18 should furnish important information about interactionsin concentrated electrolyte solutions.We thank Mr. J. G. Freeman for some additional measurements and Dr. A.Bewick, Dr. M. Fleischmann and Mr. T. H. Lilley for discussions.1 Kreevoy and Mead, J. Amer. Chem. Soc., 1962, 84,4596.2 Heitler, Quantum Theory of Radiation, 3rd edn. (Oxford, 1954).3 Covington, Tait and Wynne-Jones, Proc. Roy. SOC. A, to be published.5 Redlich and Hood, Disc. Farraday Soc., 1957, 24, 87.6 Hood and Reilly, J. Chem. Physics, 1960, 32, 127.7 Young, Rec. Chern. Prog., 1951, 12, 81.8 Young, Maranville and Smith, in Structure of Electrolytic Solutions (ed. Hamer), (Wiley, New9 Janz, Mikawa and James, Appl. Spectr., 1961, 15’47.10 Covington, Molyneux and Tait, Spectrochim. Acta, 1965, 21, 351.11 Jones, Jones, Harmon and Semmes, J. Amer. Chem. SOC., 1961, 83,2038.12 Redlich, Holt and Bigeleisen, J. Amer. Chem. Soc., 1944, 66, 13.13 Eigen, Angewandte Chem. ( I t . Ed.), 1964, 3, 1.14 Vollmar, J. Chem. Physics, 1963,39,2236.15 Krawetz, Thesis (University of Chicago, 1955).16 Chedin, h l e r c and Vandoni, Compt. rend., 1947, 225, 734.17 Chedin and Feneant, Compt. rend., 1949, 22$, 242.18 Covington and Prue, Ann. Rep., Chem. SOC., 1963, 60, 8.Hood, Redlich and Reilly, J . Chem. Physics, 1954, 22, 2067.York, 1959), p. 35