Proton Mobility in Water at High Temperatures and PressuresBY E. U. FRANCK, D. HARTMANN AND F. NENSELInstitut fur Physikalische Chemie, Technische Hochschule, Karlsruhe, GermanyReceived 15th January, 1965The electrolytic conductance of aqueous solutions of KCl, HC1 and &SO4 has been determinedbetween 45 and 220°C and up to 8000 bars. The conductivity of hydrogen ions has been derivedand the abnormal proton mobility is discussed as a function of temperature, pressure and waterdensity. The second dissociation constant of sulphuric acid is given up to 190°C for 4000 and8000 bars.The abnormal high values of the mobility of Hf and OH- ions in water havereceived extensive study. Recently, the theoretical interpretation has made con-siderable progress. Major contributions and critical reviews have been given amongothers by Gierer and Wirtz,l Conway, Bockris and Linton2 and Eigen and DeMaeyer.3 The most probable concept is that of a rapid fluctuation of the protoniccharge within HgO; complexes and structural diffusion of such complexes byformation and dissociation of hydrogen bonds.The structure diffusion determinesthe observable mobility of the positive charge in liquid water. An analogousmechanism is conceived for the migration of OH- ions. It is assumed that theobserved increase of the proton mobility with increasing temperature under satura-tion pressures 1 up to 160°C, as well as the mobility increase with rising pressure,is a consequence of an enhanced structure diffusion of the H90: complex.Electrolytic conductances of acids in water under elevated pressure have beenmeasured by several authors.4 The measurements of Zisman 5 and of Hamann andStraws6 have been extended to about 12,000 bars at temperatures between 30 and75°C. In order to discuss separately the mobility variation with temperature aswell as with pressure or density, it is desirable to have high pressure conductancedata over a wider range of temperature.For that purpose an apparatus has beenconstructed which permitted conductance measurements with dilute aqueous solu-tions of HCl and &SO4 and of various salts between 45 and 220°C up to 8000 bars.EXPERIMENTALThe main part of the apparatus is a conductance cell which is immersed in a kerosene-filled high-pressure autoclave (fig.1 a). A conventional pressure generating system isconnected with the autoclave which has a Bridgman-type unsupported area-seal with a copperpacking. The kerosene transmitted the pressure to the cell. The electrical lead from theinner electrode is extended out of the autoclave through a thick-walled tube and an in-sulated seal for connection to the conductance bridge. The autoclave is made of a Co-Cr-Ni-Fe-alloy (DEW-ATS 105). Its internal diameter and volume are 1-65cm and17 cm3. It has four deep thermocouple wells drilled into the wall at different positionsOne additional sheathed thermocouple is introduced into the autoclave with its junctionin the kerosene close to the cell.Fig. l b shows the conductance cell in detail. The container for the aqueous solutionis a bellows which has been gold-soldered to the main body of the cell.The bellows andbody are of a palladium-gold alloy (80 % Pd, 20 % Au). The body is connected to the20E . U. FRANCK, D. HARTMANN AND F . HENSEL 201autoclave and is at ground potential. Its inner surface is one of the electrodes. The secondelectrode is a platinum cylinder on a platinum wire insulated from the body by means ofa non-porous tube of very pure sintered aluminium oxide. Small changes of length ofthe platinum wire or of the insulating tube, which may be caused by temperature or pressurevariations, cannot affect the cell constant. The design of the seal using a Teflon packing isevident from fig. 16. It separates the fluid effectively from the pressure-transmitting fluid.Because of the low rigidity of the bellows the pressure differences between the solution andkerosene are negligible.The solution is introduced into the cell using a syringe beforeinserting the central electrode and closing the seal. After filling, the cell is suspended byits electrical lead in the autoclave cavity. The cell constant is about 0.3 cm-1.FIG. 1.-High pressure autoclave (a) and conductance cell (b).The conductance of the solutions was measured with an impedance bridge (WayneKerr Universal Bridge B221 and Low Impedance Adaptor Q 221) in conjunction withfrequency generator (Audio Signal Generator S 221) and tunable indicator (Rhode andSchwarz, type UBM BN 12121/2). The solutions were prepared from water with a specificconductance below 2 x 10-6 cm-1 ohm-1 at 25°C and from chemicals of guaranteed purity.Conductance data were determined at constant temperatui es while the pressure was in-creased and decreased stepwise with intervals of 1000 bars from somewhat beyond satura-tion pressure up to 8000 bals.The pressure was measured by Bourdon gauges (Dreyer,Rosenkranz and Droop, Hannover) which were repeatedly calibrated up to 3000 barsby a dead-weight gauge. At each run the frequency dependence of the conductance waschecked. Variations at frequencies greater than 10 kc/sec were always negligible. Solutionsof KCI, HC1 and H2SO4 were investigated at 45, 75, 100,130, 160, 190 and 220°C. Theinolarity of the initial solutions was always 0.01 or 0.005 (for H2SO4).Additional meas-urements with solutions of lower concentration were considered unnecessary, since only thetemperature and pressure dependence of the conductance was to be examined.RESULTSThe reproducibility of the data obtained for subsequent runs with increasingand decreasing pressure was better than 0.4 % for KCl and HCI solutions and bette202 PROTON MOBILITYthan 0.8 % for HzS04 solutions. Considering all possible sources of error theprobable inaccuracy of the specific conductances should not exceed 1 %. Thecalculated maximum error is & 1.0 % at 45"C, & 1.5 % at 130°C and 1.9 % at220°C. The new data for the specific conductance can be compared with thoseof Zisman 5 for HCl solutions at 75°C and with those of Hamann and Strauss 6I 2000 4000 6000 0000p in barof solutions at 25°C and 1 bar = 0.01.FIG.2.-Equivalent conductivity of KCl in water. Ap at pressure p , A p=l at p = 1 bar ; molarityfor KCl solutions at 45°C. In some parts of the total pressure range the new dataare lower than the previous results by 1-2 %. Preference is given to the new data,since the new cell design is probably better suited to exclude small contaminationsof the solution and to prevent minor variations of the cell constant.The specific conductance IC has been converted into equivalent conductanceA according toA(p,T) = IC(~,T)U(~,T) x 1000~-1.Instead of the specific volume of the solutions v(p,T), the specific volume of purewater has been used. c is the concentration of the solutions in equiv./l.at 25°CTABLE EQUIVALENT CONDUCTANCE h OF KCl, HCI AND H2S04 IN WATER(concentration : 0.01 equiv./l.) in cm2 ohm1 equiv.-1Tin O C 45 75 100 131 160 190 220KC1 200 295 379 484 578 670 74 5HCl 508 678 826 947 1037 1109 1160H2S04 395 435 452 465 482 490 500and 1 bar. The specific volume of water was obtained from the experimental valuesof Bridgman 7 and Kennedy.8 Some of the data had to be evaluated by extrapolationfrom the shock-wave results of Rice and Walsh.E . U . FRANCK, D. HARTMANN AND F . HENSEL 203I I II 2000 4000 6000 8000p in barFIG. 3.-Equivalent conductivity A of HCl in water, A, at pressure p, Ap=l at p = 1 bar ; molarityof solutions at 25°C and 1 bar = 0.01.p in barFIG. 4.-Equivalent conductivity A of H2S04 in water A, at pressurep, Ap-l at p = 1 bar, moIarityof solutions at 25°C and 1 bar=O.005204 PROTON MOBILITYIn fig.2, 3 and 4 the experimental results are presented as functions of pressurefor constant temperatures. The data are the ratios of the equivalent conductanceA, at pressure p over the equivalent conductance at atmospheric pressure.At all temperatures up to 220°C the conductance at saturation pressure could beused for ApSl. These ratios can be converted into absolute values of A, by multi-plication by the equivalent conductances at the saturation pressure given in table 1.DISCUSSIONCONDUCTANCE OF KCl, HCl AND H2S04The behaviour of A (KCl) as demonstrated in fig. 2 is typical for other normalsalts of strong acids and bases.1094 The decrease of the conductance is primarilythe consequence of the increase of viscosity with rising pressure.Since Walden’srule requires that A-q-1 the decrease of Ap/Ap=,l should be identical with thedecrease of ylp=l/ylp with increasing pressure. At least below 100°C, where viscositydata are available, the decrease of the conductance is less steep than that of 17-1,which suggests that the effective diameter of the hydrated ions is reduced at higherpressures. The conductance of HCl solutions behaves differently (fig. 3). Thedecrease with increasing pressure is much less pronounced than that of A (KCl),and below 130°C there is even an initial increase of A(HC1) with pressure. Thisbehaviour is ascribed to the abnormal proton mobility and will be discussed below.As is shown by fig.4, the conductance of dilute sulphuric acid is generally increasedwith rising pressure. There are considerable differences in slope, however, atdifferent temperatures. This behaviour is the result of the combined pressuredependences of viscosity of water, abnormal proton mobility and dissociation ofHSO; ions.PROTON MOBILITYIn order to demonstrate the contribution of the protons to the conductance ofthe HC1 solutions, either the “ proton conductivity ” I.(H+), or the “ excess con-ductivity ” of the protons AE(H+) can be used :A(H+) eA(HC1)- t-A(KCl),&(H+) A(HC1) - A(KC1).t- is the transport number for C1- ions in KCl solutions, which is here taken asequal to 0.5 for all temperatures and pressures. A(H+> and AE(H+) have been plottedin fig.5 . When AE(H+) is used, one assumes that there is a “ normal ” contributionto the mobility of the positive charge which is at all temperatures and pressuresequal to the mobility of the potassium ion. Although this assumption is certainlyquestionable, I&€+) will be discussed in accordance with previous usage.1It appears reasonable to look at AE(H+) not as a function of pressure but as afunction of the density of water, p . Thus AE(H+) =f(p,T) is plotted in fig. 6, andtwo conclusions are drawn.THE DENSITY DEPENDENCE OF AE(H+) is positive in whole temperaturerange. The increase with density is almost linear and not too different at all tem-peratures. With increasing density the number of water molecules in the immediatevicinity of the H90 ;t -complexes increases, which should facilitate the structuraldiffusion of these complexes.At lower temperatures, high pressures may dis-integrate water clusters producing unbonded molecules which could be the reasonfor slightly higher values of d&/dp at lower temperatures, as derived from theslopes of the isotherms of fig. 6E. U. FRANCK, D . HARTMANN AND F . HENSEL800700600500300 2000 4OOO 6000I 1'0° ZOm 4OW 6000 8000p in barFIG. 5.-" Proton conductivity ", A(H+) = A(HC1) - r-A(KCl), and " excess conductivity " ofprotons, AE(H+) = A(HC1)- A(KC1) as a function of pressure and temperature.p in g/cm3 Tin "CFIG. 6.-" Excess conductivity ", AE(H+), of protons as a function of water density p and of tem-perature ; - - - coexistence line of liquid and vapour.THE TEMPERATURE DEPENDENCE of &(H+) is very similar for all densitiesinvestigated. It is positive and very pronounced from 45 to 130°C.The temper-ature dependence is almost zero between 130 and 220°C. There may be a flatmaximum of AE(H+) at the highest temperatures206 PROTON MOBILITYFrom the slope of the AE against T curves between 45 and 130°C, " activationenergies " between 1300 and 1800 cal/mole can be formally derived at the differentconstant densities. This increase of AE with temperature at constant densities maybe due to the disintegration of water clusters and also due to an accelerated additionof unbonded water molecules to the HgOi-complexes.A decision may be possibleif recent infra-red determinations of the percentage of unbonded molecules in purewater can be extended to higher pressures.ll.12 The flat maxima of AE beyond150°C may be caused by dissociation of the weakly bonded water molecules in thehydration sphere of the H90i complexes. It is improbable that these complexesthemselves begin to decompose at such temperatures. Previous conductancemeasurements seem to indicate that no observable contributions of AE(H+) remainat 600°C and water densities below 0.7 g/cm3.13DISSOCIATION OF HSO,The second dissociation constant K2 of sulphuric acid has been derived. Thedetails are discussed elsewhere.14 Additional measurements of A(K2S04) wereused for this purpose,14 together with several assumptions : (i) the conductivity ofthe hydrogen ion can be taken from the investigations discussed above; (ii) theactivity coefficients fH+, f&o; and fs0:- can be derived from the Debye-Hiickeltheory; (iii) the relation A(HS0,) = 0.65 A(SOi-) is sufficiently valid in the wholeregion of temperatures and pressures.15TABLE 2.-sECOND DISSOCIATION CONSTANT K2 OF SULPHURIC ACIDin mole 1.-1 x 103pressure, bar 45°C 100°C 160°C 190°C4000 55.93 10.19 1-97 0.728000 7 9 14 47-59 10.36 4-*701 6-840 0.821 0.161 0.086Using the degree a of dissociation of the HSO, ion, and the molarity rn of thesulphuric acid solution, the constant K2 in mole 1.-1 for the reaction HSO;+H++SOi- follows fromThe &-values obtained for saturation pressure agree within about 15 % with thedata derived from the silver sulphate solubility results of Lietzke, Stoughton andYoung.161 Gierer and Wirtz, Ann.Physik, 1949, 6, 258.2 Conway, Bockris and Linton, J. Chem. Physics, 1956,24, 834.3 Eigen and De Maeyer, Proc. Roy. SOC. A , 1958,247,505.4 Hamann, Physico-Chemical Efects of Pressure (Butterworths Sci. Publ., London, 1957).5 Zisman, Physic. Rev., 1932, 39, 151.6 Hamann and Straws, Trans. Faraday SOC., 1955,51, 1684.7 Bridgman, The Physics of High Pressure (G. Bell and Sons, London, 1952).8 Kennedy, Amer. J. Sci., 1950, 248, 540 ; 1954, 252, 225.9 Rice and Walsh, J. Chem. Physics, 1957, 26, 815.10 Franck and Hensel, 2. Naturforsch., 1964, 19a, 127.11 Nemethy and Scheraga, J. Chem. Physics, 1962, 36, 3382.12 Luck, Ber. der BEnsengeseIlschaft 1965, in press.13 Franck, Z. physik. Chem., 1956, 8, 192.14 Hartmann, Diplomarbeit (Karlsruhe, 1964), to be published in Ber der BiinsengeselZschafi 1964.15 Shtrill and Noyes, J. Amer. Chem. SOC., 1926, 48, 1861.16 Lietzke, Stoughton and Young, J. Physic. Chem., 1961, 65, 2247