Ionization of Moderately Strong Acids in Aqueous SolutionPart 2.-Further E.1m.f. Studies of the Dissociation of the Bisulphate Ion tBY A. K. COVINGTON,* J. V. DOBSON AND K. V. SRINIVASAN $Dept. of Physical Chemistry, School of Chemistry,Newcastle upon Tyne, Newcastle NEl 7RUReceived 13th June, 1972New measurements on the cell :Pt,H2 I Na2S04, NaHS04, NaCl I AgCl I Aghave failed to substantiate the original measurements made by Hamer forty years ago and sub-sequently reanalysed many times. The range of vaIues for the dissociation constant of the bisulphateion (K2 of sulphuric acid) is substantially in agreement with that obtained from the simpler cell inwhich sodium chloride was omitted and the mercury-mercury(I) sulphate reference electrode wasused. Kz = 0.0113+0.O005 mol kg-l at 25°C where the uncertainty arises from a range of reason-able choices for the ion-size parameter.Sulphuric acid and its second ionization constant (KJ, the dissociation constantof the bisulphate ion, have been the subject of a considerable number of investigationsbut with justification because of the importance of this electrolyte.The originale.m.f. studies of Hamer have been extensivelyreanalysed 2-5 but only the latter have been repeated.6 It is now well establishedthat the value of K2 obtained from e.m.f. studies is dependent on the ion-size para-meter in the Debye-Huckel equation used to estimate the activity coefficient terms.Covington, Dobson and Wynne-Jones studied a similar cell to that used by Hamer,hoping to achieve a simplification by using the mercury-mercury(1) sulphate referenceelectrode and thereby making the mixed electrolyte simpler by omission of chloride :For the same choice of ion-size parameter the results for K2 were higher than thoseobtained from Hamer’s cell :H2 1 NaHS04(m,), Na,SO,(m,), NaCl(m,) I AgCl I Ag.Reanalysis of the results on the acid-acid cell of Davies, Jones and Monk,2restudied by Nair and Nancollas Since theactivity term is different for each cell there is no reason to expect concordant valuesfor a given choice of ion-size parameter, nevertheless the spread is large (see table 2of ref.(4)). Particularly puzzling, however, was the large slope obtained in the re-analysis of Hamer’s data when the dissociation quotient, corrected for Debye-Huckel interactions (pKi) was plotted against ionic strength (see fig.2 of ref. (4)) incontrast to the smaller slopes from the other two cells. Further, Hamer’s resultst Part 1, A. K. Covington, J. G. Freeman and T. H. Lilley, J. Phys. Chem., 1970, 74, 3773.$ present address : University of Patna, Patna 5, India.94and of Davies, Jones and MonkH2 I NaHS04(m1), Na2S04(m2) I Hg2S04 1 Hg*H2 I H a HzS04 I Agcl I Aggave values falling between theseA. K . COVINGTON, J . V. DOBSON AND K . V. SRINIVASAN 95show curvature on such plots at ionic strengths above 0.2, which was unexpected.Accordingly it was decided to repeat Hamer's work.EXPERIMENTALThree series of measurements were made in which (i) ml = mZ = m3 (ii) ml = m3 # m2(iii) ml # mz # m3.In the first two series, buffer solutions were prepared from sodiumsulphate+ hydrochloric acid. In the third series anhydrous sodium sulphate and constantboiling distillates of sulphuric acid and of hydrochloric acid were used. The first series isan exact repeat of Hamer's conditions. Each solution was prepared separately and not bydilution of a stock solution.Sodium sulphate (A.R.) was recrystallised twice from conductivity water and dried at110°C. It was then heated to near fusion and allowed to cool in a desiccator over phos-phorus pentoxide. Its purity was checked by titration of the effluent from a cation exchangecolumn (H form) with standard sodium hydroxide in a nitrogen atmosphere using the Radio-meter automatic titration apparatus. Sodium chloride was recrystallised and purified in asimilar manner.The preparation of constant boiling acid distillates has been describedel~ewhere.~~ * The sulphuric acid composition was also checked titrimetrically.Hydrogen and silver-silver chloride electrodes were prepared as previously de~cribed.~,Bias potentials were checked before and after the experiments using comparison electrodesstored continuously in 0.01 mol kg- hydrochloric acid. Silver-silver chloride electrodesdeviating more than 0.02 mV from the standard electrode were discarded. Measurementsin the solution mentioned above lo versus hydrogen electrodes showed the standard potentialto be 222.37 mV at 25°C.Three-way cell vessels were employed with the compartments separated by a tap.Eachcell contained one hydrogen and two silver-silver chloride electrodes, whose bias was checkedin each solution. Cells were rinsed three times with solution before filling and placing in thethermostat bath controlled at 25.OOk 0.01"C. Nitrogen and hydrogen with adequatepresaturation were bubbled continuously through the appropriate cell compartments.Measurements were made with a vernier potentiometer (Cambridge Instrument Co. Ltd.)and sensitive galvanometer (Tinsley type 4500L). The standard cell was frequently checkedagainst an N.P.L. certificated laboratory standard. Pressure corrections were made in theusual manner.ll Cells once they had reached steady values, which usually took about anhour, maintained these (k0.03 mV) for two hours.RESULTSExperimental results are given in table 1.The e.m.f. ( E ) of the Hamer cell isgiven by :where k = (RTln 1O)/F, and y with appropriate subscripts represents activity co-efficients.mso4 = m2+mlj; mHso4 = m , - m H ; m,, = m 3 , mNa = rnl+2m2+ni3The individual ionic molalities are :and the ionic strength Z = 2mH + 3m2 + m, + m3.Introducing the equation :for each ionic species i, where p is termed the ion-size parameter, gives from eqn (1) :(E-E")/k = -log n~Hm3 +2A13/(1 +PI*). (3)The dissociation constant of the bisulphate ion is defined as :KL = mHj%04YHYS04 /tk?HS04]1HS0496 IONIZATION OF A C I b S IN AQUEOUS SOLUTIONTaking logarithms and substituting from (2) gives :m,(m, + m,) 4AI*P K ~ = -log +------- rn,-mm, 1+p1+ (4)where the prime on pK2 denotes the fact that since eqn (2) does not include a termlinear in I, pKi may be expected to vary linearly with I.An Algol programme waswritten for the English Electric KDF9 computer to solve iteratively eqn (3) for mHand I =f(mH) for various choices of the ion-size parameter p. For each p, valuesof pKi calculated from eqn (4), against I were fitted using a linear least squaresprogramme to yield pK2 values. The values k = 59.159 mV and A = 0.5107mol-3 kg* at 25°C were Values of pK; for p = 1 .O and 1.5 are given in table 1.Some values are plotted in fig. 1, where comparison is made with previous work.Results for pK2 from the various studies are collected in table 2.4.9998.5229.96317.96817.96729.80934.7005.5468.28213.91817.8302.0616.10510.15814.23422.2444.9938.5109.95817.95117.94729.77434.6625.6268.40214.11918.0871.8945.7949.70413.63321.3324.9998.5229.96317.96817.96729.80934.7002.3733.5445.9557.6282.0616.10510.15814.23422.24451 1.60488.69482.21457.75457.55436.72430.80528.8951 1.70489.97479.90550.88502.7248 1.01467.01448.49103mHPKi103mHPK5103mHPK51 0 3 ~ ~PK’,103mHPK5103mHPKi103mHPKi103mHPKi103mHPK’,103mHPKb103mHPK5103mHPKi103mHPKi103mHPKi103mHPK‘,1 0 3 ~ ~PKip = 1.03.6971.9195.7601.9126.5 181.91610.5591.90610.5981 A9716.1191.87718.0801.8833.9811.9255.5411.9188.4321.90810.2321.9101.7321.9294.3921.91 86.6981.9088.7901.90613.1321.890p = 1.53.6011.9435.5371.9356.2351.9389.8311.9269.9071.91714.6691.89416.3031.8973.8771.9465.3441.9387.9981.9279.6091.9261.71 11.9544.2621.9426.4071.9318.3061.92812.1541.91A . K.COVINGTON, J . V. DOBSON AND K. V. SRINIVASAN 97TABLE 2.-vALUES OF pKz FOR VARIOUS VALUES OF pp = 1.0 p = 1.3 p = 1.5 p = 1.7Hamer (recalc.) 1.983 1.996 2.004 2.01 1this work 1.929 1.946 1.954 1.964ref. (4) 1.936 1.952 1.963 1.972DISCUSSIONIt is clear from fig. 1 and table 2 that the new results for pK2 are considerablylower than those of Hamer and further that the slopes of the plots of pKk against Zare smaller than those obtained from reanalysis of Hamer’s results.The new resultsare more in accord with those of Covington, Dobson and Wynne-J~nes,~ althoughnot coincident for the same choice of p. However, concordent values can be ob-tained for slightly different choices of p , e.g. pK2 = 1.954 for p = 1.5 for this workand pK2 = 1.952 for p = 1.3 from the mercury(1) sulphate cell data (see also fig. 1).One might have expected the smaller p value for the solutions containing chlorideion in that the mean distance of closest approach should be smaller when chlorideions and the larger sulphate ions are mixed but this comment is naive and placestoo much faith in the physical significance of the ion-size parameter...- “.-..........-I .....................-\1.88 -\\ I I I I I \ f0.I 0.2Z/moI kg-lFIG. 1 .-Extrapolation of data from the Hamer cell : 0, this work ( p = 1.0) ; 0, this work ( p = 1.7) ; A, this work ( p = 2.5). (No attempt has been made to distinguish the points from the separateseries as these obviously fall on the same straight line.) - - -, results of Hamer ‘ ( p = 1.0) ; - - -,results of Covington, Dobson and Wynne-Jones ( p = 1.5). This figure is plotted on exactly thesame scale as fig. 2 of ref. (4) where experimental points are included for previous work.’.The new results show a scatter about straight lines of less than 0.1 mV, somewhatbetter than do Hamer’s results,l and it remains to examine reasons for the discrepancy.The new results were obtained from three different series of measurements, that isfrom three separate series of solutions with different molality ratios whereas Hamerused only one stock solution and diIuted it.His analysis of hydrochloric acid wasgravimetric for chloride and for sodium sulphate he weighed the residue afterevaporating to dryness and fusing the salt in a muffle furnace. Less satisfactory,however, was the technique of evacuating the solutions to expel dissolved gases whensomc loss of water could have taken place. We believe that an error in stock solutionmolalities is the most likely cause for the discrepancy. A similar explanation wasI 98 IONIZATION OF ACIDS IN AQUEOUS SOLUTIONsuggested by Prue and Read,12 who were unable to reproduce results for formic acidobtained l3 in the Sterling Chemistry Laboratory at Yale in the same period.Indeeddifficulty has been experienced in substantiating two other sets of data 14* l7 fromHarned's group.We conclude that pR2 = 1.945&0.015 or K2 = 0.0113+0.0005 mol kg-' fromthe present measurements where the uncertainty represents a range of p values of1.0 to 1.7. This does not preclude a somewhat higher value being considered moreappropriate, indeed for p = 2.5 the standard deviation of pK; against I plots has aclear minimum and pK2 = 1.995. In a following paper we shall present some newdata for K2 obtained from spectrophotometric studies.One of us (K. V. S.) thanks the University of Patna for study leave (1965-8).' W. J. Hamer, J, Amer. Chem.SOC., 1934,56, 860.C. W. Davies, H. W. Jones and C. B. Monk, Trans. Faraday SOC., 1952,48,921.W. J. Hamer in Structure of Electrolytic Solutions, ed, W. J. Hamer (Wiley, New York, 1959),p. 236.A. K. Covington, J. V. Dobson and W. F. K. Wynne-Jones, Trans. Faruday SOC., 1965,61,2057.H. S. Dunsmore and G. H. Nancollas, J. Phys. Chem., 1964,68, 1579.V . S. K. Nair and G. Nancollas, J. Chem. SOC., 1958,4144. ' C. W. Foulk and M . Hollingworth, J. Amer. Chem. SOC., 1923,45, 1220.K. Kunzler, Anal. Chem., 1953, 25,93.A. K. Covington and J. E. Prue, J. Chem. SOC., 1955,3696.lo R. G. Bates, E. A. Guggenheim, H. S. Harned, D. J. G. Ives, G. J. Janz, C. B. Monk, J. E.b e , R. A. Robinson, R. H. Stokes and W. F. K. Wynne-Jones, J. Chern. Phys., 1956,25,361;1957,26,222.I-). J. G. Ives and G. J. Janz, Reference Electrodes (Academic Press, 1961), pp. 95-6. '' J. E. Prue and A. J. Read, Trans. Faruday SOC., 1966, 62,1271.l3 H. S. Harned and N. D. Embree, J. Amer. Chem. SOC., 1934,56,1042.l4 H. S. Harned and W. J. Hamer, J. Amer. Chem. SOC., 1935,57,27.l6 W. H. Beck, K. P. Singh and W. F. K. WynneJones, Tram. Faraday SOC., 1959,55,331.l7 A. K. Covington, J. V. Dobson and W. F. K. Wynne-Jones, Truns. Furaday SOC., 1965,61,2050.W. J. Hamer, J. Amer. Chem. SOC., 1935,57,9