NOTES
1579
ethylene. It appears that propylene is not formed from ethylene during the radiolysis.
Table 11: YieldB of Ethane-CI4 and Ethylene-Cl' from the Radiolysis of Methane-Cld a t 100 mm. Pressure in the Presence of Added Ethylene
% CaH, added
Aboorbed dose (e.v./g. of CHI) X 10-19
0.17
2
0.06 0.05
4
0.04 0 . 04a 0.03 0.03 0.02 0.02
2 9
43 2 2 2 2
C?(C'4eHs), molecules/ 100 e.v.
C""I4/ C"sHa
0.66 1.7
0.98
0.83 1.2 1.9
0.85 0.71 0.07 0.91 0.76
1.1 1.7 1.5 0.85
0.57
0.66 0.73
Acknowledgment. The author wishes to express his appreciation to Dr. Richard Holroyd for helpful discussions on this study.
C'4sH4 (cor.)/ C14rHs
0.98 0.84 0.85 0.99 1.16 0.91 0.93 0.86 1.14
a The 1 mc./mmole sa,mple of methane-c" was used in thiei experiment. Other experiments listed here employed the 2; mc./mmole sample.
(17) If a value of 2 is assumed for the yield of ethane in methane radiolysis and if, as is suggested by the methane-ethylene-Cl4 results, one third of the ethane observed is produced from ethylene then the initial yield of ethylene calculated from its relative yield is 1.3 molecules/100 e.v. which is in agreement with values (G = 1.4 and 1.5)suggested previously10 in studies of the irradiation of methane in the presence of added propylene and acetylene, respectively.
Dissociation of the Bisulfate Ion1
by H. S. Dunsmore Chemistry Department, The University, Glasgow W . 8, Scotland
and G. H. Nancollas ane-C14 radiolysis (G = 1.5). However, it is not unreasonable since, as demonstrated by the results of the methane-eth~1ene-C'~radiolysis, some ethane is produced from ethylene. (The yield of unlabeled ethane produced from unlabeled ethylene was not measured in the ethylene-methane-C14 radiolysis.) Using the value of 1.2 for the yield of ethane-CI4, the initial yield of ethylene is then 1.1 molecules/100 e.v.17 Other labeled products obtained in the radiolysis of methane-C14 in the presence of unlabeled ethylene included acetylene, propane, propylene, and isobutene. If propane is considered to be singly labeled as suggested by the results of the methane-eth~1ene-C~~ experiment, then an enhanced relative yield, (CHgCHZC14H3/ C142H6) = 1.6, is obtained. Assuming complete labeling, the yields of unsaturates also appear to be enhanced: L e . , (G1'12H~/C142H6)= 0.1 ; (C1'&&/ = 0.08. (These C1d2H6)= 0.2; and (i-C144H8/C14zHB) yields are approximate and could be in error by more than SO%.) The yields of propane and unsaturates are expected to be high, however, due to the relatively large quantities of added ethylene present during the radiolysis. The present study clearly demonstrates that both ethylene and propylene are important products in methane radiolysis. Ethylene appears to be a primary nlolecular product with an initial yield of approximately 1.1 molecules/lOO e.v.; however, a significant fraction of the ethylene produced is converted during the radiolysis to ethane and propane. Propylene Of pure methane and was produced in the in radiolysis of methane ln the presence of added
Chemistry Department, Brookhaven National Laboratory, Upton, New York (Received November 8 , 1963)
The second dissociation constant of sulfuric acid, K z , has been the subject of extensive study and discussion. The bisulfate ion is relatively highly dissociated and in calculating the therniodynainic equilibrium constant, which may be approxirnated by
(1) much depends upon the choice of parameters, B and C, in the activity coefficient e x p r e s s i ~ n . ~I n~ ~eq. 1, I is the ionic strength, and A and B are the usual Debye-Huckel constants. Some of the earliest work on sulfuric acid was that of Sherrill and i?rTogre~,~ who combined transference number and conductance data and obtained a value K z = 0.0115 mole 1.-I a t 25'. Assuming the first hydrogen to be completely ionized, they expressed the degree of dissociation, a,by the equation (1) Research performed in part under the auspices of the u. S. Atomic Enerm -" Commission. (2) V. 8. K. Kair and G . H . Nancollas, J . Chem. Soc., 4144 (1958). (3) w. J. Hamer in "The Structure of Electrolyte Solutions," w. J. Hamer, Ed., John Wiley and Sons, Inc., New York N. Y . , 1959, p. 236. (4) M. S. Sherrill and A. A. Noyes, J . Am. Chem. Soc., 48, 1861 (1926).
Volume 68, Number 6
June, 1964
NOTES
1580
a
(A
+ AT
- AH)/(AH
+ Aso,)
AHSO, = (A - AT - a h s o , ) / ( l - a )
where T is the stoichionietric transference number, and for the sulfuric acid solution, A is the observed conductance and AH, Aso,, and AHSO,are the equivalent conductances of H+, Sod2-, and HS04- ions, respectively. The dissociation quotient K,’ ( = [H+]. [Sod2-]/[HSOd-]) was calculated at each ionic strength, and Kz was obtained by extrapolation on a plot of log Kz’ against Ill’. Kerker5 has extended the calculations to other temperatures and to ionic strengths as high as 4.43 M . The method, however, is open to serious objection since it is impossible to correct for ion pairing in such concentrated sulfate solutions with any certainty. In addition it was assumed that the equivalent conductances of H + and s04-’ ions could be obtained from HCI and KzSOd data at the same ionic strength as that prevailing in the sulfuric acid solution under consideration. Using a high-speed DEUCE electronic computer we have recalculated the conductance and transference number data for concentrations below 0.05 m. The Kz’ values are in close agreement with those obtained by Kerkerj6 although the calculated AH SO^. given in Table I, show marked differences. AH and Aso4 a t each concentration were interpolated from ionic strength plots of HC1 and K2S04 conductance data. The steepness of these curves made estimation difficult at I < 0.01 M and, taking this into consideration, the best extrapolated K z = 0.0104 mole kg.-’; Kerkerj obtained 0.0102 mole kg.-I. Table I : The Dissociation Constant and Equivalent Conductance of HSOa- a t 25”
x loa 102Kz’(this work)
5.00 6.25 1.67 1.75 A ~ ~ ~ ~ ( t h i s w o r k4)1 . 7 41.6 102Kz’(Kerker) 1.69 , , , AH604 (Kerker) 46.8 ..,
MH28Oa
12.50 2 5 . 0 0 50.00 2.06 2.55 3.36 40.2 39.0 38.0 2.09 2.53 3.38 45.3 39.8 38.7
A number of electromotive force studies have been made in cells without liquid junction of the type Hz, PtlHC1, XI AgCl, Ag. Hanier,G using X = Na2SO4, obtained K, = 0.0120 mole kg.-I which was in poor agreement with 0.0104 from ~pectrophotonietry.~ Moreover, the temperature coefficient led to a heat of ionization, AH” = -2.2 kcal. mole-I, very different from the calorimetric value, -5.2 kcal. mole-’, of Pitzer.8 Davies, Jones, and NonkQhave recalculated Kamer’s e.ii1.f. data with allowance for the forniation of KaS04- ion pairs and obtained K z = 0.0102 mole The Journal of Physical Chemistry
kg.-I. Mixed acid cells in which X = HzS04 do not suffer from the disadvantage of secondary-ion association and two such studies have been made.2r‘0 The derived K Zvalue is markedly dependent upon the choice of parameters in eq. I ; assuming B& = 1, all the data have been recalculated using the computer programmed to yield the C value for zero slope of Kz us. I plots, a least-squares procedure being used. The results are summarized in Table 11. Although Monklo had suggested that, using C = 0.2, there was a definite change with ionic strength in the Kz values obtained by Yair and Nancollas, it is quite clear that a common C = 0.36 yields self-consistent K z values for all the available e.m.f. data. The use of C = 0.3 in the Davies equation Table I1 : The Dissociation Constant of HS0,- a t 25” Davies, Jones, and Monka
Best C value Mean K2 X l o 2 a
See ref. IO.
0.36
1.020 i 0 . 0 1 3
Nair and Nancollas
0.36 1 . 0 4 6 f 0.009
* See ref. 2.
for activity coefficients has already been proposed by DavieslI in the light of recent activity data. When X = HzS04,plots of Kz against I for different C values give a series of converging curves with the best C showing zero slope. For the sake of comparison, the computer program was then altered to set C = 0 and vary B&. Another series of convergent curves of K Zus. I was obtained, with B& = 1.59 giving zero slope and K z = 0.0102, again by a least-squares procedure. This leads to a value of 4.8 for & and extrapolated Kz values ranging from 0.0109 for B& = 1 to 0.0092 for B& = 2.5. This is shown in Fig. 1. Hamer observed nonconvergency of log K z us. I plots of his data (X = YazS04) when various & values were inserted in the activity coefficient expression, but he omitted using the same parameter in the calculation of H + activity as he used in the calculation of SO4+ activity. Recalculation of Hamer’s data ~
~~
(5) M. Kerker, J . Am. Chem. Soc., 79, 3664 (1957). (6) W. J. Hamer, ibid.,5 6 , 860 (1934). (7) I. M. Klotz and C . R. Singleterry, Theses, University of Chicago, 1940; quoted by R. A. Robinson and R. H. Stokes, “Electrolyte Solutions,” Butterworth and Co., Ltd., London, 1959. (8) K. S. Pitzer, J . Am. Chem. Soc., 59, 2365 (1937). (9) C. W. Davies, H. W. H . Jones, and C. B. Monk, Trans. Faraday Soc., 48, 921 (1952). (10) C. B. Monk, “Electrolytic Dissociation,” Academic Press, London, 1961. (11) C. mi. Davies, “Ion Association,” Butterworth and Co., Ltd.. London. 1962.
NOTES
1581
-
Table 111: T h e Dissociation of HSOd- a t Higher Ionic Strengths
I 102K2'(ref. 12) 1O2K2'(eq.2)
--
Bd
- Bd
1.0
0
= 1.59
102.
Figure 1. Variation of Kz with I when various Bd values are used in the activity coefficient expression.
using consistent parameters and a,lso allowing for SaS04- still shows that for this cell there is no convergency. The data of Nair and Nancollas2 at 0' were also recalculated varying Be, and zero slope was obtained with Bd = 1.6. This value was used to obtain Kz a t all the other temperatures. A leastsquares method then gave AH = -5.3 kcal. mole-' and A S = -27.0 cal. deg.-' mole-', which may be compared with the uncorrected values, -5.6 kcal. mole-' and -27.7 cal. deg. -l mole-', respectively. The agreement with Pitzer's values,* AH = -5.2 kcal. mole-' and A S = -26.3 cal. deg.-' mole-', is very good, but is not so satisfactor,y with those of Austin and Mair.I2 Recently, Reynolds and F u k ~ s h i i n a 'have ~ redetermined K2 a t various ionic strengths using a spectrophotometric method. Their data, when plotted according to eq. I, show an appreciable curvature with an extrapolated Kz = 9.4 X IOp3 mole l.-'. These authors, however, assumed K2 = 0.0102 and expressed its variation with ionic strength by the equation 10gKz'
=
-1.991
0.250 3.62 3.70
0.750 5.64 5.60
1.53 7.36 7.41
It is clear from the above calculations that the best value of K z is 0.0103 f 0.0001 mole kg.-'. Conductometric, spectrophotometric, and potentiometric values all fall within this range showing very good agreement for such a highly dissociated ion. Lietzke, Stoughton, and Young14 have calculated the dissocjation constant of the bisulfate ion from solubility determinations of silver sulfate in sulfuric acid a t temperatures between 25 and 225'. Although the method is least precise near room temperature when the dissociation is greatest, they give the same value, K 2 = 0.0103 mole kg.-' as the best average at 25'. Acknowledgment. We wish to thank Dr. R. W. Dodson for valuable discussions.
2.0
1.0
I x
= 1.5
0,100 2.57 2.70
+ 2.041"2/(1 + 1.7OI"') + 0.03141 (2)
Experimental and calculated values are compared in Table 111, and it is seen that deviations are appreciable at the lower ionic strengths.
(12) J. .M.Austin and A. D. -Mair, J . P h y s . Chem., 6 6 , 519 (1962). (13) W. L. Reynolds and S. Fukushima, Inorg. Chem., 2 , 176 (1963) (14) M. H. Lietrke, R. W. Stoughton, and T. F. Young, J . Phus. Chem., 6 5 , 2247 (1961).
The Conductance of Tetra-n-butplammonium Picrate in Chlorobenzene at 25'
by J. B. Ezell and W. R. Gilkerson Department of Chemistry, University of South Carolina, Columbia, South Carolina (Received Sovember 18, 1565)
The limiting equivalent conductance, ito, of a salt may be much smaller due to the "FUOSS" effect' in solvents of low dielectric constant (less than 7, generally) than one would estimate assuming the Walden product for the salt, AOVO,where 7 0 is the solvent viscosity, to be independent of solvent. If so, this would greatly affect values of the ion pair dissociation constant of the salt, K , reported in the literature. h report2 from this laboratory indicated low values of A. (as much as 50% below the estimate based on the Walden product) for tetra-n-butylammonium picrate (1) R. M . Fuoss, Proc. 'L'atl. Acad. Sei. U . S . , 45, 8 0 i (1959). ( 2 ) W. R. Gilkerson and I?. E. Stnmm. J . A m . Chem. S o c . , 8 2 , 5295
(1960).
Volume 88, -\-umber 6 J u n e , 1,964
