2061
NOTES
Dec., 1959
modynamic data available in the l i t e r a t ~ r e . ' ~ - ~ ~ For acetone-carbon tetrachloride isobaric boiling pointicomposition data were used. For the remaining systems, isothermal data were available at the temperature required. At the present time, the belief is generally held that the gradient of the chemical potential constitutes the effective driving force for diffusion. The. process of self diffusion, however, is visualized as the movement of molecules in a thermodynamically homogeneous environment such that the chemical potential gradient for the diffusion process is unity. From this it follows that self diffusivities are related to mutual diffusivities through this gradient, a principle first announced by Darken0 and recently reiterated by Carman and Stein.3 The experimental data obtained in this study were applied to Darken's proposed relationship between self and mutual diffusivities Dia = (DiXa
+ DnXdd In alld In XI)
It is apparent that, although the shape of the curve
and the location of the minima are predicted correctly for non-ideal systems, the over-all effect of the activity term is to over-correct the predicted values. This is true for both positive and negative deviations from Raoult's law since both cases are exhibited here. One would expect better agreement between theory and experiment for ideal systems. It is surprising to note, however, that for the nearly ideal system, benzene-carbon tetrachloride, theory predicts a non-linear diffusion curve, while the experimental data are linear. It seems certain from these results that the relationship between diffusion and chemical potential is not as simple as previous investigators have believed. These discrepancies between theory and experiment probably are due in part to association of the diffusing molecules. However, the difficulties in describing the diffusion mechanism for associated systems are many since one must obtain quantitative results as to the degree of association and relate these results to diffusion phenomena. At present the authors are working on this problem with encouraging results and will submit a report on it later. (12) H. Rack and W. Schroder, 2. physik. Chem. N . F., 11, 41 (1957). (13) K. C. Bachman and E. L. Simmons, Ind. En& Chem., 44, 203 (1952). (14) A. L. Edwards, B.S. Thesis, University of Washington, 1954. (15) F. Ishikawa and T. Yamaguchi, BUZZ. Inat. Phys. and Chem. Res. (Tokyo), 17, 246 (1938).
PROTON RESONANCE SHIFTS OF ACIDS I N LIQUID SULFUR DIOXIDE BY S. BROWNSTEIN' AND A. E. STILLMAN Department of Chemistry, Cornell University, Ithaca, New York Received M a y 8 , 1060
It is desirable to have a simple means for determining the dissociation constants of strong acids. A correlation between the change in frequency of the proton resonance signal of an acidic hydrogen and the dissociation constant of that acid has been (1) Division of Applied Chemistry, National Research Council, Ottawa, Canada.
- 200 6
4
2
0
-2
,
-4
-6
-8
-10
PK.
Fig. 1.-Dependence of chemical shift upon acid strength: The chemical shift is in cycles per second a t a resonance frequency of 40 megacycles.
obtained for several strong acids in aqueous solution.2J Since there is rapid exchange between the protons of the acid and those of the solvent only a single resonance line is observed for both these species. By measuring the chemical shift of this line at a variety of acid concentrations the dissociation constant for the acid may be estimated. This method is especially useful for strong acids, where most other methods are not too good. It was thought that if a solvent not containing exchangeable protons was used, a single measurement might suffice to determine an approximate acid dissociation constant. Liquid sulfur dioxide was chosen as solvent since a wide variety of compounds is soluble in it. Although relative acid strengths in liquid sulfur dioxide need not be in the same order as in water nevertheless it was found that an excellent correlation exists between the dissociation constant of an acid in water and its proton resonance shift when dissolved in liquid sulfur dioxide. Experimental The proton resonance s ectra were obtained in a manner described p r e ~ i o u s l y . ~'#he side band modulation6 was generated by a Heathkit Square Wave Generator, Model SQ1. After the frequency was adjusted for superposition of the side band with the peak due to the acid proton the ulses from the square wave generator were counted on an fnstrument Development Laboratories Model 161 Scaling Unit. The modulating frequency could be adjusted to within one cycle per second and its value determined within one tenth of a cycle per second. The sample cell was the inner tube of a precision bore concentric tubing assembly6 to which was attached a male (2) H. S. Gutowsky and A. Saika, J. Chen. Phys., 21, 1688 (1953). (3) G. C. Hood, A. C. Jones and C. A. Reilly, THISJOURNAL, 68,
101 (1959), contains earlier reference@. (4) 8. Brownstein, J. Am. Chem. Xoc., 80, 2300 (1958). (5) J. T. Arnold and M. E. Packard, J. Chem. Phys., 19, 1608 (1951). (6) J. R. Zimmerman and M. R. Foster, THIS JOURNAL, 61, 282
(1957).
NOTES 6/20 standard taper joint. With a known weight of acid in it, the cell was pIaced on a vacuum line and sulfur dioxide condensed into it a t -60'. The cell was capped quickly and the weight of sulfur dioxide determined. The reference for the chemical shifts was benzene. in the annular space between the concentric tubes. The shifts are in cycles per second with the more positive values at higher field. Diamagnetic susceptibility corrcctions were made in the usual manner.? The volume magnetic susceptibilities of the solutions were calculated from those of the pure components assuming ideal behavior. Even if the diamagnetic susceptibilities are not exactly additive only a small error would be introduced.
Results The correlation between chemical shifts of the acidic proton and the pK of the acid in aqueous solut,ion are shown in Fig. 1 and in Table I. The chemical shift for acetic acid was found to be constant up to a concentration of a t least 7.40 molal. None of the determinations listed were made for concentration higher than 4.70 molal to assure the absence of concentration effects on the chemical shift.
Vol. 63
exchange of acid and water protons is no longer affecting the observed chemical shift. A general treatment of shifts in line positions due to proton exchange has been presented.s Simplifying assumptions were made and an equation obtained that related displacement of the lines of two species in equal concentration with the rate of exchange of the two species. For the case where the mole fractions of the exchanging species are not equal, but the line widths are small compared with the distance between them, one obtains
-
AW[~T~(A.W ~ ~) ~(
bf w 21 ) ~
SW(@B
- PA)
The symbols have the same meaning as in ref. 8. From this one may calculate that a 2.13 molal solution of 60% perchloric acid in liquid sulfur dioxide has the proton exchange rates ~
E
= ~ 2.05 O sec.-l
~ H C I O=~
15.0 set.-'
These exchange rates are in a convenient region for measurement by proton resonance spectroscopy. Jt is likely that they would depend upon TABLE I the molality of the aqueous acid in sulfur dioxide RESONANCE POSITION OF ACIDICPROTONS IN LIQUID SULFUR and upon the concentration of the aqueous acid. The exchange rates might be related to the concenDIOXIDE tration of ion pairs in the solution. Obsd. Cor. Acid pK Molality shift shift All the acids shown in the figure have the acidic (CH3)sC-COOH 5.1 1.46 -139.8 -152.1 proton attached to oxygen. If the proton is CHaCOOH 4.75 2 15 -132.3 -154.2 bonded directly to another element different HCOOH 3.68 4.05 -134.9 -156.2 magnetic anisotropy effects would overshadow CHzClCOOH 2.81 0.98 -135.6 -156.7 the change in shielding of the proton due to its CHClzCOOH 1.30 2.16 -129.5 -147.3 different acidity. One such example is hydrogen 0.52 2.19 -127.5 -143.6 C ClsCOOH bromide. An 18.4 molal solution in liquid sulfur CFaCOOH -0.26 4.70 -114.6 -128.9 dioxide has a corrected chemical shift of +375 C HaS08H -0.6 1.71 -117.5 -126.6 cycles. This is much higher than would be ex-3 1.03 - 59.0 - 83.2 pected from its acid strength alone and is considHiSOa HClO4 (70%) - 10 2.12 +207 +I89 erably higher than that for the pure l i q ~ i d . ~ HBr -9 18.4 $380 +375 There is evidence for 1:l complexes of SO2 and HI - 10 $203 +202 hydrogen halides in aqueous solution and such a complex if present in liquid sulfur dioxide could Spectra of 51, 60, 65 and 70% aqueous perchloric easily give unusual shielding effects.I0 It was acid dissolved in liquid sulfur dioxide were ob- necessary to keep the sample in a Dry Ice-bath tained. A single line, due to rapid exchange of the until shortly before running the spectra since a t acid and water hydrogens, was observed at the room temperature it reacted fairly quickly to give lowest concentration. At higher concentrations bromine, sulfur and water. Hydrogen iodide in tjwo lines are observed with the one a t highest liquid sulfur dioxide had a corrected chemical field attributed to perchloric acid because of its shift of +202 cycles, in agreement with its acid lesser intensity. The data are given in Table 11. strength. This is much lower than the value obIt is assumed that the chemical shift of 100% served for the pure liquid.9 In this case no chemHC104 dissolved in liquid sulfur dioxide would be ical reaction is observed for the solution in sulfur that shown by the 70% acid since the rate of dioxide. Discussion TABLE I1 It appears that there may be a correlation PROTONRESONANCE OF AQUEOUS PERCHLORIC ACID I N between the chemical shift of an acidic proton in LIQUIDSULFUR DIOXIDE liquid sulfur dioxide solution and the dissociation Aq. acid, Molality in % concn. SOe soln. Cord. shift constant of the corresponding acid in aqueous solu51 2.33 HzO - 15.0 tion. Therefore this method might be useful as an HClOi - 15 0 easy way to get approximate dissociation constants 60 2.13 H20 + 15.8 of strong acids. If concentrated aqueous solutions HClO4 + 18.7 of strong acids are dissolved in sulfur dioxide, one 65 2.51 HzO + 28.7 may determine the exchange rates between the HClOi $189 water and the acidic protons. 70
2.12
HzO HClO4
+ 45
$189
(7) A. A. B o t h e r - B y and R. E. Glick, J . C h e m Phys., 26, 1651 (1957).
(8) H. 9. Gutowsky and C. H. Holm, ibid., 26, 1228 (1950). (9) W.0 . Sohneider, H. J. Bernstein and J. A. Pople, ibid.,28, 601 (1958). (10) S. Witekowa, T. Paryjczak and T. Witek, Zeszty Nauk Polilech. Lodz., N o . 22, Clrem.. 7, 17 (1958);C . A . , 89, 1975e (1959).
