1364
Vol. 67
KOTES I
I
the enthalpy functions. The result, is also 18.33 kcal./ mole for the heat of sublimation at 25".
I
THE POTENTIOMETRIC MEASUREMENT OF ION-PAIR, DISSOCIATIOK CONSThNTS. T H E ALKALI CHLORIDES AXD (CH3)dNCl IN 70% DIOXSKE-SO% WATER1
-3
By E.
L E E PVRLEE' AND
ERKEST GRUSWALD
CLemzstry Department, Florida State C'ninersity, Tallahassee, PZa.
-
Receised Nouember 16, iQ62
E E
pl
Some years ago3 we described a poteiit'iometric method for measuring ion-pair dissociation const'ants, based on the cell represented in eq. 1.
-4
-0
Glass electrode,/HCl(cl), MC1(cz), in 70.00 vit. 70dioxane-30.00 wt. yowater/AgCl-Ag (1)
-5
-
I
I
I
3.8
40
4.2
IOOO/T
Fig. 1.-Decaborane
O K ,
vapor pressure data, this work.
between 240 and 270'K. (68 cal.) probably reflects the uncertainty in the vapor pressure data, since 68 cal. would correspond to an error in P of oiily 13%. From the calorimetric value of L at 378"IL,6 one obtains, with eq. 2 , AHoo = 19171 cal./mole. Thus it appears that the vibrational frequency assignment used in these calculations7 is essentially correct. VALUESOF T ,OK. 240 250 260
AH00 OF
TABLE I1 SUBLIMATION OF DECABORAKE FROM VAPOR PRESSURE DATA
- Go) 10890 11328 11761 12193 15349 15739 16008 16378
A(H00
-RTInP
AH@
8230" 19120 7818" 19146 7405" 19166 6995" 19188 270 3662b 19011 345.45 3411b 19150 355.12 310@ 19116 361.81 3O4gb 19427 371.53 -liquid 2754" 19164 371.93 16410 2546' 19161 380 16615 a This work, from smoothed values of the vapor pressure. Reference 6, experimental values of the vapor pressure. Refer( ( 6, smoothed values of the vapor pressure as represented 2 the equation log P ( m m . ) = -4225.345/T - 0.0107975T 6.63911.
+
The above calculations would seem to indicate ail over-all value, AHoo = 19.16 rt 0.02 kcal./mole. This value niay be used in eq. 1 and 2 to calculate the folowing quantities for decaborane at 25': heat of sublimation, 18.33 kcal. /mole; standard free energy of vaporization, 5.77 kcal./niole; vapor pressure, 4.48 X mm. Alternately, the calorimetric value of L at 378°K. may be corrected to 25' by use of
We showed that this cell accurately measures the activity product', UHUC1, of the ions of hydrochloric acid. Using a plausible aiid consistent method of allowing for long-range interionic eff ects,3>4we then could calculate the concentration product, CHCCl, of the dissociated ions. Data for cells with c2 = 0 thus enable us to obtain the ion-pair dissociation constant of hydrochloric acid (since CH = c c 1 < el), the precision of fit to the data being excellent. Data for cells containing a mixed electrolyte, e . g . , HC1 aiid XaC1, enabled us to evaluate not oiily CH and ccI, but also the concent'ration of free sodium ions (exa = cc1 - CH) and of YaCl ions pairs ( c x a ~ l = c2 - exa) in each solution. Although this method of studying the ion-pair dissociation of NaCl is rather indirect, the precision of the dissociation constants, Kd, was very satisfactory, the standard deviation for a long series of experiments being less than 2yG. We now report' an extension of this work to other chloride salts. The experinieiital and computational methods are identical with those used previously3 and need not be described again. A typical set of experiments, to illustrate the range of c1 and c2 aiid the precision of Kd, is showii for CsCl in Table I. All measureineiits were made at 25.00'. The consistency of our new results with those reported previously was checked by a new series of measurements for SaC1. The new yalue of 103Kdis 5.32 f 0.14; the previous value was 5.35 f 0.07. TABLE I POTESTIOMETRIC RIEASUREhlEST OF Kd FOR CESIUM CHLORIDE IN
70.00 WT. 10%
2,880 5,610 8.204 10,669 9,192 8.609 8.095 7.639
70 DIOXANE-30.00
WT.
104~~
8,376 8.159 7.953 7,758 3,774 7,070 9.972 12,547
70 W A T E R AT 25' 10aKd
2.62 2.72 2.80 2.82 2.55 2.75 2.70 2 .62
Our potentiometric values of Kd for chloride salts (1) This ivork was supported by the National Science Foundation. ( 2 ) E. L. P. Newport Tews Sliil>building and Dry Llocli C o . , Xicnuort
K e w , T.a. (3) E. L.Purlee and E. Grunwald, J . A m . Chcm. Soc., 79, 1388 ( l Q 5 7 ) . (4) H. P. RIarshall and E. Grunwald, J . Chem. Piiys., 21, 2143 (19.531.
NOTES
June, 1963 are summarized in Table 11. These values, in common with all values of ion-pair dissociation constants, are subject to a n unavoidable determinate error, since they depend on tlie particular model chosen for calculating the long-range interionic effects. Thus, for KCl in TOYo dioxane-30yo water at 25O, our potentiometric value of lo3& is 2.35 f 0.16, while the conductometric value reported recently by Lind and Fuoss5 is 6.0 f 0.2, or more than twice as large. A substantial part of this discrepancy results from a difference of models: Lind and Fuoss limit the concept of "ion pair" to a pair of ions a t distance of closest approach, while the model used by us is more inclusive, allowing the interionic distance in the ion pair to extend to the Bjerruni distaiice q = -zxlzze2/2DkT. We do not claim a fundamental superiority for tlie model on which the present values are based; nor do we profess a strong aesthetic preference, except that this model does fit the data better than other models we have tried.3
1365
E/Eo = exp(- 2 / 3 y 2 G 2 D ~ 3 ) (1) in which y is the nuclear gyromagnetic ratio, D is the bulk liquid self-diffusion coefficient, r is the time interval between the two pulses, G is the magnetic field
gradient along the direction of the applied magnetic field, Eo js the echo amplitude when G is zero, and E is the spin-echo amplitude for the given G value. The derivation of this expression assumes that the diffusing molecules move in an infinite reservoir so that the Einstein relation ((Ax)2),, = 2Dr holds. Suppose, now, that the reservoir is not infinite so that the molecules experience physical barriers to their diffusive movements. The average displacement a molecule undergoes during a time interval 7 should be less than that for an infinite reservoir. But as T is decreased toward zero, the displacement of the average molecule should approach that for an infinite reservoir because fewer and fewer molecules move far enough to experience the barriers. The size of the infinite reservoir to which eq. 1 applies is great enough so that the average distance bletween molecules and constrictive barriers is very large compared to ~ ( D T ) ' the / ~ , average distance a molecule moves in any direction during the time 27. For water at room temperature, this diffusion distance is 14 p for r = 0.02 sec. The size which a reservoir must attain i;o that eq. 1 applies then, increases with increasing r values. Systems such as porous rocks and viscous colloidal suspensions should provide barriers so that eq. 1 no longer applies. This has been observed for water in a geological core and for water in aqueous suspensions of silica spheres. For 7 values in the range of 0.01 tlo 0.03 see., the values of E/Eowere measured4 as a funation of G for fixed r values. Plots of In (E/Eo) us. G2 showed that In ( E / E o )is directly proportional to G2, as is the case for bulk liquids. These data can thus be interpreted by use of eq. 1 with the bulk liquid selfdiffusion coefficient D replaced by a spin-echo diffusion coefficient D'. For a qualitative discussion, one may use the relation D' = ((Ax)2),v/(4~),where A AX)^),, refers to the mctlecular disp1acemen.t during 27. From the above considerations, one would expect D' t o be a function of the ~ of the distance from diffusion distance ~ ( D T ) ' 'and molecules to barriers. I n particular, D' should decrease as the ratio of diffusion distance to the molecubto-barrier distance increases. Also, in the limit when r = 0, it is expected. that D' = D; and with increasing values of T, D' should decrease. These expectations are in agreement with the following data. When 'T becomes long enough so that the diffusion distance is very large compared to the average molecule-to-barrier distance, D' should become independent of r and be the diffusion coeffilcient obtainable by conventional means. This will occur when the relation = 2D't holds for all 1 > t, such that t,
