KOTES
June, 1963
1363
TABLE I SUMMARY OF EXPERIMENTAL DIFFUSIVITIES FOR DILUTE SOLUTIOXS OF ETHASOL IN CARBOX TETRACHLORIDE Mole fraction ethanol in soln. A 0 0 0.0023 0,0035 0.0116 0.0231 Mole fraction ethanol in soln. B 0 0046 0.0100 ,0114 .0143 .0205 ,0326 0.0050 IO069 ,0089 ,0160 ,0279 Av. mole fraction 0.0023 I
DABX 105, cm.Z/sec.
SUMMARY O F
Mole fraction methanol in soln. A Mole fraction methanol in soln. B Av. mole fraction DABX lo6, cm.2/sec.
1.901
1.756
TABLE I1 EXPERIMEXTAL DIFFUSIVITIES FOR 0 0.00513 0.00256 2.446
THE VAPOR PRESSURE O F SOLID DECABORANE BY GEORGE A. MILLER School of Chemzstrv, Georgia Instttute of Technologg, Atlanta, Georgza
Recezsed November 9, 1969
This paper presents results of the measurement of the vapor pressure of decaborane (BI0Hl4)in the range iiim. These results have been of about 10-6 to combined with vapor pressure data in the vicinity of the triple point and the thermodynamic properties of the solid, liquid, and gas in a third law calculation. It is found that the internal consistency of these data is good enough to permit a reliable calculation of the heat of sublimation a t 25'. Experimental The vapor pressure of solid decaborane was measured with a Knudsen gage and special procedure, described earlier in connection with the measurement of the vapor pressure of naphthalene.' From a maximum deflection measurement2 the collisip diameter molecule was found to be about 9.6 A. a t room of the BIOHU temperature. This value was used in an approximate form of the Weber equation3 to calculate the thermal transpiration
TABLE I THERNODPNAMIC FUXCTIONS OF IDEAL GASEOUS DECABORANE IN CALORIES PER MOLEPER DEGREE
240 250 260 270 280 290 300 310 320 330 340 350 360 370 380
(->
19.288 20.057
25.587 26.385
(1) G. A. Miller, J . Chem. Eng. Data, 8, 69 (1963). ( 2 ) G. A. Miller, Rev. Scz. Instr., 33, 8 (1962). ( 3 ) G. A. Miller, J . Phys. Chem., 67, 1359 (1963).
1.168
1.499
LfETHANOL-CARBON
.993
TETRaCHLORrDE
0 0.0055 0.0132 0.0952 0.2020 0.393 0.596 0.793 0.900 0.9913 0,0108 ,0145 .0201 ,1076 ,2108 ,405 ,602 ,801 ,896 I . 000 0.0054 ,0100 ,0167 .lo14 ,2064 ,399 ,599 ,797 ,898 0.998 2.173 1.769 1.363 ,710 .556 .489 ,799 1.264 1.723 2.248
minations was made for solutions dilute in alcohol so that the data could be extrapolated to pure carbon tetrachloride. This was necessary for calculations being made at the time. Acknowledgment.-This work was supported by the U. S. Army Research Office (Durham).
T,OK.
1.635
("eTI"> 60.602 61.254 61.908 62.565 63,225 63.888 64.555 66.225 65.899 66.576 67.257 67.941 68.628 69 318 70.011
effect between sample and gage. It was found that the Knudsen limiting law was actually accurate enough for this purpose. Decaborane was obtained from the Olin Matheson Corporation and purified by a special procedure of slow sublimation in V U C U O . ~ The purified sample ivas resublimed in DUCUO into the sample bulb. During the period of measurement, which lasted three weeks, the sample deromposed very slowly, although it was kept a t low temperatures This was evidenced by a build-up of hydrogen above the sample to sub-micron pressures from one day to the next. The hydrogen could be detected by the fast rate a t which it could be pumped off into the vacuum system proper. During measurement of the vapor pressure, the sample was pumped a t least once every 30 min. No detectable amount of hydrogen could form in this period of time. The other products of decomposition were assumed to be boranes of negligible vapor pressure.5 I n fact, the vapor pressure was not found to change with @time. Smoothed values of the vapor pressure were obtained from the best straight line fit to a plot of log Pus. 1/T (Fig. 1). The estimated reliability is .t5% in the middle of the range and somewhat less (about &lo%) a t either extreme. The four values used in the calculations below are T,"K.
1000/T
log P , mm.
240 250 260 270
4.167 4.000 3.846 3.704
0.387-5 0.047-4 0 657-4 0.219-3
Resuits The equations used to relate the vapor pressure (1') and the latent heat of vaporization ( L ) with the thermodynamic furictions oi solid, liquid, and vapor are
+ AH8 L = aHO= A(Ho - Ho") + Moo
-RT 111 P
=
A(Go - Ho")
(1) (2)
They are valid if the vapor is ideal and if the standard state of the condensed phase is a t the saturation pressure. The equation of state of decaborane vapor is not known; however, since the highest pressure under consideration is 25 mm., the lack of knowledge of the gas imperfection terms is not serious. The thermodyna,mic functions for the condensed phase at saturation pressure and the vapor pressure near the triple point (371.93'K.) are given by Furukawa and Park.6 Thermodynamic functions for the ideal gas a t one atmosphere were calculated for the rigid-rotor harmonic-oscillator approximation, using molecular constants recommended by Evans' (Table I). From the results of the calculation of AHoowith equation l a t ordinary :tiid very lorn pressures (Table 11), there appears to he no appreciable, long range drift in this quantity with temperature. The drift in AHoo (4) A. H a a l a n d , Thesis, Georgia Institute of Technolony, 1901. ( 5 ) B. Aierel a n d J. L. Mack, J Phys Chem., 62, 37,s (1958) (6) G. T. Furukawa a n d 12. P. P a r k J Res Xatl Bur Std., 36, 255 (19S5). ( 7 ) W. H. E v a n s , private communication.
1364
Vol. 67
KOTES I
I
the enthalpy functions. The result, is also 18.33 kcal./ mole for the heat of sublimation a t 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 P V R L E E ' 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.
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 3662b 19011 3411b 19150 310@ 19116 3O4gb 19427 -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. 240 250 260 270 345.45 355.12 361.81 371.53
+
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 a t 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 a t 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 O F 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 T e w s 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.
