NOTES
3355
kcal mole-', respectively, for the enthalpies of vaporization and fusion of tungsten hexafluoride a t 25'. These data, in conjunction with the present value for AHf"(wF6, g), have been used to calculate AHf"(WF6, 1) and DHfO(WFs, c). Standard entropies, So, a t 25", of W(c), FZ(g), WFs(g), and WFs(l) have been taken from ref 9; XO(WFe)c) was estimated to be 45.6 cal deg-I mole-'. The uncertainties given are uncertainty intervalsI5 equal to twice the combined standard deviations arising from all known sources.
Discussion Myers and Brady16 measured the enthalpy of solution of WFs(g) in aqueous NaOH, and derived a value 4 kcal mole-' for AHfO(WF6, g). JANAFs of -416 has revised this value to -421 f 4 kcal mole-', but both values are in disagreement with the present measurements. This discrepancy, of unknown origin, parallels that observed3 previously for MoF6. The determination reported in this paper is based on direct combination of the elements in a well-defined reaction, and is regarded as being more reliable.
*
efficient, the relationship advanced first by Darken and by Hartley and Crank,S" in absence of dimerization, is
b In a, (NwDu* 3 In Nu
D
=-
+ N,D,*)
(1)
where a,, is activity per mole of urea, N i is mole fraction of i, and Di* is its self-diffusion coefficient. When concentrations, ci moles/cc, are used, it is convenient to transform this to
DV
=Vw-b In a , (cwDu*+ cUDw*) b In cu
(2)
Equations 1 and 2 are derived by assuming each component has an independent diffusive flux determined by the mobility, p i , Le. J i - - c . 1qi.Vpi. (3) where
pi
is the molar chemical potential, i.e. Vpi =
RT V In ai
(4)
and qi is related to Di* by
Acknowledgments. The authors are grateful to H. AI. Feder and J9. Ader for helpful discussions. They wish to thank Doris Huff for performance of spectrochemical analyses, and Gerald I(.Johnson for preparation of the high-purity fluorine used in this work and for checking calculations.
When dimerization occurs, however, eq 5 is no longer valid for urea. If a! is the fraction of monomeric urea, the concentrations of the two forms are
(15) F. D.Rossini, Chem. Em., 18, 233 (1936). (16) 0.E. Myers and A. P. Brady, J . Phys. Chem., 64, 591 (1960).
and, if the mobilities of the two forms are q1 and qz, Stokes has shown, in effect, that D,* is given by
CI =
a!cu and cz = l/2(1 - a)c,
D,* = R T [ a q i
Interdiffusion and Self-Diffusion in Urea Solutions
(5)
Di* = qiRT
+ (1 -
a ) ~ 2 1
(6)
(7)
Furthermore, eq 1 and 2 assume a modified form, as can be seen in the following. The fluxes J1 and J z are given by
by P. C. Carman National Chemical Research Laboratory, South African Council for Scientijic and Industrial Research, Pretoria, South Africa (Received April 86,1966)
I n a recent paper, Stokes1 has shown that, by taking dimerization into account in aqueous solutions of urea, the results of Albright and Mills2 for selfdiffusion of urea are consistent with a simple relationship between the mobility of monomeric urea and viscosity. It is shown here that his model can be extended to the correlation between interdiffusion and self-diffusion coefficients. If subscripts u and w refer to total urea and water, respectively, and D v represents the interdiffusion co-
whence
Owing to equilibrium between monomer and dimer
~~~
(1) R. H. Stokes, J . Phys. Chem., 69,4012 (1965). (2) J. G.Albright and R. Mills, ihid., 69,3120 (1965). (3) L. S. Darken, Trans. Am. Inst. Mining Met. Engrs., 175, 184 ( 1948). (4)G.S. Hartley and J. Crank, Trans. Faraday Soc., 45, 801 (1949). (5) P. C.Carman and L. 5. Stein, ibid., 52, 619 (1956). (6) S.Prager, J . Chem. Phys., 21, 1345 (1953).
Volume YO, Number 10 October 1966
NOTES
3356
Table I ---DV la -
1000eu
Itr
0.5 1.0 2.0 3.0 4.0 a
Dv X 106
0.969 0.941 0.891 0.848 0.812
1.022 1.044 1,074 1.111 1.140
From St.okes Table I.
0.983 0,971 0.954 0.952 0.955
0.981 0.960 0.916 0.870 0.822
= -C,[aqr
+ 2(1 - c~)q.z]Vp,
(10)
NOW,in the derivation of (1) and (2), it is assumed that Ju
(exptl)
1.344 1.305 1.234 1.163 1.107
1.340 1,308 1,244 1.188 1.144
DW*
1.340 1,303 1.238 1.192 1.160
With Dw*/qr
1.340 1.301 1.231 1.175 1.126
Using 41/42 = 0.7.
whence
J,
D,* x 105
X 10s (ca1cd)-
With
=
-cuquVpu
(3%)
and D,* is evaluated from D,* = q,RT
(54
By comparison of (10) and (3a), it f o l l o w s that a modified form of (1) and (2) is obtained by replacing qu with the term in square brackets in (10). Further, as D,* is now given by (7), it can be introduced by replacing Du* with D,*.f(a), where
y u given by Bower and Robinson,’ but the differences are not large enough to affect the calculation in Table I. The self-diffusion coefficient of water in urea solutions has not been measured. The value for water cmz/sec, and, as possible itself is about 2.5 X extremes, either this has been used or the value obtained by dividing by the relative viscosity of the solution, vr, using values given by Stokes. Values of concentrations below 0.5 mole/l. have not been included as D,* and DV are very close in this range. It can be seen that the experimental values of Dv lie on the whole between the two calculated values, up to the highest concentration of 4 moles/l. (7) 1‘. E. Bower and R . A. Robinson, J . Phys. Chem., 67, 1524 (1963).
Le., eq 2 modifies to
+
b In a, Dv = pw-(cuDu**f(a) cUDW*) (12) b In c, I n Albright and Mills’ paper, experimental values of
Du*are given, as well as expressions for Dv and Vu. From the latter, taking pw as 18.04 cc for the whole range of concentrations, cw can be derived, as cwVw = 1Stokes gives values of a,calculated on the assumption that activities of monomer and of dimer equal their respective mole fractions. With regard to the relative mobilities of monomer and dimer, a reasonable choice for qz/ql, following considerations advanced by Stokes, is 0.7, but f(a) is not very sensitive to this over the range of concentrations considered and gives almost the same vaIues for ratios between 0.6 and 0.8. The values for ( b In a,)/b In c,) in Table I have been calculated from a, using Stokes theory that monomer and dimer form ideal solutions. They are almost identical with the values calculated from In yu, as given by Albright and Mills, and tend to be a little lower than those calculated from the experimental values of
curu.
The Journal of Physical Chemistry
Effect of Inert Gas Pressure and Solubility on Fused Salt Conductance. 11.
Nitrogen with Sodium Nitrate by James L. Copeland and Steven Radak Department of Chemistry, Kansas State University, Manhattan, Kansas 66602 (Received May 2, 1966)
As a continuation o f the studies of Copeland and Zybko1*2on the manner in which the specific conductance of simple fused salts is affected by “inert” gas pressure and solubility, we wish to report our rather unusual and interesting results for Nz in high-pressure equilibrium with molten NaN08. (1) J. L. Copeland and W. C. Zybko, J . Am. Chem. Soc., 86, 4734 (1964).
(2) J. L. Copeland and W. C. Zybko, J. Phys. C h a . , 70, 181 (1966).
