J . Phys. Chem. 1987,91,4635-4638 0 500
1
0.1
0.2
0.3
I
I
I
I
0.5
0.6
0.7
0.8
I
I
I
I
1
(A07171f) v_s. concentration c for the V3 spectral envelope of LiAsFg in 2MeTHF
J @
E
2
C(M)0.4
300
r2=0.994 (A:”//)=1,1+863C+ 832C2 -1384C3
” L o 200
a
v
1001 ”
Id ( A , 7 0 2 / f ) v_s. concentration c for the V3 spectral envelope of
4635
similar to the one in 2-MeTHF at similar concentrations. Notice that the band at 676 cm-I is practically invisible for the spectrum of LiAsF, in acetone (Figure 9), where only a minuscule band contribution at B = 682 cm-’ is needed in order to describe the lower “wing” of the spectrum. On the other hand, for LiASF6 in DMC, dimers were found to be present,8 with an apparent formation constant K, zz 50 M-I. One could then argue that lowering of the oh symmetry of AsF, is also due to some contact dimers, contributing to the band at B z 676 cm-l. This band appears to be present in different but increasing relative amplitudes in THF, 1,2-DME, 2-MeTHF, and DMC. In acetone the satellite bands at 718 and 682 cm-’ are almost absent. Energetically, dimers should not be stable configurations in acetone, the dipole-dipole energy being small with respect to kT, due to the permittivity e = 20.7 a t T = 298.2 K. Lack of visibility of the dimers in the infrared spectrum of LiAsF6 in 2-MeTHF, despite their formation constants K , = 1.8 M-I at 25 “C, may be rationalized if they are in the majority of the outer-sphere or solvent-separated type. This was suggested cm by theoretical calculations above, indicating a, = 9.4 X r 2d, d being the ion-pair separation distance. Because of the likely contribution of both species LiS,AsF6 and ( L ~ S , A S Fto ~)~ the band at B = 702 cm-l, we believe that any attempt at calculating formation constants from the absorbances of the two visible bands at 702 and 717 cm-’ may lead to meaningless results. In order to facilitate future calculations from the present data, as reported in Table 111, we have expressed the absorbances per unit length, AO7l7/l,AO7O2/1,and A06761,by polynomials in the electrolyte concentration c (mol/dm3). Specifically, nonlinear regression gives AO7I7/l= -1.1 Ao7OZ/l= -1.5
+ 863c + 832c2 - 13842, with r2 = 0.994 + 1199c - 1006c2 + 239.5c3, with rz = 0.997
A0616/1= 0.062
+ 2006.4~+ 2 3 3 . 9 ~-~241.5c3, with r2 = 0.996
having given a 50% statistical weight to the origin. Acknowledgment. This work was supported by the Army Office for Scientific Research, Durham, NC, under Grant No. DAAG29-85-K0048. Thanks are expressed for their generous support. Registry NO. LiASF6, 29935-35-1.
Diffusion of Aqueous Carbon Dioxide, Sulfur Dioxide, Sulfuric Acid, and Ammonia at Very Low Concentrations Derek G. Leaist Department of Chemistry, University of Western Ontario, London, Ontario, Canada N6A 5B7 (Received: February 23, 1987)
Equations are developed to predict binary diffusion coefficients, D, for very dilute aqueous solutions of C02, SO2,and NH3. As the concentration of each solute drops, D initially rises because a higher proportion of rapidly diffusing H+ or OH- ions is produced by hydrolysis ( C 0 2+ H 2 0 = H+ + HC03-, SO2 + H 2 0 = HS03-, or NH3 + H 2 0 = OH- + NH4+). The diffusion coefficients reach maximum values at concentrations near 10” mol L-I. At lower concentrations where H+and OH- ions produced by dissociation of water are no longer negligible, values of D decrease by 3040% and approach limiting diffusivities of the solute ions. Values of D for dilute aqueous solutions of H2S04are also reported.
Introduction Information on diffusion of trace constituents in aqueous solutions is required to estimate the rates of many processes, such as corrosion: transport of pollutants, and gas exchange between the atmosphere and water. In the latter context, diffusion of C 0 2 , SOz, and N H 3 is of particular interest. Although accurate diffusivities for these substances have been determined,’-3 the 0022-3654/87/2091-4635$01.50/0
measurements were made at solute concentrations of about mol L-’ or greater, whereas the concentrations in naturally occurring solutions are often lower than 10” mol L-I. At such low (1) Leaist, D. G. Ausf. J . Chem. 1985, 38, 249. (2) Leaist. D. G . J. Chem. Enp. Dura 1983. 29. 281. (3) Tang, Y.P.; Himmelblau,-D. M. Chem. Eng. Sci. 1965, 20, 7
0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 17, 1987
4636
concentrations aqueous COP,SO2,and NH3 hydrolyze extensively. In view of the exceptional mobilities of the hydroxyl or hydrogen ions that are produced, the dilute solutes will diffuse more rapidly than suggested by simple extrapolation of measurements made at higher concentrations. In very dilute solutions (
