~ALTING-IN OF NONPOLAR GASESIN AQUEOUS TETRAALKYLAMMONIUM BROMIDE Table IV. A0 at each temperature is taken as the average of the two values in Table I1 €or the purpose of this calculation. X o ~ s p -increases with temperature in a reasonable way as can be seen in Table Iv by multiplying each value by the viscosity of water at that temperature. The relative constancy of this product (Walden's rule) l2 is expected of ionic conductances at
1803
infinite dilution, and this finding adds confidence t o the validity of the methods used in this study. ~ ~ k ~ ~ We~ are ~ grateful l ~ d to ~ Professor ~ ~ ~ Robert I. Gelb for his help with the experimental techniques of conductivity measurement and also to the Research Corporation for partially supporting this study.
The Salting-In of Nonpolar Gases in Aqueous Tetraalkylammonium Bromide Solutions and the Apparent Molal Volume of These Salts in Water by Michel Lucas" and Anne de Trobriand Department de Chimie, Centra d'Etudes Nuclhaires, Fontenay-aux-Roses, France
(Received October 8, 1970)
Publication costs assisted by the Commissariat ct 1'Energie Atomique, France
The apparent molal volume of tetrapropylammoniumbromide in water at 5, 15, and 25", tetrabutylammonium bromide at 5 and 25", and tetraethylammonium bromide at 5" have been measured at various concentrations. The experimental variation of the salting-out constants with the molality of the solution and the temperature has been compared to the variation calculated according to the scaled particle theory for some nonpolar gases. The calculated and experimental constants both have a similar concentration dependence, though their actual values are quite different. The discrepancy may be ascribed to the influence of dispersion forces which are not taken into account in our calculations.
Introduction The salting-out constant k for a gas in an aqueous salt solution is given by the equation S" log - = km
S
Here So is the solubility of the gas in water and S its solubility in the salt solution of molality m. The salting-out constants calculated from data in the literature for t etraalkylammonium bromide solutions .show rather large variations with the salt molality. To compare the experimental constants with those calculated from the scaled particle t h e ~ r y , ~the - ~apparent molal volumes of the salts are required. Most but not all of these apparent molal voIumes can be found in the literature.6 T o complete the salt series, the apparent molal volumes of tetrapropylammonium bromide in water a t 5 and 15" and those of tetrabutyl- and tetraethylammonium compounds were determined a t 5".
Experimental Section Chemicals. The tetraethyl- and tetrabutylammonium bromides, Carlo Erba, polarographic grade,
were dried at 70" i n vacuo before use. The tetrapropylammonium bromide, Eastman Kodak, was purified according to the procedure given in ref 5. Measurements. Density measurements were made with 25-ml pycnometers, standardized with doubly distilled water. The procedure of Weissberger was followed.6 Density measurements were reliable to within f0.00005. The corresponding precision for the apparent molal volume was A0.3 ml/mol for m smaller than 0.3 and f0.1 ml/mol for higher molalities. The water bath was maintained at h0.02" at all temperatures.
Results The apparent molal volumes of the salts at various temperatures are listed in Table I. They were calculated from the density data by means of the equation (1) W. Y. Wen and J. Hung, J . Phys. Chem., 74, 170 (1970). (2) S. K. Shoor and K. E. Gubbins, ibid., 73, 448 (1969). (3) M. Lucas, Bull. Soc. Chim. Fr., 2994 (1969). (4) W. L. Masterton and T. P. Lee, J . P h y s . Chem., 74, 1776 (1970). (5) W. Y. Wen and 8. Saito, ib{d., 68, 2639 (1964). (6) A. Weissberger, "Physical Methods of Organic Chemistry," Vol. I, 2nd ed, part I, Interscience, New York, N . Y., 1949.
T h e Journal of Physical Chemistry, Vol. 76,No. 18, 1971
t
.
1804
MICHAEL
LUCASA N D ANNEDE: TROBRIAND
Table I : Apparent Molal Volumes of Tetraalkylammonium Bromides in Aqueous Solutions a t 5, 15, and 25' (units of ml/mol) Concn,
(C4Hg)rNB--
7 -
0.05 0.1 0.15 0.2 0.25 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 2.0
25O
293.7
299.9
293.3
298.9
292.3 291.5 290.7 Limit of solubility
298.2 297.6 297.0 296.5 295 8 295.5 295.4 295.1
1 1000
vz = ; (
(CaH?)4NB
,---
50
nt
+ mM2 - 7 ) d
5"
15O
236.0 235.6 235.4 235.2 234.9 234.5 233.8 233.0 232.4 231.7 231.3 230.8 230.3 229.5 228.7 227.2
--
(C2Hs)rNBr
25O
239.3 238.8 238.4 238.1 237.8 237.5 237.0 236.6 236.2 235.7 236.3 234.8 234.4 233.7 233.0 231.6
237.0 236.7 236.5 236.2 236.0 235.3 234.7 233.9 233,5 232.9 232.6 232.3 231.5
50
171.7 171.2
170.8 170.6 170.2 170.0 169.8 169.6 169.4 169.2 168.8 168.5 167.5
k
(2)
where do is the density of pure water, Mz the molecular weight of the salt, d the density of the solution, and m its molality. The shape of the curves obtained when V 2is plotted against m is very similar to that reported by Wen,6 but a t 25" there are some differences between his values and ours for tetrabutylammonium bromide.
"2 ml
J
0
300
Discussion We have plotted the experimental values of the apparent molal volume V 2of a given salt and of the salting-out constant for a given gas against the square root of the molality of a solution of the salt at a given temperature. Figure 1 shows the plots for methane and tetrabutylammonium bromide. The values of Vz decrease with increasing molality, and a minimum is found near m = 1.4. The values of k increase with increasing molality, and there is a maximum near m = 0.9. Both sets of curves are somewhat similar in shape; but variations are opposite in sign. Figure 2 shows the corresponding plots for propane and tetrapropylammonium bromide. I n this case the values of V 2 decrease with increasing m values and breaks in the curves are observed at 5 and 15' but not 25". Similar characteristics are shown by the k curves. The variation is always opposite in sign. Figures 3 and 4 show the data for methane, ethane, and propane in aqueous ammonium or tetrahydroethylammonium bromide solutions. I n those cases, T i 2 increases with increasing m, and k varies in the opposite direction. Also small variations of k with the molality and the temperature correspond to small variations of V 2 . (Data for V zare taken from ref 7 for (EtOH)4NBrand calculated for NH4Br on the assumption that the relation V2 = Vz" Sym1/2holds
+
The Journal of Physical Chemistry, Vol. 76,N o . 18, 1971
-0.0
2 95
-0.11
2 90
0
0.5
1
6
Figure 1. Salting-out constant for methane and apparent molal volume of salt in aqueous tetrabutylammonium bromide solutions: open circles, k; black circles, V2.
up t o m = 1 with V," taken from ref 8 and S , from ref
9.)
Now we should compare the experimental results with those predicted from the scaled particle theory. Pierottilohas divided the process of solution of a non(7) W. Y . Wen and S.Saito, J . Phys. Chem., 69, 3569 (1965). (8) K. Fajans and 0. Johnson, J . Amer. Chem. Soc., 64, 676 (1942). (9) H . 9 . Harned and B. B. Owen, "The Physical Chemistry of Electrolytic Solutions," 3rd ed, Reinhold, New York, N. Y . , 1958, pp 360-370. (10) R. A. Pierotti, J. Phys. Chem., 69, 281 (1965).
SALTING-IN O F
1805
NONPOLAR GASESIN AQUEOUS TETRAALKYLAMMONIUM BROMIDE
k
k
"2
50
-
0.0 5
2 10
.07
43 -0.10
235
2
1
t
2 .5
11 0
1
6
Figure 4. Salting-out constant for butane and apparent molal volume of salt in aqueous NHaBr solutions: open circles, k; black circles, Vz.
-
0.1 5
230
solute with the solvent particles through dispersion forces, polarizability, etc. The free energy associated with this step is The solubility of a gas is described by the Henry constant G
0
i
b
K = -P
(3)
X 0.5
0
6
1
where p is the partial pressure of the gas over the solution and x its molar fraction in the solution. Pierotti states that K is related to the free energies Go and Gi and the molar volume of the solvent by the equation
Figure 2. Salting-out constant for propane and apparent molal volume of salt in aqueous tetrapropylammonium bromide solutions: open circles, k; black circles, VZ.
R T In K = G,
+ Gi + R T ln-RVT
(4)
where T is the absolute temperature. The quantity G, RT In RT/V may be calculated for a very slightly soluble gas in a mixture of solvents by means of the equations given by Lebowitz and Rowlinson. l1 We shall write these equations on a molal basis. The same symbols as in ref 11are used. Let us consider i particles constituting the solvent. pi is the number density and Ri the hard-sphere diameter for a given particle. For a mixture of i particles, the quantities 4, X , and Y are defined as
+
"2
I
I
I
I
I
0
.5
l v i
I
Figure 3. Salting-out constant for methane and ethane and apparent molal volume of salt in aqueous (Et0H)aNBr solutions: open circles, IC; black circles, Vz.
polar gas in water into two steps. First, a cavity has to be made in the solvent to accommodate the solute particle. Its diameter is exactly the hard-sphere diameter of the gas. This is referred to as the cavity formation process. The scaled particle theory allows the computation of the free energy involved in this step which for a mole of solute is Go. The second step is to consider the interactions of the
The value of G, for a solute of diameter D is given by Gc RT
- = -In (1 - 6)
+ 3D2Y
9X2D2
1-Ef2jl-[)
+-13DX -,$
(6)
Now consider a solvent which is an aqueous salt (11) J. L. Lebowitz and J. S. Rowlinson, J . Chem. Phys., 41, 133 (1904). The Journal of Physical Chemistry, Vol. 76, N o . 18, 1971
1806
MICHAELLUCASAND ANNEDE TROBRIAND
solution. On a molal basis, there are 55.5 mol of water (1000 g) for m mol of the salt,. The apparent molal volume of the salt is given by eq 2. It follows then that the density of the solution is given by the relation
I
k
0
(7) where MnzO is the molecular weight of water and VH*O the molar volume of pure water. The number density P H ~ Oof the water in the aqueous salt solution is PHzO =
55.5Nd 55.5N 1000 mM2 55.5VH20 mV2
+
+
(8)
-0.0:
where N is the Avogadro number. The number density of one of the two ionic species is p+ = p- =
mN 55.5V~,04-mV2
(9)
Kow if a, b, and c are the hard-sphere diameters of the water and of the anion and cation of the salt, from eq 5, 8, and 9, it follows that
E = - N.rr55.5a3 + m(b3 + c3)
+
55.5V~,0 mV2
6
(10)
Similar relations are found for X and Y except that a3,b3, and c3 are replaced by u2,b2, and c2 or a, b, and c. I n addition, the volume V in eq 4 is given by the equation
Then the value of G, may be calculated by means of eq 6, 10, and 11. Now if K" is the Henry constant for the gas in pure water, the salting-out, constant is given by
- G,"
k = k,
+ i n rV) +
+ ki with k,
+ In
= 1
hi = A ( G i
2.3mRT
%>
(13)
- Gi")
Here Gi", G,", and V" are the corresponding values for Gi, G,, and V , when the molality is equal to zero. It should be outlined that kc is a funct,ion of the constants D,a, b, c, and VH20 for a given salt and solute and of the variables m and V 2 . This is apparent from eq 6, 10, 11, and 13; then a relation between k, and V z can be given, but it is rather complex. The Journal of Physical Chemistry, Vol. 76, N o . I B , 1971
-0.1 0
0
0.5
f
i
1
Figure 5 . Plots of experimental and calculated salting-out constants against m1I2for methane and aqueous tetrabutylammonium bromide solutions.
For the calculation of k,, the values of a, b, c, and D for are required. From ref 10, a is equal to 2.76 water; b is chosen:qual to the crystal ionic diameter of Br-, that is, 3.92 A. In ref 12 the values given, respectively, for the cations tetrapropyl- and tetrabutylammonium are 8.7 and 8.0 A. The valueso for methane and propane are, respectively, 3.8 and 5.1 A.13 The calculation of Gi may be done by means of the equations given in the l i t e r a t ~ r e . ~However '~ this calculation rests upon the assumption that Gi, the free energy of interaction, is equal to Hi,the enthalpy of interaction. lo We had shown that this assumption leads to an inconsistency, l4 except when the solvent has an expansivity coefficient equal to zero or very small, which is the case only for pure water and not for aqueous salt solutions. Then Hi and Gi can no longer be considered as equal quantities, and at present we cannot evaluate Gi and ki. We shall only compare lc and k,. The values for kc have been calculated for methane and aqueous tetrabutylammonium bromide solutions and for propane and tetrapropylammonium bromide at 5, 15, and 25". Figure 5 shows the plots of k, for methane and tetra(12) B. E. Conway, R. E. Verrall, and J. E. Desnoyers, Trans. Faraday Soc., 6 2 , 2738 (1966). (13) J. 0. Hirschfelder, C. F. Curtiss, and R. B. Bird, "Molecular Theory of Gases and Liquids," Wiley, New York, N. Y., 1967, P 1110. (14) M. Lucas and A. Feillolay, Bull. Soc. Chim. Fr., 1267 (1970).
SALTING-IN OF NONPOLAR GASESIN
1807
AQUEOUSTETRAALKYLAMMONIUM BROMIDE
k
k 0
k
-0.05
0
-0.05
-0.05
-0.1 0
-0.lO
-0.15
-041 5
0.60
-0.10
0.55
CH4
BuL NBr k
0.8
kc 1.4
OS!
1.35
-0.15
0.50
I. 3
0.5
230 0
0.5
v
i
1
Figure 6. Plots of experimental and calculated salting-out constants against m'lZ for propane and aqueous tetrapropylammonium bromide solutions.
butylammonium bromide solutions against m"'. The experimental values for k are plotted on the same figure. The main features of experimental curves are reproduced by the calculated ones. Figure 6 shows similar plots for propane and tetrapropylammonium bromide. Both sets of curves are similar, especially as the existence of breaks a t 5 and 15" is shown. The only discrepancy is that in the last case the variation of k, with the temperature and the salt molality is smaller than the experimental one. The values taken for the gas and the cation diameters are mainly tentative and may be slightly in error. However, in both cases. the variation of k with the temperature and the
235
V22&0 290
295
Vz 30
Figure 7. Plots of k and k, against the apparent molal volume of the salts for methane and aqueous tetrabutylammonium bromide solutions and for propane and aqueous tetrapropylammonium bromide solutions.
salt molality is consistent, at least qualitatively, with the variation calculated according to the scaled particle theory, even if the possible variation of ki with the same parameters has been ignored. The values of ki are always negative, as the interaction forces always cause salting-in. Therefore the values of k, are strongly in excess of the experimental ones. I n any event the data necessary for the calculation of Ici are lacking, and all that we can do is to compare the variations of k and k, and not the magnitude of calculated and experimental salting-out constants. Finally the plots of k and k, against Ti2 are shown in Figure 7. The dependence of k and IC, on V 2is rather complex, although in some cases it may be described approximately by a linear relation.
The Journal of Physical Chemistry, Vol. 76, No. l a , 1971
