2148
W.-Y. WEN, K. MIYAJIMA, AND A. OTSUKA
Free Energy Changes on Mixing Solutions of Alkali Halides and Symmetrical Tetraalkylammonium Halides
by Wen-Yang Wen,* Koichiro Miyajima, and Akinobu Otsuka Jeppson Laboratory, Chemistry Department, Clark University, Worcester, Massachusetts
01610
(Received October 16, 1970)
Publication costs assisted by the National Science Foundation and the Public Health Service
The excess free energy changes on mixing solutions of alkali halides and tetraalkylammonium halides having common anions were determined at 25' by the isopiestic method. The systems studied include KBr-R4NBr (where R = Me, Et, Pr, and Bu), PrdNBr-MBr (where M = Li, Na, K, Cs, Me, and Et), MerNBr-RaNBr (where R = Et, Pr, and Bu), and KC1-BudNCl at y = 0.5 and I = 0.1 to 4.0, where I is the total molal ionic strength and y is the fraction of ionic strength due to an electrolyte in a mixture of two electrolytes. For the KBr-PrrNBr system, y was varied from 0.1 to 0.9. The experimental osmotic coefficients were treated by the formalisms of Scatchard and of Friedman to yield the excess free energy, A@., and the free energy interaction parameter, go. Values of go obtained were discussed in terms of the ionic solution theory of Friedman to gain insights into the nature of the cation-cation interaction. The results have been interpreted to indicate that, in dilute solution ( I = 0.5), the free energies of interaction between two large tetraalkylammonium cations are small, probably much smaller than those between two alkali metal ions. The relative mutual attraction between two tetraalkylammonium ions may be an instance of hydrophobic interaction. Introduction The osmotic and activity coefficients for aqueous mixtures of two electrolytes having a common ion were first reported by Owen and Cooke' in 1937 for LiC1KC1 system a t 25". Since 1952 Robinson and his coworkers2 have investigated for many years mixtures containing alkali metal ions and alkaline earth metal ions. Recently, Rush and his coworkers in the Oak Ridge National Laboratory3 have determined osmotic coefficients for various three-component systems (two electrolytes and water) and treated their experimental results with equations suggested by S ~ a t c h a r d . ~ Using these equations Rush5 has recalculated the parameters of osmotic and activity coefficients for 31 aqueous mixtures of two electrolytes a t 25". A more elegant approach in dealing with the free energies of mixed electrolyte solutions has been proposed by Friedman,6who has pointed out the existence of a limiting slope for the interaction parameters a t infinite dilution. This approach has been taken up by others, particularly by Wood and his coworker^.^ The studies mentioned above have dealt with systems containing only inorganic electrolytes. There seems to be no investigation of excess free energy of mixing involving organic electrolytes. On the other hand, various workers have investigated aqueous solutions of tetraalkylammonium halides and uncovered many interesting properties.8 One of the physical properties of these salts which is of particular interest to us is the nature of cation-cation interaction between the large tetraalkylammonium ions. Studies on volume changes on mixings and enthalpy changes on mixing'O seem to suggest the importance of the cation-cation pair interT h e Journal of Physical Chemistry, Vol. 76, N o . l.GV1971
action and cation-anion-cation triplet interaction. This and other related questions on hydrophobic interaction1' have led us to investigate the excess free energy of mixing solutions of tetraalkylammonium halides and alkali halides having common anions. The thermodynamic parameters were derived from osmotic coefficients obtained by the isopiestic method a t 25". (1) B. B. Owen and T. F. Cooke, J . A m e r . Chem. Soc., 59, 2273 (1937). (2) (a) R. A. Robinson, ibid., 74, 6035 (1952); (b) R. A. Robinson and C. K. Lim, Trans. Faraday SOC.,49, 1144 (1953); (c) R. A. Robinson, ibid., 49, 1147 (1953); (d) R. A. Robinson, J . P h y s . Chem., 65, 662 (1961); (e) R . A. Robinson and V. E. Bower, J . Res. N a t . Bur. Stand. Sect. A, 69, 19, 439 (1965); ibid., 70, 313 (1966); (f) R. A. Robinson and A. K. Covington, ibid., 72, 239 (1968). (3) (a) R. M. Rush and R. A. Robinson, J . Tenn. Acad. Sci., 43, 22 (1968); (b) R. M. Rush and J. S. Johnson, J . Phys. Chem., 72, 767 (1968); (0) Y. C. Wu, R. M. Rush, and G . Scatchard, ibid., 72,4048 (1968); 73, 2047 (1969). (4) G. Scatchard, J . A m e r . Chem. Soc., 83, 2636 (1961). (5) ,R,. M. Rush, "Parameters for the Calculation of Osmotic and Activity Coefficients and Tables of These Coefficients for 22 Aqueous Mixtures of Two Electrolytes at 25OC," Oak Ridge National Laboratory, ORNL-4402, 1969. (6) (a) H. L. Friedman, J . Chem. Phys., 32, 1134, 1351 (1960); (b) H. L. Friedman, "Ionic Solution Theory," Interscience, New York, N. Y., 1962; (c) J. C. Rasaiah and H.L. Friedman, J . Chem. Phys., 48, 2742 (1968). (7) P. J. Reilly and R. H. Wood, J . Phys. Chem., 73, 4292 (1969), and references cited therein. (8) See, e.g., references cited in W.-Y. Wen and J. H. Hung, ibid., 74, 170 (1970) (9) (a) W.-Y. Wen and K. Nara, ibid., 71, 3907 (1967); (b) W.-Y. Wen and K. Nara, ibid., 72, 1137 (1968); (c) W.-Y. Wen, K. Nara, and R. H. Wood, ibid., 72, 3048 (1968). (10) R. H. Wood and H. L. Anderson, ibid., 71, 1871 (1967). (11) (a) W. Kauzmann, Advan. Protein Chem., 14, 1 (1959); (b) G. Nemethy and H. A. Scheraga, J . Phys. Chem., 66, 1773 (1962); 67, 2888 (1963); (c) H. Nemethy, Angew. Chem., 6, 195 (1967).
FREEENERGY CHANGES ON MlXINCi SOLUTIONS OF HALIDES
Procedure A . Formalism According to Friedman. Friedman has extended NIayer's ionic solution theory12 to mixed electrolyte solutions and derived the excess free energy of mixing
A G ~ ~ ( ~=, I12RTy(l ) - 9) X [go Ql(1 - 2Y) 920 - 2YI2
+
+
+
*
"
1
From eq 5 we obtain In yk = -(1 - (6)
AGeX(y,I) = Gex(y,I) -
Jo
where G e x ( l , I )applies to a solution of pure AX and Gex(O,I) applies to a solution of pure BX. The quantity A P x is clearly the increase in excess free energy on forming the mixture from the component solutions at the same I , T, and pressure, and is a measure of the change in molecular interaction in the process. The changes of excess free energies on mixing solutions of R4NX and I\IX at constant total ionic strength can be determined by use of the concept of a pseudobinary solution. The pseudo-binary salt yR4NX. (1 y)MX dissociates in water according to
~
4
~
+
(3)
~*'(R~NX)Y*'-'(MX)
Gex(O,I) = 2RTI[ln Y*(B)
rndln y& = -d[m(l - 411
(9)
(10)
dj
7
CA,I"/'; i =1
(A1 = 0.3908)
(11)
Once these coefficients are determined by a computer program, it can be easily shown that G"(y,I)
=
-4RTC(At/i)I'if2'2;
+ (1 - 4)]
(A1
(4)
(5)
where y5 is the "mixed" coefficient as defined in eq 4 and 4 is the osmotic coefficient of the pseudo-binary solution to be determined by the isopiestic experiments. Thus, by measuring 4 at any constant y it would be possible to get the pseudo-binary yrt for that y as a function of total ionic strength. It turns out, however, that it is not necessary to evaluate the values of yrt: to obtain the values of GBx. An expression for the excess free energy of a simple salt is 2RTI[In yk
+A)]
i =1
The change in excess free energies is given by eq 2 where I is the total molality in this case and y is the mole fraction of RdNX in the mixture. To obtain Gex we start from the Bjerrum form of the Gibbs-Duhem equation, namely
=
(7)
The integral in eq S for the mixed electrolyte solutions was evaluated by two methods. The first method is the graphical method in which the values of (1 - $I)/ djare plotted against and the area under the curve is evaluated. I n this plot (1 - 4 ) / d j approaches a value of 0.3908 as I approaches zero according to the Debye-Huckel limiting law for 1-1 electrolytes at 25". The second method concerns with the least-squares evaluation of the coefficients (A, through A,) in the following empirical equation.
= ( y f f R 4 N + * y &tIl - ' ~ ~ x - ) ' ' *
Gex
+ (1 + (1 - 4~11
G"(1,I) = 2RTI[ln Y ~ ( A )
1-4 =
The mean activity coefficient of the pseudo-salt may be defined as yh =
1
Since the osmotic and activity coefficients of R,NX solution (subscript A) and AIX solution (subscript B) are avaihble in literature, one can obtain the values of AGex by use of eq 2, 8-10.
yR&X (1 - y)llIX ---j y
'qd I
and substitution of eq 7 into eq 6 yields
yG"x(1,I) - (1 - y)G""(O,I) (2)
+ (1 - y)MX + + (1 - y ) n I + + x-
- ['
(1)
where R and T have their usual meaning, I is the molal ionic strength, y is the fraction of ionic strength due to an electrolyte in a mixture of two electrolytes AX and BX, and the g's are interaction parameters. The excess free energy of the mixed solution is defined as
yR4NX
2 149
(6)
0.3908) (12)
B. Formalisin A c c o ~ l i n gto Xcatchard. Equations employed in this formalism are derived from those of S ~ a t c h a r d . ~ ,The ' ~ b parameters were derived from the observed osmotic coefficients (4) at ionic strength I and ionic strength fraction YB. These same parameters can then be used to calculate the activity coefficients y5 of either component. The other relationships used are 2mJ(4J - 1 ) / I J
CYJ
(AJ
+
CYJ)=
( ~ ~ J In / IYJ~ )J C J )
where QJ is the osmotic coefficient of pure J and ~ * J ( J ) is the activity coefficient of component J in pure J both taken at the ionic strength of the mixture in question. It is thus possible to calculate the contributions of the (12) J . E. Mayer, J . Chem. Phys., 18, 1426 (1950). (13) Notations of this formalism are conveniently summarized in Table I, p 8 of ref 5 .
The Journal
of
Physical Chemistry, Vol. 76, N o . 14, 1071
W.-Y. WEN, E(. MIYAJIMA, AND A. OTSUKA
2150
Table I : Osmotic and Activity Coefficients of CsBr, PrdNBr, and BuaNBr in Water at 25" Molality
--PraNBr--4
