Page 326 - Physical Chemistry

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In the pure liquid state, a true electrolyte is a good conductor of electricity. In con- Section 10.5
trast, a potential electrolyte is a poor conductor in the pure liquid state. Solutions of Electrolytes
Because of the strong long-range forces between ions in solution, the use of ac-
tivity coefficients in dealing with electrolyte solutions is essential, even for quite dilute
solutions. Positive and negative ions occur together in solutions, and we cannot read-
ily make observations on the positive ions alone to determine their activity. Hence, a
special development of electrolyte activity coefficients is necessary. Our aim is to de-
rive an expression for the chemical potential of an electrolyte in solution in terms of
experimentally measurable quantities.
For simplicity, we consider a solution composed of a nonelectrolyte solvent A, for
example, H O or CH OH, and a single electrolyte that yields only two kinds of ions
3
2
in solution, for example, Na SO , MgCl , or HNO but not KAl(SO ) . Let the elec-
3
2
2
4 2
4
trolyte i have the formula M X , where n and n are integers, and let i yield the ions
n n
M and X in solution:
z
z
M X 1s2 S n M 1sln2 n X 1sln2 (10.33)
z
z

n n
where sln indicates species in solution. For example, for Ba(NO ) Eq. (10.33) is
3 2

2
Ba1NO 2 1s2 S Ba 1sln2 2NO 1sln2. For Ba1NO 2 and BaSO , we have
3
4
3 2
3 2
Ba1NO 2 : M Ba, X NO ; n 1, n 2; z 2, z 1

3
3 2

BaSO : M Ba, X SO ; n 1, n 1; z 2, z 2

4
4

When z 1 and z 1, we have a 1:1 electrolyte. Ba(NO ) is a 2:1 electrolyte;

3 2
Na SO is a 1:2 electrolyte; MgSO is a 2:2 electrolyte.
2 4 4
Don’t be intimidated by the notation. In the following discussion, the z’s are
charges, the n’s (nu’s) are numbers of ions in the chemical formula, the m’s (mu’s) are
chemical potentials, and the g’s (gamma’s) are activity coefficients.
Chemical Potentials in Electrolyte Solutions
We shall restrict the treatment in this section to strong electrolytes. Let the solution be
prepared by dissolving n moles of electrolyte i with formula M X in n moles of
i n n A
solvent A. The species present in solution are A molecules, M ions, and X ions. Let
z
z
n , n , and n and m , m , and m be the numbers of moles and the chemical poten-
A A
tials of A, M , and X , respectively.
z
z
The quantity m is by definition [Eq. (4.72)]

m 10G>0n 2 (10.34)

T,P,n j
where G is the Gibbs energy of the solution. In (10.34), we must vary n while hold-

ing fixed the amounts of all other species, including n . However, the requirement of

electrical neutrality of the solution prevents varying n while n is held fixed. We

can’t readily vary n(Na ) in an NaCl solution while holding n(Cl ) fixed. The same
situation holds for m . There is thus no simple way to determine m and m experi-

mentally. (Chemical potentials of single ions in solution can, however, be estimated
theoretically using statistical mechanics; see Sec. 10.7.)
Since m and m are not measurable, we define m , the chemical potential of the

i
electrolyte as a whole (in solution), by
m 10G>0n 2 (10.35)
i
i T,P,n A
where G is G of the solution. The number of moles n of dissolved electrolyte can read-
i
ily be varied at constant n , so m can be experimentally measured (relative to its value
A i
in some chosen standard state). Definitions similar to (10.35) hold for other partial

molar properties of the electrolyte as a whole. For example, V 10V>0n 2 , where
i

i T,P,n A
V is the solution’s volume. V i for MgSO in water was mentioned in Sec. 9.2.
4