Page 335 - Physical Chemistry

lev38627_ch10.qxd 3/14/08 1:07 PM Page 316

316
Chapter 10 Ionic association reduces the number of ions in solution and hence reduces the
Nonideal Solutions electrical conductivity of the solution. For example, in CaSO solutions, Ca 2 and
4

SO 2 associate to form neutral CaSO ion pairs; in MgF solutions, Mg 2 and F form
4
2
4

MgF ion pairs. The degree of association in an electrolyte solution can best be deter-
mined from conductivity measurements on the solution (Sec. 15.6). For example, one
finds that MgSO in water at 25°C is 10% associated at 0.001 mol/kg; CuSO in water
4
4
at 25°C is 35% associated at 0.01 mol/kg and is 57% associated at 0.1 mol/kg. From
conductivity data, one can calculate the equilibrium constant for the ionic association
reaction M X z ∆ MX z z . Conductivity data indicate that for 1:1 electrolytes
z
ionic association is unimportant in dilute aqueous solutions but is sometimes signifi-
cant in concentrated aqueous solutions; for most electrolytes with higher z z values,

ionic association is important in both dilute and concentrated aqueous solutions. In the
limit of infinite dilution, the degree of association goes to zero. Figure 10.10 plots the
percentage of cations that exist in ion pairs versus molality in aqueous solutions for
typical 1:1, 2:1, 2:2, and 3:1 electrolytes.
Conductivity measurements have shown that the qualitative conclusions of the
Bjerrum theory are generally correct, but quantitative agreement with experiment is
sometimes lacking.
Ion pairs should be distinguished from complex ions. Complex-ion formation is
Figure 10.10
common in aqueous solutions of transition-metal halides. In the complex ions

Typical ion-pairing extents in AgCl(aq) and AgCl (aq), the Cl ions are in direct contact with the central Ag ion
2
water at 25°C versus molality. and each AgOCl bond has a substantial amount of covalent character. In contrast, the
(See Probs. 11.17 and 11.22 for positive and negative ions of an ion pair usually retain at least part of their solvent
the method used to calculate these
curves.) sheaths and are held together by ionic (electrostatic) forces. The absorption spectrum
of the solution can frequently be used to distinguish between ion-pair and complex-
ion formation. In some solutions, both ion pairs and complex ions are present.
Thermodynamics of Ion Pairing
With allowance for formation of MX z z ion pairs [Eq. (10.69)], the Sec. 10.5 ther-
modynamic treatment of a solution containing n moles of the strong electrolyte
i
M X in solvent A is modified as follows.
n n
Let n , n , n , and n and m , m , m , and m be the numbers of moles and the
IP

A

IP
A

chemical potentials of A, M , X , and MX z z , respectively. With ion pairing
z
z
included, the Gibbs equation (10.36) becomes
dG S dT V dP m dn m dn m dn m dn IP (10.70)

A
IP
A
If no ion pairs were formed, the numbers of moles of cations and anions from M X
n n
would be n n n and n n n [Eq. (10.33)]. With ion-pair formation, the num-
i

i
ber of moles of cations and anions are each reduced by n [Eq. (10.69)]:
IP
n n n n , n n n n IP (10.71)

i
i
IP
dG S dT V dP m dn m 1n dn dn 2 m 1n dn dn 2

A
IP
A
IP
i
i
m dn IP
IP
Use of the equilibrium condition m m m for the ion-pair formation reaction
IP

(10.69) simplifies dG to
dG S dT V dP m dn 1n m n m 2 dn i (10.72)

A
A

which is the same as (10.37) in the absence of ion pairs.
The chemical potential m 10G>0n 2 of the electrolyte as a whole is thus
i
i T,P,n j i
the same as (10.38). Therefore, Eq. (10.46) for m i is still valid. However, the molalities
m and m in (10.46) are changed. Let a be the fraction of the ions M that do not
z