6.5 Thermodynamic Functions of Nonideal Solutions 275
PROBLEMS
Section 6.4: The Activities of Nonvolatile Solutes
6.35 a.Look up the value of the dielectric constant and density
for methanol. Calculate the values of the
Debye–Hückel parametersαandβfor methanol as the
solvent at 298.15 K.
b.Calculate the value ofγ±for a 0.0100 mol kg−^1 NaCl
solution in methanol at 298.15 K. Calculate the percent
difference between this value and that in water at the
same temperature and molality.
6.36 a.Calculate the value ofγ±for a 0.0075 mol kg−^1 KCl
solution at 298.15 K using the Debye–Hückel
formula, Eq. (6.4-27), and using a value ofβa
equal to 1.00 kg^1 /^2 mol−^1 /^2. Repeat the calculation
for a 0.0075 mol kg−^1 FeSO 4 solution at the
same temperature, using the same value
ofβa.
b.Repeat the calculations of part a using the Davies
equation. Calculate the percent difference between
each value in part a and the corresponding value in
part b.
6.37 a.Make a plot ofγ±as a function of the molality for a
1-1 electrolyte at 298.15 K, using the Davies equation.
Compare your graph with that of Figure 6.10 and
comment on any differences.
b. Make a plot ofγ±as a function of the molality for a
1-2 electrolyte at 298.15 K, using the Davies equation.
Compare your graph with that of Figure 6.10 and
comment on any differences.
c.Make a plot ofγ±as a function of the molality for a
2-2 electrolyte at 298.15 K, using the Davies equation.
Compare your graph with that of Figure 6.10 and
comment on any differences.
6.38Find the activity coefficient of a 0.200 mol kg−^1 solution
of NaCl in water at 298.15 K, using (a) the Debye–Hückel
equation and (b) the Davies equation. Which is more
nearly correct for this molality? The experimental value is
found in Table A.11 of the appendix.6.5 Thermodynamic Functions of Nonideal Solutions
We begin with the expression for the chemical potential of a component of a nonideal
solution, using convention I:μiμ∗i+RTln(ai)μ∗i+RTln(
γi(I)xi)
(6.5-1)
Manipulation of this equation allows us to obtain formulas for all of the thermodynamic
variables for a nonideal solution.Partial Molar Quantities in Nonideal Solutions
An expression for the partial molar entropy can be obtained by use of Eq. (4.5-14):
(
∂S
∂ni)
T,P,n′Si−(
∂μi
∂T)
P,n(6.5-2)
Si−(
∂μ∗i
∂T)
P,n−Rln(
γ
(I)
i xi)
−RT
⎛
⎝
∂ln(
γi(I)xi)
∂T
⎞
⎠
P,n