6.5 Thermodynamic Functions of Nonideal Solutions 281
temperature is equal to 252 torr. An aqueous solution of
n-propanol with a mole fraction ofn-propanol equal to
0.100 has a partial vapor pressure of water equal to
22.7 torr and a partial vapor pressure ofn-propanol equal
to 13.2 torr.
a.Find the mole fraction ofn-propanol in the vapor phase
at equilibrium with the solution at 298.15 K.
b. Using convention II, find the activities and activity
coefficients of the two substances in the solution. State
any assumptions.
c.Using convention I, find the activities and activity
coefficients of the two substances in the solution. State
any assumptions.
d.Find the Gibbs energy change of mixing of a solution
containing 0.900 mol of water and 0.100 mol of
n-propanol. Find the excess Gibbs energy of the
solution.6.43 For a mixture of ethylene glycol (substance 1) and
methanol (substance 2) at 298.15 K, the excess enthalpy
and excess Gibbs energy were found to be
x 2 HE/cal mol−^1 GE/cal mol−^100 0
0.1 8.2 17.71
0.2 18.63 32.58
0.3 25.67 44.72
0.4 29.62 52.13
0.5 31.47 55.39
0.6 31.70 54.18
0.7 28.40 48.48
0.8 22.35 39.95
0.9 14.07 21.35
1.0 0 0a.Calculate∆Hmixand∆Gmixfor a solution consisting
of 0.100 mol of methanol and 0.4 mol of ethylene
glycol.
b. Calculate∆Hand∆Gfor mixing the solution of part a
with a solution consisting of 0.4 mol of methanol and
0.100 mol of ethylene glycol.6.44 Find the value of∆Gmixand the excess Gibbs energy for
the solution of Example 6.12. The partial pressure of
ethanol at this composition and temperature is equal to
12.45 torr, and the vapor pressure of pure ethanol at this
temperature is equal to 44.40 torr. The partial vapor
pressure of diethyl ether at this composition and pressure is
equal to 408.6 torr, and the vapor pressure of pure diethyl
ether at this temperature is equal to 442.6 torr.
6.45A solution of ethanol (substance 1) and 2,2,4-trimethyl
pentane (substance 2) hasx 2 0 .2748 anda 2 0 .8184,
using convention I. The value ofa 1 is 0.9513.
a. Find the activity coefficient of each substance, using
convention I.
b. Find the Gibbs energy change of mixing of a solution
with this composition containing a total of 2.000 mol.
6.46 In a liquid solution of tetrachlorosilane, SiCl 4 , and
tetrachloromethane, CCl 4 , the mole fraction of SiCl 4 is
equal to 0.472. At 25◦C, the vapor in equilibrium with this
solution has a mole fraction of SiCl 4 equal to 0.648. At this
temperature, the vapor pressure of pure SiCl 4 is equal to
238.3 torr, and the vapor pressure of pure CCl 4 is equal to
114.9 torr. The total vapor pressure of the solution is equal
to 179.1 torr.
a. Find the total vapor pressure that would be predicted by
Raoult’s law for this solution at this temperature, and
find the activity coefficient of each component, using
convention I.
b. Calculate∆Gmixand the excess Gibbs energy of this
solution if it contains a total of 1.000 mol of the two
substances.
6.47A liquid solution of acetone (A) and chloroform (C) with
liquid mole fractionxA 0 .7090 has a total equilibrium
vapor pressure at 308.4 K equal to 286 torr with
yA 0 .8062.
a. Using convention I, find the activities and activity
coefficients of both components in the liquid phase.
b. Find the Gibbs energy change of mixing for a liquid sol-
ution containing 0.7090 mol of A and 0.291 mol of C.
c.The Henry’s law constant for C in A at this temperature
iskC145 torr. Find the activity and activity
coefficient of chloroform in the solution of part a using
convention II.
6.48 In a solution of diethyl ether (substance 1) and acetone
(substance 2) at 30◦C withx 2 0 .400,γ 1 (I) 1 .14,γ 2 (I)
1.31, andγ 2 (II) 0 .63.
a. Find the value of∆Gmixfor a solution of 0.800 mol of
acetone and 1.200 mol of diethyl ether at 30◦C. Find
the value of the excess Gibbs energy.
b. Find the activity coefficient of acetone in the solution
of part a using the molality description, treating diethyl
ether as the solvent.
6.49 Using data in the appendix, find the standard-state
differential heat of solution of CO 2 in water at 298.15 K.
State in words what this quantity represents, including the
definition of the standard state.