CHEM 331
Physical Chemistry
Fall 2014
Problem Set 10
Problems
1.
Show that:
= -
2.
a) For H2O(l) at 289K, find Gf(298.15, 100 barr), the Gibbs Free Energy of formation at
100 barr.
Data: Gfo(298.15) = - 237.129 kJ/mol
V ~ 1.000 cm3/g
M = 18.01528 g/mol
[Ans. -236.951 kJ/mol]
b) Find the Standard Gibbs Free Energy of Formation of H2O(g) at 298.15K from the
above Tabulated value for the liquid. The Vapor Pressure of Water is 23.756 Torr at
25oC. Make reasonable approximations, but state them. The Tabulated value for this
result is -228.572 kJ/mol. What is the percentage error in your calculation?
3.
a) Derive an equation for the Molar Gibbs Free Energy of a gas G(T,P) relative to the
Standard value for the gas at the same temperature, in terms of Virial Coefficients.
Recall,
Z = 1 + B’P + C’P2 + D’P3
with B’, C’ and D’ being functions of temperature.
b) For Methane at 200K:
B’ = -5.66 x 10-3 barr-1
C’ = 6.68 x 10-6 barr-2
D’ = 17.3 x 10-9 barr-3
Calculate the Gibbs Free Energy of 1 mole Methane at 100 barr and 200K, relative to
Go(200K). Compare this result with the Ideal value.
[Ans. 6782, 7658 Joule]
c) Calculate the fugacity for Methane at 100 barr and 200K.
4.
Plot a graph showing the Molar Gibbs Functions for Methanol Liquid and Methanol Ideal
Gas at 298K over a pressure range from 50 to 750 Torr. Label the points corresponding to
the Standard States. Show, by a heavy line, the sections of the curves representing the
stable phases. What is the value of P at the point of intersection? What is the significance
of this result?
Data: Gf,liqo(298) = -166.27 kJ/mol
Gf,gaso(298) = -161.96 kJ/mol
(Take the Gibbs function values for the elements in their Standard Reference States to be
zero.)
5.
For gaseous mixtures, the Virial expansion of the Compressibility Factor Z to first order
becomes:
Z = 1 + B’P
with B’ given by:
B’ = x12B1 + 2x1x2B12 + x22B2
where B1, B2 and B12 are functions of temperature only. The coefficients B1 and B2 are
obtained from Equation of State data for the two components, while the interaction
constant B12 requires data for mixtures of else must be estimated.
a) Find the expression for V(T,P,n1,n2) for the mixture.
b) Find expressions for and . Put these in terms of mole fractions.
c) Find the fugacity for component 1 assuming:
B12 = (B1 + B2)/2
[Ans. f1 = x1PeB1P]
6.
For solutions of KI in CH3OH, it has been found:
= a + bm + cm3/2
where
is the volume per unit mass of solvent, of a solution of molality m.
Data: a = 1271.5 cm3/kg
b = 21.45 cm3/mol
c = 11.45 cm3kg1/2/mol3/2
a) Find an expression for V(n1, m).
b) Show that:
=
c) Find expression for and as functions of molality.
d) Find the standard values
and
for solvent and solute.
e) Find the volume change which results when one mole of KI (M = 166.0 g/mol, d = 3.13
g/cm3) is dissolved in a large volume of Methanol.
[Ans. -31.58 cm3]
f) Find the volume change which results when one mole of KI dissolves in one liter of
Methanol (M = 32.04 g/cm3).
[Ans. -18.64 cm3]
7.
Compute the
,
,
in producing a mole of Methane-Helium mixture that
is 75% Helium at 298K and 101.3 kPa. Assume the gaseous mixture is behaving ideally.