Page 155 - Physical Chemistry

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Chapter 4 From the Gibbs equations for dU, dH, and dG, expressions for the variations in U,
Material Equilibrium H, and G with respect to T, P, and V were found in terms of the readily measured prop-
erties C , a, and k. Application of the Euler reciprocity relation to dG SdT
P
VdP gives (
S/
P) (
V/
T) ; (
S/
V) is found similarly from the Gibbs equa-
P
T
T
tion for dA. These relations allow calculation of U, H, and S for arbitrary changes
of state.
For a system (open or closed) in mechanical and thermal equilibrium with P-V
a
a
work only, one has dG SdT VdP m dn , where the chemical poten-
a
i
i
i
a
a
a
tial of substance i in phase a is defined as m 10G >0n 2 a . This expression for
i
i T,P,n j i
dG applies during an irreversible chemical reaction or transport of matter between
phases.
The condition for equilibrium between phases is that, for each substance i, the
a
b
chemical potential m must be the same in every phase in which i is present: m m .
i
i
i
The condition for reaction equilibrium is that n m 0, where the n ’s are the reac-
i
i
i
i
tion’s stoichiometric numbers, negative for reactants and positive for products. The
chemical potentials are the key properties in chemical thermodynamics, since they
determine phase and reaction equilibrium.
Important kinds of calculations dealt with in this chapter include:
• Calculation of U, H, and S for changes in system temperature and pressure
and calculation of G and A for isothermal processes (Sec. 4.5).
• Calculation of C C , (
U/
V) , (
H/
P) , (
S/
T ) , (
S/
P) , etc., from read-
T
V
P
T
T
P
ily measured properties (C , a, k) (Sec. 4.4).
P
Although this has been a long, mathematical chapter, it has presented concepts and
results that lie at the heart of chemical thermodynamics and that will serve as a foun-
dation for the remaining thermodynamics chapters.
FURTHER READING
Zemansky and Dittman, chaps. 9, 14; Denbigh, chap. 2; Andrews (1971), chaps. 13, 15,
20, 21; Van Wylen and Sonntag, chap. 10; Lewis and Randall, App. 6; McGlashan,
chaps. 6, 8.
PROBLEMS
Section 4.3 boiling point of 80.1°C and 1 atm; (c) adiabatic expansion of
4.1 True or false? (a) The quantities U, H, A, and G all have 0.100 mol of a perfect gas into vacuum (Joule experiment) with
the same dimensions. (b) The relation G H T S is initial temperature of 300 K, initial volume of 2.00 L, and final
valid for all processes. (c) G A PV. (d) For every closed volume of 6.00 L.
system in thermal and mechanical equilibrium and capable of
only P-V work, the state function G is minimized when material Section 4.4
equilibrium is reached. (e) The Gibbs energy of 12 g of ice at 4.3 Express each of the following rates of change in terms of
0°C and 1 atm is less than the Gibbs energy of 12 g of liquid state functions. (a) The rate of change of U with respect to tem-
water at 0°C and 1 atm. (f ) The quantities SdT, TdS, VdP, and perature in a system held at constant volume. (b) The rate of
2
VdP all have dimensions of energy. change of H with respect to temperature in a system held at con-
1
stant pressure. (c) The rate of change of S with respect to tem-
4.2 Calculate G, A, and S univ for each of the following perature in a system held at constant pressure.
processes and state any approximations made: (a) reversible
melting of 36.0 g of ice at 0°C and 1 atm (use data from Prob. 4.4 The relation (
U/
S) T [Eq. (4.37)] is notable because
V
2.49); (b) reversible vaporization of 39 g of C H at its normal is relates the three fundamental thermodynamic state functions
6
6