Page 133 - Physical Chemistry

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114
Chapter 4
Material Equilibrium accurately estimate V of the gas from the ideal-gas law: V RT/P 30.6
m
m
3
3
3
3
10 cm /mol. Therefore V 30.6 10 cm and
3
3
3
w 1 30.6 10 cm atm218.314 J2>182.06 cm atm2 3.10 kJ ¢A
Exercise
Find G and A for the freezing of 1.00 mol of H O at 0°C and 1 atm. Use data
2
from Prob. 2.49. (Answer: 0, 0.16 J.)
5
What is the relation between the minimization-of-G equilibrium condition at con-
stant T and P and the maximization-of-S equilibrium condition? Consider a system
univ
in mechanical and thermal equilibrium undergoing an irreversible chemical reaction
or phase change at constant T and P. Since the surroundings undergo a reversible
isothermal process, S q /T q /T. Since P is constant, q H and
surr surr syst syst syst
S H /T. We have S S S and
surr syst univ surr syst
¢S univ ¢H syst >T ¢S syst 1¢H syst T ¢S syst 2>T ¢G syst >T
¢S univ ¢G syst >T closed syst., const. T and P, P-V work only (4.21)
where (4.20) was used. The decrease in G as the system proceeds to equilibrium at
syst
constant T and P corresponds to a proportional increase in S . The occurrence of a
univ
reaction is favored by having S positive and by having S positive. Having
syst surr
H negative (an exothermic reaction) favors the reaction’s occurrence because the
syst
heat transferred to the surroundings increases the entropy of the surroundings ( S
surr
H /T).
syst
The names “work function” and “Gibbs free energy” arise as follows. Let us drop
the restriction that only P-V work be performed. From (4.11) we have for a closed
system in thermal and mechanical equilibrium that dA SdT dw. For a constant-
temperature process in such a system, dA dw. Forafinite isothermal process, A w.
Our convention is that w is the work done on the system. The work w done by the sys-
by
tem on its surroundings is w w, and A w for an isothermal process.
by by
Multiplication of an inequality by 1 reverses the direction of the inequality; therefore
w ¢A const. T, closed syst. (4.22)
by
The term “work function” (Arbeitsfunktion) for A arises from (4.22). The work
done by the system in an isothermal process is less than or equal to the negative of the
change in the state function A. The equality sign in (4.22) holds for a reversible
process. Moreover, A is a fixed quantity for a given change of state. Hence the max-
imum work output by a closed system for an isothermal process between two given
states is obtained when the process is carried out reversibly.
Note that the work w done by a system can be greater than or less than U,
by
the internal energy decrease of the system. For any process in a closed system, w
by
U q. The heat q that flows into the system is the source of energy that allows w by
to differ from U. Recall the Carnot cycle, where U 0 and w 0.
by
Now consider G. From G A PV, we have dG dA PdV VdP, and use
of (4.11) for dA gives dG SdT dw PdV VdP for a closed system in ther-
mal and mechanical equilibrium. For a process at constant T and P in such a system
dG dw P dV const. T and P, closed syst. (4.23)
Let us divide the work into P-V work and non-P-V work w non-P-V . (The most common
kind of w non-P-V is electrical work.) If the P-V work is done in a mechanically reversible