Page 55 - Basic physical chemistry for the atmospheric sciences

Chemical thermodynamics 41

show that for a reversible transformation at constant pres­
sure and temperature, da is equal to the decrease in the
Gibbs free energy (da = - d g).
2. 1 9 . The Helmholtz f r ee energy o f a unit mass o f a system is
defined as

f= u - T s
Show that the criterion for the thermodynamic equilibrium
of a system at constant temperature and volume is that the
Helmholtz free energy of the system have a minimum value.
2 . 2 0. U s ing the definition of f given in Exercise 2. 1 9 and the
definition of dw101a1 given in Exercise 2 . 1 8 , show that for a
i
reversible, s othermal transformation
d f
dwtotal = -
2
2. 1 . Calculate Ll"&j! and K at 298K for the forward reaction
P
2N O(g) + 0 2 (g) � 2N Oi(g)
Are the reactants or products favored for the forward reac­
tion at equilibrium?
2 . 2 2 . By considering the signs o f LlS 0 and t},,H:x determine
whether the reaction
2N O(g) � N 2(g) + 02 (g)

is favored at high or low temperatures. Consider the impli­
cation of your conclusion with respect to NO(g) pollution
from combustion processes.
2 . 2 3 . Derive the relationship given i n Exercise 2 . 1 1 using the
Gibbs-Helmholtz equation (2.29) and Eq. (2.43).
2.2 . Calculate the equilibrium constants KP at 298K and SOOK
4
for the reaction
H202 (g)� H2 0(g) + !02(g)
2.25. Calculate the change in chemical potential when an ideal gas
expands from 1 atm to 0.5 atm at l5°C.
2.26. Show that

dq = dh - a dp
2
where the symbols are as defined in Section . 1 .