7.7 Chemical Equilibrium and Biological Systems 349a. Find the value of∆G◦for this reaction at 298.15 K.b. Find the value ofKfor this reaction at 298.15 K.c.Find the value ofKxfor this reaction at 298.15 K and
1.000 bar.d.Find the value of∆H◦for this reaction at 298.15 K.e.Using the principle of Le Châtelier, specify the
conditions of temperature and pressure (high or low
temperature, high or low pressure) that would increase
the yield of ammonia from the process.f.The process is actually carried out at high pressure
(around 500 bar) and fairly high temperature (around
500 ◦C). Comment on this practice. Why might this
temperature be used instead of a lower temperature?g.Calculate the value ofKat 500◦C, using values of
∆G◦and∆H◦at 298.15 K and assuming that∆H◦is
constant.h.Calculate the value ofKat 500◦C, using values
of−(G◦m−Hm,298◦ )/Tfrom Table A.8 of Appendix A
and interpolating. Compare with your result from
part g.i.If equilibrium is attained at a total pressure of 1.000 bar
at 298.15 K, calculate the partial pressure of each
substance if a stoichiometric mixture of hydrogen and
nitrogen is introduced into the system at the start of the
reaction.j.Find the value ofKxat 298.15 K and 1.000 bar. Find
the value ofKxat 298.15 K and 500 bar.k.Find the value ofKxat 500◦C and 1.000 bar. Find the
value ofKxat 500◦C and 500 bar.l.If equilibrium is attained at a total pressure of 500 bar
at 298.15 K, calculate the partial pressure of each
substance if a stoichiometric mixture of hydrogen and
nitrogen is introduced into the system at the start of the
reactionm. If equilibrium is attained at a total pressure of 500 bar
at 500◦C, calculate the partial pressure of each sub-
stance if a stoichiometric mixture of hydrogen and
nitrogen is introduced into the system at the start
of the reaction.7.67 Identify the following statements as either true or false. If a
statement requires some special circumstance to make it
true, label it as false.
a.Equilibrium constants are true constants.
b.Equilibrium constants depend on temperature, but do
not depend on pressure.
c.Equilibrium constants for reactions involving only gases
depend on temperature, but do not depend on pressure.
d.Dilution of a solution of a weak acid at constant
temperature increases the degree of ionization of the
acid.
e.Dilution of a solution of a weak acid can lower the pH
of the solution.
f.According to the principle of Le Châtelier, changing the
pressure on the system always causes a gas-phase
reaction to shift its equilibrium composition.
g.According to the principle of Le Châtelier, changing the
temperature always causes the equilibrium composition
of a system to shift.
7.68 The following reaction is known as the “water–gas
reaction”:H 2 (g)+CO 2 (g)H 2 O(g)+CO(g)The reaction has been used industrially as a source of
carbon monoxide, which is used as a reducing agent in
obtaining metallic iron from its ore. The system is allowed
to approach equilibrium, using an iron catalyst.
a.Find the value of∆G◦and ofKfor this reaction at
298.15 K and at 1000 K.
b.Find the value of∆H◦for this reaction at 298.15 K and
at 1000 K.
c.What experimental conditions will favor the maximum
yield of carbon monoxide?
d.Find the value of∆G◦and ofKat 1259 K, interpolating
between values of−(G◦m−Hm,298◦ )/Tin Table A.8 of
Appendix A. Compare your value ofKwith the
accepted value of 1.60.
e.Find the value of∆G◦and ofKfor this reaction at
1259 K, using the values at 1000 K and assuming that
∆H◦is constant between 1000 K and 1259 K. Compare
your result with the result of part (d).
7.69 For a sparingly soluble 1-1 electrolyte, the molality at
saturation is given bymsat/m◦√
KspwhereKspis the
solubility product constant, if it can be assumed that
activity coefficients are equal to unity. Derive a modified
version of this equation, assuming the Debye–Hückel
expression for activity coefficients.