Physical Chemistry Third Edition

7.6 The Temperature Dependence of Chemical Equilibrium. The Principle of Le Châtelier 341

PROBLEMS

Section 7.6: The Temperature Dependence of Chemical

Equilibrium. The Principle of Le Châtelier

7.46 Calculate∆G◦and the equilibrium constant for the

reaction

CaCO 3 (s)
CaO(s)+CO 2 (g)

at 500 K and at 1000 K.

a. Use the value of∆G◦at 298.15 K and assume that the

heat capacities are constant over the temperature range.

b. Find the temperature at which the equilibrium pressure

of CO 2 is equal to 1.00 atm (1.01325 bar). Compare

your result with the experimental value of 898◦C

(1171 K).

7.47 a. Find the value of the ionization constant of water at
50.0◦C.
b.What is the molality of H+ions in pure water at 50◦C?
What is the pH of pure water at 50.0◦C?
c.What is the pH at 50.0◦C of a solution containing
1.000 mol of NaCl and 1.000 kg of water? What is the
molality of H+ions? Assume that the Davies equation
can be used for the activity coefficients, and assume
thatγ(OH−)γ(H+)γ±.
7.48 Using thermodynamic data at 298.15 K, find the value of
the equilibrium constant at 400.0◦C for the reaction

2SO 2 (g)+O 2 (g)
2SO 3 (g)

Compare your value with the value at 298.15 K and relate

it to the principle of Le Châtelier.

7.49 If a reacting gaseous system is held at constantTandP

instead of at constantTandV, under some circumstances

addition of one of the reactants or products can shift the

equilibrium to produce more of the added substance.

a.Derive an expression for the derivative

(

∂ln(Kx)

∂ni

)

,

whereniis the amount of substancei.

b.Under what circumstances could addition of N 2 to an

equilibrium system containing gaseous N 2 ,H 2 , and

NH 3 shift the equilibrium to produce more N 2?

7.50 Multiply Eq. (7.6-5) byd(1/T) and carry out an

integration to obtain a formula analogous to Eq. (7.6-8).

Comment on your result.

7.51 a.Find the equilibrium constant for the reaction

N 2 +3H 2 
2NH 3

at 400 K. State any assumptions.

b.Find the equilibrium composition of a system

originally consisting of 1.000 mol of N 2 and 3.000 mol

of H 2 , maintained at 400 K and 1.000 atm. Neglect gas

nonideality.

7.52 For the reaction

2NOCl(g)
2NO(g)+Cl 2 (g)

a.Find∆H◦,∆S◦, and∆G◦at 298.15 K.

b.FindKat 298.15 K and at 373.15 K. State any

assumptions.

c.Find the degree of dissociation of 1.000 mol of NOCl

placed in a volume of 31.026 L at 373.15 K and

allowed to equilibrate. State any assumptions.

7.53 a.Find the value of the equilibrium constant at 298.15 K

for the reaction

H 2 (g)+CO 2 (g)
H 2 O(g)+CO(g)

b.Find the value of the equilibrium constant for this

reaction at 373.15 K. State any assumptions. Assume

that∆H◦is independent of temperature.

c.Equal amounts (in moles) of H 2 and CO 2 are

introduced into a vessel of variable volume and

maintained at 373.15 K and a total pressure of 1.000

bar. Find the equilibrium partial pressures of all

substances. Assume that all gases are ideal.

d.Tell qualitatively what will occur if the pressure is

increased to 5.000 bar. Give the reason for your answer.

7.54 The solubility product constant for MgF 2 is equal to

7. 1 × 10 −^9 at 18◦C, and equal to 6. 4 × 10 −^9 at 27◦C.

Find the value of∆G◦,Ksp,∆H◦, and∆S◦at 25◦C.

7.55 a.Find∆H◦,∆G◦, andKat 298.15 K for the reaction

I 2 (g)
2I(g)

b.Assuming that∆H◦constant, findKat 1000 K.