Chemical Equilibrium

Homework 4 Solutions have not been released yet.

Use

$$R=8.314\ \mathrm{J\,mol^{-1}K^{-1}}$$

Unless otherwise stated, pressures are given in bar.

Show the main steps of your calculations. For equilibrium-composition problems, clearly define the change in pressure before solving.

Pure solids are not included in equilibrium-constant expressions.

Equilibrium Constants

Problem 1Medium

For each equilibrium below, write the expression for the equilibrium constant. If a substance does not appear in the expression, briefly explain why.

a)

$$2CO(g)+O_2(g)\rightleftharpoons2CO_2(g)$$

b)

$$C(s)+O_2(g)\rightleftharpoons CO_2(g)$$

c)

$$2NH_3(g)\rightleftharpoons N_2(g)+3H_2(g)$$

d)

$$2C(s)+O_2(g)\rightleftharpoons2CO(g)$$

Manipulating Equilibrium Constants

Problem 2Medium

At a certain temperature,

$$N_2(g)+3H_2(g)\rightleftharpoons2NH_3(g)$$

has

$$K_p=36.0$$

Without using thermodynamic data, determine the equilibrium constant for each of the following reactions.

a)

$$2NH_3(g)\rightleftharpoons N_2(g)+3H_2(g)$$

b)

$$\frac{1}{2}N_2(g)+\frac{3}{2}H_2(g)\rightleftharpoons NH_3(g)$$

c)

$$NH_3(g)\rightleftharpoons\frac{1}{2}N_2(g)+\frac{3}{2}H_2(g)$$

For each part, indicate what operation was performed on the original reaction.

Equilibrium Composition

Problem 3Hard

A rigid vessel initially contains only ammonia gas at a pressure of

$$6.00\ \mathrm{bar}$$

At constant temperature, the following equilibrium is established:

$$2NH_3(g)\rightleftharpoons N_2(g)+3H_2(g)$$

At equilibrium, the total pressure is

$$8.00\ \mathrm{bar}$$

Calculate:

a) the equilibrium partial pressure of each gas;

b) the equilibrium constant for the reaction.

Equilibrium Composition

Problem 4Hard

At a certain temperature,

$$2CO(g)+O_2(g)\rightleftharpoons2CO_2(g)$$

has

$$K_p=4.00$$

Initially,

$$P_{CO}=3.00\ \mathrm{bar}$$ $$P_{O_2}=2.00\ \mathrm{bar}$$ $$P_{CO_2}=0$$

The system is allowed to reach equilibrium at the same temperature.

Determine:

a) the equilibrium partial pressure of each gas;

b) the total pressure at equilibrium.

Set up the initial-change-equilibrium relations before solving.

Combining Equilibria

Problem 5Medium

At the same temperature, the following equilibrium constants are known:

$$2C(s)+O_2(g)\rightleftharpoons2CO(g)$$ $$K_{p,1}=5.00$$

and

$$2CO(g)+O_2(g)\rightleftharpoons2CO_2(g)$$ $$K_{p,2}=20.0$$

Using only these two reactions, determine the equilibrium constant for

$$C(s)+O_2(g)\rightleftharpoons CO_2(g)$$

Show how the given reactions must be combined.

Thermodynamics and Equilibrium

Problem 6Medium

For the reaction

$$3O_2(g)\rightleftharpoons2O_3(g)$$

suppose that at

$$T=298\ \mathrm{K}$$

the thermodynamic quantities are

$$\Delta H^\circ=+285.0\ \mathrm{kJ\,mol^{-1}}$$

and

$$\Delta S^\circ=-138.0\ \mathrm{J\,mol^{-1}K^{-1}}$$

Calculate:

a) the standard Gibbs energy change at this temperature;

b) the equilibrium constant at this temperature;

c) based on the value of the equilibrium constant, state which side of the equilibrium is strongly favored under standard-state conditions.

Thermodynamics and Equilibrium

Problem 7Hard

For the reaction

$$H_2(g)+Cl_2(g)\rightleftharpoons2HCl(g)$$

the standard Gibbs energy change at

$$298\ \mathrm{K}$$

is

$$\Delta G^\circ=-5.71\ \mathrm{kJ\,mol^{-1}}$$

A rigid vessel initially contains

$$P_{H_2}=1.00\ \mathrm{bar}$$ $$P_{Cl_2}=1.00\ \mathrm{bar}$$ $$P_{HCl}=0$$

Calculate:

a) the equilibrium constant at this temperature;

b) the equilibrium partial pressure of each gas;

c) the percentage of the initial hydrogen that reacts.

Combining Equilibria

Problem 8Hard

At the same temperature,

$$C(s)+O_2(g)\rightleftharpoons CO_2(g)$$

has

$$K_{p,1}=10.0$$

and

$$2CO(g)+O_2(g)\rightleftharpoons2CO_2(g)$$

has

$$K_{p,2}=20.0$$

Determine the equilibrium constant for

$$2C(s)+O_2(g)\rightleftharpoons2CO(g)$$

The final reaction must be obtained algebraically from the two given reactions. Simply writing an equilibrium-constant expression is not sufficient.