The water–gas shift reaction (at

CHEMISTRY · Multi-part · A Level · Chemistry · Chemical equilibria (Le Chatelier’s principle and Kc) · Chemical equilibria (Le Chatelier’s principle and Kc)

Problem

The water–gas shift reaction

CO(g) + H_{2}O(g) \rightleftharpoons CO_{2}(g) + H_{2}(g)

K_c = 10.3

(at

700\,\text{K}

, forward reaction endothermic) occurs in a rigid vessel. The mixture is first brought to equilibrium at

700\,\text{K}

with the following concentrations:

[CO] = 0.40\,\text{M}

[H_{2}O] = 0.40\,\text{M}

[CO_{2}] = 0.20\,\text{M}

[H_{2}] = 0.20\,\text{M}

. A sequence of three stresses is then applied while the temperature or volume is varied as indicated. Concentrations are recorded continuously. •

t_{1} = 0\,\text{min}

Volume is halved instantaneously (from

2.00\,\text{L}

1.00\,\text{L}

) at constant temperature. •

t_{2} = 8\,\text{min}

After the system has re-established equilibrium,

0.050\,\text{mol}

CO_{2}

is removed rapidly;

T

and

V

remain constant. •

t_{4} = 22\,\text{min}

Immediately after the second re-equilibration, the temperature is raised to

750\,\text{K}

; the new equilibrium constant is

K_{c}' = 14.7

. Answer the following questions about the system’s behavior. (Assume ideal gases throughout.) (a) Immediately after the volume is halved at

t_{1}

, calculate the reaction quotient

Q_{c}

using the instantaneous concentrations that result solely from the volume change. Show numerically that the system is no longer at equilibrium. (b) Using the

Q_{c}

value from part (a), determine the direction of the net reaction between

t_{1}

and

t_{2}

. Explain your reasoning with reference to

Q_{c}

and

K_{c}

. (c) Just after the removal of

CO_{2}

t_{2}

, calculate the new

Q_{c}

and predict the direction in which the system will shift between

t_{2}

and the next equilibrium point at

t_{3}

. (d) Explain qualitatively how the temperature increase at

t_{4}

(

700\,\text{K} \to 750\,\text{K}

) affects the relative concentrations of reactants and products once the system reaches the new equilibrium, taking into account both the magnitude of

K_{c}

and the stated thermochemistry of the reaction.

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