Chemistry 9701 · AS & A Level · Equilibria

Equilibria — practice question

One way to make hydrogen from natural gas is through the reaction of hydrogen sulfide with methane: $2\text{H}_2\text{S(g)} + \text{CH}_4\text{(g)} \rightleftharpoons \text{CS}_2\text{(g)} + 4\text{H}_2\text{(g)}$.
(a)[2]

State the expression for $K_p$ for this reaction, and give its units.

(b(i))[2]

Calculate the equilibrium partial pressures of $\text{H}_2\text{S(g)}$ and $\text{H}_2\text{(g)}$ if initially $p(\text{H}_2\text{S}) = 200\ \text{atm}$ and $p(\text{CH}_4) = 100\ \text{atm}$, and at equilibrium $p(\text{CS}_2) = 2\ \text{atm}$ while the remaining $p(\text{CH}_4) = 98\ \text{atm}$.

(b(ii))[1]

Calculate the value of $K_p$ at this temperature.

(c(i))[1]

Predict the sign of $\Delta S^\circ$ for this reaction. Explain your answer.

(c(ii))[2]

At $1000\,\text{K}$, the free energy change, $\Delta G^\circ$, for this reaction is $+51\,\text{kJ mol}^{-1}$. Calculate the value of $\Delta S^\circ$ for this reaction, and state its units.

(d)[2]

How would the value of $\Delta G^\circ$, and therefore the spontaneity (feasibility) of this reaction, change as the temperature increases? Explain your answer.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: The required expression is $K_p = \dfrac{p(\mathrm{CS_2})\,p(\mathrm{H_2})^4}{p(\mathrm{H_2S})^2\,p(\mathrm{CH_4})}$.

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