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Equilibria: Question 1

Syllabus 7.1

Multiple choice AS 1 mark

A gaseous equilibrium is established in a sealed, rigid container of fixed volume:

X(g)+Y(g)⇌2Z(g)ΔH=−114 kJ mol−1\text{X(g)} + \text{Y(g)} \rightleftharpoons 2\text{Z(g)} \qquad \Delta H = -114\ \text{kJ mol}^{-1}

With no other change made to the system, the temperature of the container is then lowered.

Which row correctly describes the effect on the position of equilibrium and on the value of KcK_c?

Choose an answer to check it, then compare with the worked solution below.
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Worked solution

Step 1: Identify which direction is exothermic and which is endothermic

The forward reaction, X(g)+Y(g)→2Z(g)\text{X(g)} + \text{Y(g)} \rightarrow 2\text{Z(g)}, has ΔH=−114 kJ mol−1\Delta H = -114\ \text{kJ mol}^{-1}, so it is exothermic. It follows that the reverse reaction, 2Z(g)→X(g)+Y(g)2\text{Z(g)} \rightarrow \text{X(g)} + \text{Y(g)}, is endothermic (ΔH=+114 kJ mol−1\Delta H = +114\ \text{kJ mol}^{-1}).

Step 2: Apply Le Chatelier’s principle to the temperature decrease

Le Chatelier’s principle states that a system at equilibrium responds to a decrease in temperature by shifting in whichever direction releases heat energy, i.e. the exothermic direction. Here that is the forward reaction, so the position of equilibrium shifts right, towards Z\text{Z}.

Step 3: Determine the effect on KcK_c

Kc=[Z(g)]2[X(g)][Y(g)]K_c = \frac{[\text{Z(g)}]^2}{[\text{X(g)}][\text{Y(g)}]}

Since the position moves right, the equilibrium concentration of Z\text{Z} rises relative to X\text{X} and Y\text{Y}, so the ratio above, and hence KcK_c, increases. This matches the general rule for equilibrium constants: lowering the temperature always increases KcK_c for a reaction whose forward direction is exothermic (as here), and always decreases KcK_c for a reaction whose forward direction is endothermic. Note that this is unlike a change in pressure or concentration, which can shift the position of equilibrium without changing the value of KcK_c at all, only a change in temperature alters KcK_c itself.

Why the other options are wrong

  • A: pairs a leftward shift with a decrease in KcK_c. This combination would be correct only if the forward reaction were endothermic, but it is exothermic here.
  • C: a rightward shift cannot occur alongside a decrease in KcK_c; shifting towards products always corresponds to a larger value of the equilibrium constant, not a smaller one.
  • D: a leftward shift cannot occur alongside an increase in KcK_c, for the same reason, shifting towards reactants always corresponds to a smaller equilibrium constant.

Final answer

  • Position shifts right (towards Z\text{Z}); KcK_c increases, option B.