$$ \ce{X(g) + 2Q(g) <--> R(g) + Z(g) } \hskip{2em} K_c=1.3\times 10^5 \text{ at } 50^\circ\text{C}$$

A 1.0 mol sample of \(\ce{X(g)}\) and a 1.0 mol sample of \(\ce{Q(g)}\) are introduced into an evacuated, rigid 10.0 L container and allowed to reach equilibrium at \(50^\circ\text{C}\) according to the equation above. At equilibrium, which of the following is true about the concentration of the gases?

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Since the value for \(K_c\) is very large, the reaction goes essentially to completion.

We can make an ICE table to find the values at equilibrium:

$$ \ce{X(g) + 2Q(g) <--> R(g) + Z(g) }$$ $$ \begin{array}{c|c|c|c|c|} \hline & \ce{X(g)} & \ce{Q(g)} & \ce{R(g)} & \ce{Z(g)} \\ \hline \text{I} & 1.0 & 1.0 & 0.0 & 0.0 \\ \hline \text{C} & -x & -2x & x & x \\ \hline \text{E} & 1-x & 1-2x & x & x \\ \hline \end{array} $$

Since the reaction essentially goes to completion, the reactants will react fully. Think of this as a limiting reactant problem. The maximum value for \(x\) is 0.5, at which point no further reactions will occur.

$$ \begin{array}{c|c|c|c|c|} \hline & \ce{X(g)} & \ce{Q(g)} & \ce{R(g)} & \ce{Z(g)} \\ \hline \text{I} & 1.0 & 1.0 & 0.0 & 0.0 \\ \hline \text{C} & -0.5 & -2(0.5) & 0.5 & 0.5 \\ \hline \text{E} & 0.5 & 0 & 0.5 & 0.5 \\ \hline \end{array} $$