At 500 K, the equilibrium constant $K_c$ for the reaction $A(g) + B(g) \rightleftharpoons C(g) + D(g)$ is 0.040. If the initial concentrations of A and B are each $1.0\,mol\,dm^{-3}$ and no C or D are present initially, what is the equilibrium concentration of C? (Let $x$ = moles per dm³ of C formed at equilibrium.)

At equilibrium: $[A]=[B]=1.0-x$ and $[C]=[D]=x$. So $K_c = x^2/(1.0-x)^2 = 0.040$. Taking the square root of both sides: $x/(1.0-x) = 0.200$, giving $x = 0.200 - 0.200x$, so $1.200x = 0.200$ and $x = 0.200/1.200 \approx 0.167 \approx 0.17\,mol\,dm^{-3}$. Option B results from equating $x$ directly to $K_c$, and option D from forgetting to take the square root of $K_c$.