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In a chemical reaction, $$A + 2B \rightleftharpoons 2C + D$$, the initial concentration of $$B$$ was 1.5 times of the concentration of $$A$$, but the equilibrium concentrations of $$A$$ and $$B$$ were found to be equal. The equilibrium constant ($$K$$) for the aforesaid chemical reaction is
Let the initial concentrations be $$[A] = a$$, $$[B] = 1.5a$$, and let $$x$$ of $$A$$ react. At equilibrium $$[A] = a - x$$, $$[B] = 1.5a - 2x$$, $$[C] = 2x$$, $$[D] = x$$. Equal $$[A]$$ and $$[B]$$ give $$x = 0.5a$$, so $$[A] = [B] = [D] = 0.5a$$ and $$[C] = a$$. Then $$K = \frac{[C]^2[D]}{[A][B]^2} = \frac{a^2 \times 0.5a}{0.5a \times 0.25a^2} = 4$$.
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