Question

The equilibrium constant at 298 K for a reaction \(\mathrm{A + B \rightleftharpoons C + D}\) is 100. If the initial concentration of all the four species were 1 M each, then equilibrium concentration of D (in \(\mathrm{mol\ L^{-1}}\)) will be:

• A. 0.818
• B. 1.818
• C. 1.182
• D. 0.182

Hint:

Since \(Q = 1 < K\), the reaction goes forward; let x mol/L of A and B react and use \(K = \frac{(1+x)^2}{(1-x)^2}\).

Answer 1

The Correct Option is B

Initially \(Q = \frac{1 \times 1}{1 \times 1} = 1 < K = 100\), so the reaction proceeds forward.
At equilibrium: \([A] = [B] = 1 - x\), \([C] = [D] = 1 + x\).
\(K = \frac{(1+x)^2}{(1-x)^2} = 100 \Rightarrow \frac{1+x}{1-x} = 10\).
\(1 + x = 10 - 10x \Rightarrow 11x = 9 \Rightarrow x = 0.818\).
\([D] = 1 + x = 1.818\ \mathrm{mol\ L^{-1}}\).
Answer: (2) 1.818