An amount of 1 mole each of A and D is introduced in 1L container. Simultaneously: A ⇌ B + C; = 10^6 — Chemical Equilibrium Chemistry Question

💡 Solution & Explanation

Two simultaneous equilibria in 1 L with initial 1 mol A and 1 mol D: \begin{align} \text{A} &\rightleftharpoons \text{B} + \text{C}, \quad K_{c1} = 10^6\ \text{M}^2 \tag{1} \\ \text{B} + \text{D} &\rightleftharpoons \text{A}, \quad K_{c2} = 10^{-6}\ \text{M}^{-1} \tag{2} \end{align} \textbf{Step 1:} $K_{c1} = 10^6$ is very large $\Rightarrow$ reaction (1) goes nearly to completion. After nearly complete dissociation of A: $[\text{B}] \approx 1\ \text{M}$, $[\text{C}] \approx 1\ \text{M}$. \textbf{Step 2:} $K_{c2} = 10^{-6}$ is very small $\Rightarrow$ reaction (2) barely occurs. D barely reacts. \textbf{Step 3:} Apply $K_{c1}$ exactly: \[ K_{c1} = \frac{[\text{B}][\text{C}]}{[\text{A}]} = 10^6 \] \[ [\text{A}] = \frac{[\text{B}][\text{C}]}{10^6} \approx \frac{1 \times 1}{10^6} = 10^{-6}\ \text{M} \] \textbf{Answer: A} — $[\text{A}]_{\text{eq}} = 10^{-6}\ \text{M}$