For a reversible reaction, the rate constants for the forward and backward reactions are 0.16 and 4 — Chemical Equilibrium Chemistry Question

💡 Solution & Explanation

Step 1 - Define the Equilibrium Constant kinetically For any general reversible reaction: \[\ce{A <=> B}\] The equilibrium constant (\(K_{\text{eq}}\)) from a kinetic perspective is defined as the ratio of the rate constant of the forward reaction (\(k_{\text{f}}\)) to the rate constant of the backward reaction (\(k_{\text{b}}\)): \[K_{\text{eq}} = \frac{k_{\text{f}}}{k_{\text{b}}}\] Step 2 - Substitute the given values into the formula We are given: * Rate constant for the forward reaction (\(k_{\text{f}}\)) = \(0.16\) * Rate constant for the backward reaction (\(k_{\text{b}}\)) = \(4 \times 10^4\) Substituting these values into our relation: \[K_{\text{eq}} = \frac{0.16}{4 \times 10^4}\] Step 3 - Calculate the final value To simplify the division, we can express the decimal \(0.16\) in scientific notation as \(16 \times 10^{-2}\): \[K_{\text{eq}} = \frac{16 \times 10^{-2}}{4 \times 10^4}\] \[K_{\text{eq}} = \left(\frac{16}{4}\right) \times 10^{-2 - 4}\] \[K_{\text{eq}} = 4 \times 10^{-6}\] Thus, the equilibrium constant of the reaction is: \[K_{\text{eq}} = \boxed{4 \times 10^{-6}}\] Step 4 - Evaluate the given options * **Option (A) \(0.25 \times 10^6\)**: Incorrect. This is the inverse of the ratio (\(k_{\text{b}} / k_{\text{f}}\)) scaled incorrectly by a factor of 10. * **Option (B) \(2.5 \times 10^5\)**: Incorrect. This is the reciprocal ratio (\(k_{\text{b}} / k_{\text{f}} = 4 \times 10^4 / 0.16\)), which represents the equilibrium constant of the reverse reaction rather than the forward reaction. * **Option (C) \(4 \times 10^{-6}\)**: Correct. This is the exact value of \(K_{\text{eq}}\) calculated using the correct forward-to-backward rate constant ratio. * **Option (D) \(4 \times 10^{-4}\)**: Incorrect. This value represents an arithmetic error in managing powers of 10 during division.