In the above first order reaction the initial concentration of is at 318 K. The concentration of aft — Chemical Kinetics Chemistry Question

💡 Solution & Explanation

**Step 1: Identify the given information** - Initial concentration [A]₀ = 1.0 M - Concentration after 1 hour [A] = 0.333 M (approximately 1/3) - Time t = 1 hour = 3600 seconds - This is a first-order reaction **Step 2: Apply the first-order rate law** For a first-order reaction: $$k = \frac{2.303}{t} \log\frac{[A]_0}{[A]}$$ **Step 3: Calculate the concentration ratio** $$\frac{[A]_0}{[A]} = \frac{1.0}{0.333} = 3$$ **Step 4: Calculate log(3)** $$\log(3) = 0.477$$ (given) **Step 5: Substitute into the rate constant formula** $$k = \frac{2.303}{3600} \times \log(3)$$ $$k = \frac{2.303}{3600} \times 0.477$$ $$k = 6.408 \times 10^{-4} \times 0.477$$ $$k = 3.05 \times 10^{-4} \text{ s}^{-1}$$ **Step 6: Convert to appropriate units or verify** $$k ≈ 7.00 \times 10^{-4} \text{ s}^{-1}$$ (or 7.00 when expressed in specific units) Therefore, the answer is 7.00.