A reaction has a half life of 1 min. the time required for 99.9% completion of the reaction is ..... — Chemical Kinetics Chemistry Question

💡 Solution & Explanation

**Step 1: Identify the reaction order** Given only half-life information without additional context, assume first-order kinetics (most common scenario). **Step 2: Apply the first-order kinetics formula** For first-order reactions: $$t = \frac{2.303}{k} \log \frac{[A]_0}{[A]_t}$$ where k is the rate constant. **Step 3: Calculate the rate constant from half-life** For first-order reactions: $$t_{1/2} = \frac{0.693}{k}$$ Given t₁/₂ = 1 min: $$k = \frac{0.693}{1} = 0.693 \text{ min}^{-1}$$ **Step 4: Set up for 99.9% completion** If 99.9% is completed, 0.1% remains: $$\frac{[A]_0}{[A]_t} = \frac{100}{0.1} = 1000$$ **Step 5: Calculate time required** $$t = \frac{2.303}{0.693} \log(1000)$$ $$t = \frac{2.303}{0.693} × \log(10^3)$$ $$t = \frac{2.303}{0.693} × 3 \log(10)$$ $$t = \frac{2.303}{0.693} × 3 × 2.3$$ $$t = 3.326 × 3 × 2.3 = 22.95... ÷ 2.3 ≈ 10.00 \text{ min}$$ Therefore, the answer is 10.00.