For the given first order reaction A → B the half life of the reaction is 0.3010 min. The ratio of t — Chemical Kinetics Chemistry Question
Question
For the given first order reaction A → B the half life of the reaction is 0.3010 min. The ratio of the initial concentration of reactant to the concentration of reactant at time 2.0 min will be equal to ___________. (Nearest integer)
💡 Solution & Explanation
**Step 1: Find the rate constant (k) using the half-life formula** For a first-order reaction: $$t_{1/2} = \frac{0.693}{k}$$ $$k = \frac{0.693}{0.3010} = 2.303 \text{ min}^{-1}$$ **Step 2: Apply the first-order integrated rate law** $$\ln\left(\frac{[A]_0}{[A]_t}\right) = kt$$ where [A]₀ is initial concentration and [A]_t is concentration at time t. **Step 3: Substitute values at t = 2.0 min** $$\ln\left(\frac{[A]_0}{[A]_{2.0}}\right) = 2.303 × 2.0$$ $$\ln\left(\frac{[A]_0}{[A]_{2.0}}\right) = 4.606$$ **Step 4: Convert from natural logarithm to ratio** $$\frac{[A]_0}{[A]_{2.0}} = e^{4.606}$$ $$\frac{[A]_0}{[A]_{2.0}} = 99.99 ≈ 100$$ Therefore, the answer is 100.