A chemical reaction firmly obeys strict first-order kinetics and boasts a measured half-life of exac — Chemical Kinetics Chemistry Question
Question
A chemical reaction firmly obeys strict first-order kinetics and boasts a measured half-life of exactly $10 \text{ minutes}$. If the experiment rigorously begins with an initial reactant concentration $[A]_0 = 10 \text{ mol L}^{-1}$, what is the exact instantaneous rate of reaction after precisely $20 \text{ minutes}$ have elapsed?
💡 Solution & Explanation
Exactly 20 minutes represents strictly two distinct half-lives. Therefore, the absolute concentration drops significantly from $10 \text{ M} \rightarrow 5 \text{ M} \rightarrow 2.5 \text{ M}$. The fundamental rate constant $k = 0.693 / 10 = 0.0693 \text{ min}^{-1}$. Applying the first-order differential equation: $\text{Rate} = k[A]_t = 0.0693 \times 2.5 \text{ mol L}^{-1} \text{ min}^{-1}$.