For any generalized pure first-order chemical reaction, what is the exact mathematical ratio rigorou — Chemical Kinetics Chemistry Question

💡 Solution & Explanation

For first order kinetics, $t \propto \log(a / (a-x))$. Therefore, $t_{99\%} \propto \log(100/1) = 2$. Similarly, $t_{99.9\%} \propto \log(1000/1) = 3$. The precise calculated mathematical ratio evaluating $t_{99.9\%} / t_{99\%}$ cleanly resolves to exactly $3 / 2$, which evaluates perfectly to $1.5$.