In a heavily studied third-order gas-phase complex reaction , if the baseline initial concentration — Chemical Kinetics Chemistry Question

💡 Solution & Explanation

According to the general kinetic relation $t_{1/2} \propto \frac{1}{a^{n-1}}$, for a third-order reaction ($n=3$), we get $t_{1/2} \propto \frac{1}{a^2}$. If the initial concentration $a$ is multiplied by 2 (doubled), the new half-life becomes proportional to $\frac{1}{(2a)^2} = \frac{1}{4a^2}$. This represents exactly $\frac{1}{4}^{\text{th}}$ of the original half-life. Thus, the integer value of $X$ is 4.