For an unknown chemical reaction , a plot of versus yields a perfect straight line with a mathematic — Chemical Kinetics Chemistry Question

💡 Solution & Explanation

The relationship between half-life and initial concentration for an $n^{\text{th}}$ order reaction is $t_{1/2} \propto [A]_0^{1-n}$. Taking the logarithm of both sides gives $\log t_{1/2} = \text{constant} + (1-n)\log[A]_0$. This is the equation of a straight line $y = mx + c$, where the slope $m$ is $(1-n)$. Given the slope is $-2$, we have $1 - n = -2 \Rightarrow n = 3$.