JEE Main · 2025 · 24 Jan 2025 · Shift 2 · Chemical Kinetics

For a first-order reaction, the half-life $t_{1/2}=\frac{\ln 2}{k}$ is a constant, independent of the initial concentration $[R{]}_0$ — a plot of $t_{1/2}$ against $[R{]}_0$ is a flat horizontal line. This independence from initial concentration is Statement I, which is therefore true.

The integrated first-order rate law is $\ln \frac{[R{]}_0}{[R]}=kt$, or in base-10 form, $\log \frac{[R{]}_0}{[R]}=\frac{k}{2.303}t$ — a straight line through the origin with slope $k/2.303$ when $\log ([R{]}_0/[R])$ is plotted against time. Statement II instead plots the reciprocal ratio $\log ([R]/[R{]}_0)$ as a straight line with a positive slope of $k/2.303$; but $\log ([R]/[R{]}_0)=-\frac{k}{2.303}t$ actually decreases with time, giving a negative slope, not the positive one claimed. The relationship as depicted in Statement II is false.

Statement I is true but Statement II is false.