Chemistry - Chemical Kinetics Question with Solution | TestHub

The graph shows $\log t_{50\%}$ vs. $\log a$ is a horizontal line, meaning $\log t_{50\%}$ is constant. This implies $t_{50\%}$ is independent of initial concentration $a$, which is characteristic of a first-order reaction.

For a first-order reaction, the half-life ($t_{50\%}$ or $t_{1/2}$) is given by:

$$t_{1/2}=\frac{0.693}{k}$$

where $k$ is the rate constant.

Since $t_{50\%}$ is constant, the reaction is first order ($n=1$), and $t_{50\%}=\frac{0.693}{k}$.