The half life of a certain reaction is 50 seconds and it remains constant even if the initial concentration of the reactant is doubled. What is the order of the reaction ? a) Zero order reaction b)…

The order of a reaction can be determined by how the half-life ($t_{1/2}$) depends on the initial concentration of the reactant.

• For a zero-order reaction, the half-life is directly proportional to the initial concentration ($t_{1/2}\propto [A{]}_0$). If $[A{]}_0$ is doubled, $t_{1/2}$ also doubles.
• For a first-order reaction, the half-life is independent of the initial concentration ($t_{1/2}=\frac{\ln 2}{k}$). Doubling $[A{]}_0$ does not change $t_{1/2}$.
• For a second-order reaction, the half-life is inversely proportional to the initial concentration ($t_{1/2}\propto \frac{1}{[A{]}_0}$). If $[A{]}_0$ is doubled, $t_{1/2}$ is halved.

In this problem, the half-life remains constant even when the initial concentration is doubled. This matches the behavior of a first-order reaction.

Answer: b) First order reaction