Question

The rate equation for a reaction $A \rightarrow B$ is $r = k[A]^{0}$. If the initial concentration of the reactant is $a$ mol dm$^{-3}$, the half-life period of the reaction is

• A. $\frac{a}{2k}$
• B. $\frac{k}{a}$
• C. $\frac{a}{k}$
• D. $\frac{2a}{k}$

Hint:

Half-life of zero-order reaction is directly proportional to initial concentration.

Answer 1

The Correct Option is A

Step 1: Identify Order
The rate equation $r = k[A]^{0}$ indicates a zero-order reaction.
Step 2: Half-life Formula
For a zero-order reaction, the half-life $t_{1/2}$ is given by $\frac{[A]_{0}}{2k}$.
Step 3: Substitution
Given initial concentration $a$, the half-life is $t_{1/2} = \frac{a}{2k}$.
Final Answer: (a)