## Question

If the initial concentration of the reactant is $a$, then the correct expressions for the zero and first-order reactions are:

A $t_{1/2} \propto a$, $t_{1/2} \propto \frac{1}{a}$

B $t_{1/2} \propto a$, $t_{1/2} \propto a^{0}$

C $t_{1/2} \propto a^{0}$, $t_{1/2} \propto a$

D $t_{1/2} \propto a$, $t_{1/2} \propto \frac{1}{a^{2}}$

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## Answer

The correct answer is **B**:
$$
t_{1/2} \propto a, \quad t_{1/2} \propto a^{0}
$$

**Explanation**:

- For a
**zero-order reaction**, the half-life ($ t_{1/2} $) is**directly proportional**to the initial concentration ($ a $), i.e., $ t_{1/2} \propto a $. - For a
**first-order reaction**, the half-life is**independent**of the initial concentration, described by $ t_{1/2} \propto a^{0} $.

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