In a first order reaction $A \rightarrow B$, if $k$ is rate constant and initial concentration of the reactant

Question

In a first order reaction $A ightarrow B$, if $k$ is rate constant and initial concentration of the reactant A is $0.5 	ext{ M}$ then the half-life is:

Accepted Answer

For a first-order reaction, the half-life period ($t_{1/2}$) is given by the integrated rate equation :
$t_{1/2} = \frac{\ln 2}{k} = \frac{2.303 \log 2}{k} = \frac{0.693}{k}$
As seen from the formula, the half-life of a first-order reaction is constant and independent of the initial concentration of the reactant . Therefore, the given initial concentration of $0.5 	ext{ M}$ does not change the formula, and the half-life remains $\frac{\ln 2}{k}$.

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