In a first order reaction $\mathrm{A} \rightarrow \mathrm{B}$ if $k$ is rate constant and initial…

In a first order reaction $\mathrm{A} \rightarrow \mathrm{B}$ if $k$ is rate constant and initial concentration of the reactant $\mathrm{A}$ is $0.5 \mathrm{M}$, then the half-life is:
  1. $\frac{\log 2}{k}$
  2. $\frac{\log 2}{k \sqrt{0.5}}$
  3. $\frac{ln 2}{k}$
  4. $\frac{0.693}{0.5 k}$

Solution

For a first order reaction.
$k=\frac{2.303}{t} \log _{10} \frac{a}{a-x}$
when $t=t_{1 / 2}$
$k=\frac{2.303}{t_{1 / 2}} \log _{10} \frac{a}{a-\frac{a}{2}}$
or $t_{1 / 2}=\frac{2.303}{k} \log _{10} 2=\frac{\ln 2}{k}$
A Caution
The half-life of first order reaction is constant because the initial concentration of the reactant has no influence on the half-life of the reaction, i.e. the half-life is constant regardless of the concentration of the reactant.

Asked in: NEET 2007

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