Chemical Kinetics - Result Question 34
####34. In a first-order reaction $A \to B$, if $k$ is rate constant and inital concentration of the reactant $A$ is $0.5 M$, then the half-life is
[2007]
(a) $\frac{\log 2}{k}$
(b) $\frac{\log 2}{k \sqrt{0.5}}$
(c) $\frac{\ln 2}{k}$
(d) $\frac{0.693}{0.5 k}$
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Solution:
- (c) 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-a / 2} $
or $t _{1 / 2}=\frac{2.303}{k} \log _{10} 2=\frac{\ln 2}{k}$
