Chemical Kinetics - Result Question 80
79. A first order reaction is $20 \%$ complete in $10 $ $min$. Calculate
(i) the specific rate constant of the reaction, and
(ii) the time taken for the reaction to go to $75 \%$ completion.
(1983, 2M)
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Solution:
- For a first order reaction,
$ k t=\ln \dfrac{[A] _0}{[A]} $
where $[A] _0=$ Initial concentration of reactant
$ [A]=\text { Concentration of reactant remaining } $
unreacted at time $t$.
(i) $\Rightarrow k=\dfrac{1}{t} \ln \dfrac{[A] _0}{[A]}=\dfrac{1}{10} \ln \dfrac{100}{100-20}=\dfrac{1}{10} \ln \dfrac{5}{4}$
$ =\dfrac{2.303(\log 5-2 \log 2)}{10} \min ^{-1}=0.023 $ $min^{-1} $
(ii) $ t=\dfrac{1}{k} \ln \dfrac{100}{25}=\dfrac{2 \ln 2}{k}=\dfrac{2 \times 0.693}{0.023}=60 $ $min $
BETA
