Chemistry - Chemical Kinetics Question with Solution | TestHub

For a first order reaction, the integrated rate law is given by:

$k=\frac{2.303}{t}\log \left(\frac{a}{a-x}\right)$

Given that the reaction is $75\%$ complete in $30$ minutes:

$t=30\text{minutes}$

$x=0.75a$

$a-x=a-0.75a=0.25a$

Substituting these values into the rate equation:

$k=\frac{2.303}{30}\log \left(\frac{a}{0.25a}\right)$

$k=\frac{2.303}{30}\log (4)$

$k=\frac{2.303}{30}\times 0.6020$

$k=\frac{1.386}{30}=0.0462{\text{minute}}^{-1}$

Alternatively, $75\%$ decomposition corresponds to two half-lives:

$t_{75\%}=2\times t_{1/2}\Rightarrow 30=2\times t_{1/2}\Rightarrow t_{1/2}=15\text{minutes}$

$k=\frac{0.693}{t_{1/2}}=\frac{0.693}{15}=0.0462{\text{minute}}^{-1}$

The closest given option is $0.0463{\text{minute}}^{-1}$.

Answer: $0.0463{\text{minute}}^{-1}$