Chemistry - Chemical Kinetics Question with Solution | TestHub

For a first order reaction, the concentration after $n$ half-lives is given by:

$[A{]}_t=\frac{[A{]}_0}{2^n}$

Substituting the given values:

$50=\frac{400}{2^n}$

$2^n=8\Rightarrow n=3$

The total time $t$ is related to the half-life $t_{1/2}$ by:

$t=n\times t_{1/2}$

$7.5\times 10^3=3\times t_{1/2}$

$t_{1/2}=2.5\times 10^3$ s

The rate constant $k$ for a first order reaction is:

$k=\frac{0.693}{t_{1/2}}$

$k=\frac{0.693}{2.5\times 10^3}=2.77\times 10^{-4}$ s${}^{-1}$

Answer: $2.77\times 10^{-4}$ s${}^{-1}$