Chemistry - Chemical Kinetics Question with Solution | TestHub

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

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

Given $[A{]}_0=0.4$ M and $[A{]}_t=0.1$ M, we can write:

$0.1=\frac{0.4}{2^n}$

$\frac{1}{4}=\frac{1}{2^n}$

${\left(\frac{1}{2}\right)}^2={\left(\frac{1}{2}\right)}^n$

Therefore, $n=2$.

The total time $t$ is related to the half-life $t_{1/2}$ by $t=n\times t_{1/2}$.

Given $t=x$ hour, we have:

$x=2\times t_{1/2}$

$t_{1/2}=\frac{x}{2}$ hour

Answer: $\frac{x}{2}$ hour