Question

Choose the correct option regarding first order reaction:

Answer 1

Since $\left[A\right]=[A{]}_0{e}^{-kt}$
Here
$[A{]}_0$ is the intial concentration.
$\left[A\right]$ is the concentration at time t
Now, at $t=t_{\frac{1}{2}},\left[A\right]=\frac{[A{]}_0}{2}$
Putting the value in equation:
$\frac{[A{]}_0}{2}=[A{]}_0{e}^{-k{t}_{\frac{1}{2}}}$
Solving,
$t_{\frac{1}{2}}=\frac{\ln 2}{k}$
So half life for first order does not depend on the concentration of the reactants.

Average Life for First Order Reaction $\left(t_{av}\right)=\frac{1}{k}$

Time of completion of reaction:
Since $\left[A\right]=[A{]}_0{e}^{-kt}$
At completion, reactant concentration will be zero.
$\left[A\right]=0$
$0=[A{]}_0{e}^{-kt}$
$e^{-kt}=0$
$\Rightarrow t=\infty$