$75\%$ of a first order reaction was completed in $32$ minutes. When was $50\%$ of the reaction completed? ......... $\min$

The half-life period of a first order reaction is $15 \ minutes$. The amount of substance left after one hour will be

Identify $True$ $(T)$ and $False$ $(F)$ statements for the following equations related to a first-order reaction $R \rightarrow P$:
$(i) \ln [R] = -kt + \ln [R]_{0}$
$(ii) \ln [R] = +kt + \ln [R]_{0}$

If the rate constant for a first order reaction is $2.303 \times 10^{-3} \ s^{-1}$,find the time required to reduce $4 \ g$ of the reactant to $0.2 \ g$. (in $hours$)

Calculate the half-life of a first order reaction from the rate constants given below:
$(i) \ 200 \ s^{-1}$
$(ii) \ 2 \ min^{-1}$
$(iii) \ 4 \ years^{-1}$

For a first order reaction,show that the time required for $99 \%$ completion is twice the time required for the completion of $90 \%$ of the reaction.