In a first order reaction,$60 \%$ of the reactant converts into product in $45 \ minutes$. Calculate the rate constant of the reaction.

For a first order reaction,the concentration of reactant was reduced from $0.03 \ mol \ L^{-1}$ to $0.02 \ mol \ L^{-1}$ in $25 \ min$. What is its rate (in $mol \ L^{-1} \ s^{-1}$)?

$10 \ g$ mixture of two gases $A_2$ (mol. wt. $= 20$) and $B_2$ (mol. wt. $= 30$),which decompose by first order kinetics,was taken in a vessel. The half-life of decomposition of $A_2$ and $B_2$ are $2 \ hours$ and $3 \ hours$ respectively. After $6 \ hours$,the weight of the mixture of $A_2$ and $B_2$ is found to be $2 \ g$. Find the weight of $A_2$ in the initial mixture in $g$.

The time required for completion of $93.75 \%$ of a first order reaction is $x$ minutes. The half life of it (in minutes) is

Derive the half-life $t_{1/2}$ of a first-order reaction.

$A$ first order reaction is found to have a rate constant,$k = 5.5 \times 10^{-14} \ s^{-1}$. Find the half-life of the reaction.