In a first order reaction,the ratio $\frac{a}{a-x}$ was found to be $8$ after $10 \, \text{min}$. The rate constant is:

The rate constant for a first order reaction is $4.606 \times 10^{-3} \ s^{-1}$. The time required to reduce $2.0 \ g$ of the reactant to $0.2 \ g$ is......... $s$

Identify True $(T)$ and False $(F)$ statements of the following for a first-order reaction $R \rightarrow P$.
Statement $I$: $k = \frac{1}{(t_1 - t_2)} \ln \frac{[R]_1}{[R]_2}$
Statement $II$: $k = -\frac{1}{(t_1 - t_2)} \ln \frac{[R]_2}{[R]_1}$

How much time is required for a first-order reaction to be $3/4$ complete?

$10 \ g$ 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 $g$.

For a first order reaction,the initial concentration of a reactant is $0.05 \ M$. After $45 \ minutes$,it is decreased by $0.015 \ M$. Calculate the half-life period $(t_{1/2})$ (in $min$)?