At $T(K)$,if the rate constant of a first order reaction is $4.606 \times 10^{-3} \ s^{-1}$,the time to reduce the initial concentration of the reactant to $1/10$ of its initial value in seconds is:

The rate constant for the decomposition of $H_2O_2$ is $3.66 \times 10^{-3} \ s^{-1}$. If the initial concentration of $H_2O_2$ is $0.882 \ M$,then in how many seconds will its concentration become $0.600 \ M$?

For the reaction $R \rightarrow P$,the half-life is independent of the initial concentration of the reactant,$R$. Which one of the following graphs is not correct for this reaction?

Which equation represents the $1/4^{th}$ life for a first-order reaction?

An organic compound undergoes first order decomposition. The time taken for its decomposition to $\frac{1}{8}$ and $\frac{1}{10}$ of its initial concentration are $t_{1/8}$ and $t_{1/10}$ respectively. What is the value of $\frac{t_{1/8}}{t_{1/10}}$? $[\log 2 = 0.30]$

Time required for $99.9 \%$ completion of a first order reaction is . . . . . . . times the time required for completion of $90 \%$ reaction. (nearest integer).