The rate constant for the oxidation of hydrogen peroxide by $KMnO_4$ is $6.93 \times 10^{-5} \ s^{-1}$. How much time will it take for the volume of a standard $KMnO_4$ solution to decrease from $20 \ mL$ to $8 \ mL$?

Which of the following plots is(are) correct for the given reaction? $( [P]_0$ is the initial concentration of $P$ $)$

$A$ first order reaction was started with a decimolar solution of the reactant. $8$ minutes and $20$ seconds later,its concentration was found to be $M/100$. The rate constant of the reaction is:

For an elementary reaction,$X_{(g)} \rightarrow Y_{(g)} + Z_{(g)}$,the $t_{1/2}$ is $10 \text{ minutes}$. In what period of time would the concentration of $X$ be reduced to $10 \%$ of its original concentration?

The decomposition of the smog component peroxyacetyl nitrate $(PAN)$ follows a first-order reaction into peroxyacetyl radical and $NO_{2(g)}$,with a half-life of $32 \ min$.
$CH_3COONO_2 \to CH_3COO^{\bullet} + NO_2$
If the initial concentration of $PAN$ in an air sample is $5.0 \times 10^{14} \ molecules/L$,what will be the concentration after $1.5 \ hr$?

The rate of a first-order reaction is $0.04 \ mol \ L^{-1} \ s^{-1}$ at $10 \ minutes$ and $0.03 \ mol \ L^{-1} \ s^{-1}$ at $20 \ minutes$ after initiation. The half-life of the reaction is . . . . . . minutes. (Given $\log 2 = 0.3010, \log 3 = 0.4771$)