For which of the following graphs of a first-order reaction will the value of the slope be $\frac{K}{2.303}$?

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 $1.5 \ hr$?

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 half-life period of a reaction is $1386 \ s$. What is the value of the specific rate constant for the reaction?

The integrated rate law equation for a first-order gas-phase reaction $A(g) \rightarrow B(g) + C(g)$ is given by (where $P_i$ is the initial pressure and $P_t$ is the total pressure at time $t$):

In a first order reaction,the concentration of the reactant is reduced to $12.5 \%$ in one hour. When was it half completed?