Calculate the rate constant for the first order reaction,$A \rightarrow B$ if the rate of reaction is $5.4 \times 10^{-6} \ mol \ dm^{-3} \ s^{-1}$ and $[A]=0.3 \ M$.

Calculate the time required for a reactant to decrease in concentration from $100 \%$ to $20 \%$,if the rate constant of the first-order reaction is $0.02303 \ hour^{-1}$. (in $hour$)

$N_{2}O_{5(g)} \rightarrow 2NO_{2(g)} + \frac{1}{2}O_{2(g)}$
In the above first order reaction,the initial concentration of $N_{2}O_{5}$ is $2.40 \times 10^{-2} \ mol \ L^{-1}$ at $318 \ K$. The concentration of $N_{2}O_{5}$ after $1 \ hour$ was $1.60 \times 10^{-2} \ mol \ L^{-1}$. The rate constant of the reaction at $318 \ K$ is $..... \times 10^{-3} \ min^{-1}$. (Nearest integer)
[Given: $\log 3 = 0.477, \log 5 = 0.699$]

What is the value of the slope when a graph is plotted of $\log \frac{[R]_0}{[R]}$ versus $t$ (time) for a first-order reaction?

For a first order reaction,the half-life period is

Which of the following graphs represent a first order reaction ($a =$ initial concentration of reactant,$x =$ concentration of reactant consumed,$t =$ time)?