The rate constant of a first order reaction is $1.15 \times 10^{-3} \ s^{-1}$. How long will $5 \ g$ of reactant take to reduce to $3 \ g$ (in $s$)?

If the rate constant for a first order reaction is $k$,the time $(t)$ required for the completion of $99\%$ of the reaction is given by:

The experimental data for decomposition of $N_2O_5$ in the gas phase at $318 \, K$ are given below:

$t/s$	$0$	$400$	$800$	$1200$	$1600$	$2000$	$2400$	$2800$	$3200$
$10^2 \times [N_2O_5] / mol \, L^{-1}$	$1.63$	$1.36$	$1.14$	$0.93$	$0.78$	$0.64$	$0.53$	$0.43$	$0.35$

$(i)$ Plot $[N_2O_5]$ against $t$.
$(ii)$ Find the half-life period for the reaction.
$(iii)$ Draw a graph between $\log[N_2O_5]$ and $t$.
$(iv)$ What is the rate law?
$(v)$ Calculate the rate constant.
$(vi)$ Calculate the half-life period from $k$ and compare it with $(ii)$.

What is a first-order reaction? Determine the integrated rate equation for a first-order reaction $R \to P$.

Rate of first order reaction $A \rightarrow \text{product}$ is $0.01 \ mol \ dm^{-3} \ s^{-1}$. Calculate the rate constant if the concentration of the reactant is $0.2 \ M$. (in $s^{-1}$)

Which of the following represents the integrated rate law equation for the gas-phase first-order reaction,$A_{(g)} \rightarrow B_{(g)} + C_{(g)}$? If $P_{i}$ is the initial pressure of $A$ and $P$ is the total pressure of the reaction mixture at time $t$.