The reaction $A_{(g)} \to 2B_{(g)} + C_{(g)}$ obeys the rate law,$r = K[A]$ where $K = 0.023 \ s^{-1}$. If $2.5 \ moles$ of $A$ were taken in a $5 \ L$ flask,how many moles of $A$ would remain left after $50 \ seconds$?

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 $(ii)$.

The rate of a first-order reaction is $1.5 \times 10^{-2} \, mol \, L^{-1} \, min^{-1}$ when the concentration of the reactant is $0.5 \, M$. Find the half-life $(t_{1/2})$ of the reaction in $min$.

Half-life period of a first-order reaction is $10 \ min$. Starting with an initial concentration of $12 \ M$,the rate after $20 \ min$ is:

For a reaction,the rate constant is $2.34 \ s^{-1}$. The half-life period for the reaction is ....... $s.$

For the reaction $A \to B$,the rate law expression is: $\text{Rate} = k[A]$. Which of the following statements is incorrect?