Half life of a first order reaction is $3 \ minute$. What is the time required to reduce the concentration of reactant by $90 \%$ of its initial concentration?

The half-life of a first-order reaction is $900 \text{ s}$. If the initial concentration of the reactant is $0.08 \text{ mol dm}^{-3}$, find the concentration that remains after $35 \text{ minutes}$?

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 decomposition of benzene diazonium chloride is a first order reaction. The time taken for the decomposition of $\frac{1}{4}$ and $\frac{1}{10}$ of its initial concentration are $t_{1/4}$ and $t_{1/10}$ respectively. The value of $\frac{t_{1/4}}{t_{1/10}} \times 100$ is (Given: $\log 2 = 0.3, \log 3 = 0.477$)

For a first order reaction,the initial concentration of a reactant is $0.05 \ M$. After $45 \ minutes$,it is decreased by $0.015 \ M$. Calculate the half-life period $(t_{1/2})$ (in $min$)?

The half-life period of a first order reaction is $100 \, \text{sec}$. The rate constant of the reaction is