The thermal decomposition of a molecule follows a first-order reaction. The molecule decomposes $50\%$ in $120 \text{ minutes}$. How many minutes will it take for $90\%$ decomposition?

The following is a first-order reaction:
$N_2O_5 \text{ (solution)} \rightarrow 2 NO_2 \text{ (solution)} + \frac{1}{2} O_2 \text{ (g)}$
In this reaction,$CCl_4$ is the solvent. The rate constant is $k = 5.0 \times 10^{-4} \ s^{-1}$. The initial concentration of $N_2O_5$ is $0.25 \ mol \ L^{-1}$.
$(i)$ What will be the initial rate of reaction?
$(ii)$ Calculate the half-life $(t_{1/2})$.
$(iii)$ How much time is required to complete $75\%$ of the reaction?
$(iv)$ Calculate the concentration of $N_2O_5$ and $NO_2$ after $30 \ min$.

The half-life period for a first order reaction is $693 \ sec$. The rate constant for this reaction would be: (in $sec^{-1}$)

Azo isopropane decomposes according to the equation:
$((CH_3)_2CHN)_2N_{2(g)} \xrightarrow{250 - 290 \ ^oC} N_{2(g)} + C_6H_{14(g)}$
It is found to be a first order reaction. If the initial pressure is $P_o$ and the total pressure of the mixture at time $t$ is $P_t$,then the rate constant $K$ is given by:

What is the half-life of a first-order reaction if the time required to decrease the concentration of the reactant from $0.8 \text{ M}$ to $0.2 \text{ M}$ is $12 \text{ hours}$ (in $\text{ hours}$)?

The half-life of a first order reaction $X \to Y$ is $100 \ min$. The concentration of $X$ would be reduced to $10 \%$ of the initial concentration in .......... $min$.