The half-life period of a reaction is $1386 \ s$. What is the value of the specific rate constant for the reaction?

When methyl acetate is hydrolyzed in $0.05 \, M$ $HCl$,the reaction occurs as follows: $CH_3COOCH_3 + H_2O \rightarrow CH_3COOH + CH_3OH$. $A$ $25 \, mL$ sample of the reaction mixture is taken at different time intervals,added to ice to stop the reaction,and then titrated with $0.05 \, M$ $NaOH$ solution. Prove that the reaction is first order using the data provided below:

Time (minute)	$0$	$20$	$75$	$120$	$\infty$
Volume of $0.05 \, M$ $NaOH$ ($V_t$ in $mL$)	$24.40$	$25.82$	$29.35$	$31.75$	$47.50$

The initial concentration of $N_2O_5$ in the first order reaction,$N_2O_5 \rightarrow 2NO_{2(g)} + \frac{1}{2}O_{2(g)}$ was $1.24 \times 10^{-2} \ mol \ L^{-1}$ at $300 \ K$ temperature. The concentration of $N_2O_5$ after $60 \ min$ was $0.20 \times 10^{-2} \ mol \ L^{-1}.$ Calculate the rate constant of the reaction.

$A$ first order reaction is half completed in $45 \ min$. How long does it need $99.9 \%$ of the reaction to be completed (in $Hours$)?

If benzene diazonium chloride undergoes first order decomposition at $T \ K$ with a rate constant of $6.93 \times 10^{-2} \ min^{-1}$,the time for completion of $90 \%$ of the reaction (in $min$) is (nearest integer) $(\log 2 = 0.30, \log 3 = 0.477)$.

The rate constant of the reaction $2 NO_2Cl_{(g)} \longrightarrow 2 NO_{2(g)} + Cl_{2(g)}$ is $4.7672 \text{ minute}^{-1}$. Calculate the half-life of the reaction.