Consider a general first order reaction $A_{(g)} \rightarrow B_{(g)} + C_{(g)}$. If the initial pressure is $200 \ mm$ and after $20 \ minutes$ it is $250 \ mm$,then the half-life period of the reaction (in minutes) is. $(\log 2 = 0.30, \log 3 = 0.48, \log 4 = 0.60)$

Thermal decomposition of a compound is of first order. If $50\%$ of a sample of this compound is decomposed in $120 \ min$,then how long will it take $90\%$ of the compound to decompose? ........ $min.$

$A$ first order reaction is found to have a rate constant,$k = 5.5 \times 10^{-14} \ s^{-1}$. The half life of reaction is . . . . . . .

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 half-life of a first-order reaction is $69.35 \, \text{sec}$. The value of the rate constant of the reaction is .......... $\sec^{-1}$.

Assertion : For a first order reaction,$t_{1/2}$ is independent of initial concentration.
Reason : For a first order reaction,rate constant $k \propto [R]$.