In a first-order reaction of the type: $A_{(g)} \to 2B_{(g)}$,the initial pressure is $P_i$ and the total pressure at time $t$ is $P_t$. The rate constant $k$ can be expressed as:

Among the following statements,the correct statement about the half-life period for a first order reaction is

Hydrolysis of methyl acetate in aqueous solution has been studied by titrating the liberated acetic acid against sodium hydroxide. The concentration of the ester at different times is given below:

Time $(t)$ $(\min)$	$0$	$30$	$60$	$90$
Conc. of ester $(C)$ $(M)$	$0.850$	$0.800$	$0.754$	$0.710$

Show that it follows a pseudo first order reaction as the concentration of $H_{2}O$ remains nearly constant $(55 \ mol \ L^{-1})$ during the course of the reaction. What is the value of $k^{\prime}$ in this reaction?

Consider the following first order gas phase reaction at constant temperature:
$A_{(g)} \rightarrow 2B_{(g)} + C_{(g)}$
If the total pressure of the gases is found to be $200 \ torr$ after $23 \ s$ and $300 \ torr$ upon the complete decomposition of $A$ after a very long time,then the rate constant of the given reaction is . . . . . . $\times 10^{-2} \ s^{-1}$ (nearest integer).
[Given: $\log_{10}(2) = 0.301$]

At $27^{\circ} C$ temperature,the time required for $75 \%$ completion of a first order reaction is $20 \ s$. What will be its rate constant?

In a first order reaction,the concentration of the reactant is reduced from $0.6 \ mol \ L^{-1}$ to $0.2 \ mol \ L^{-1}$ in $5 \ min$. What is the rate constant of the reaction (in $min^{-1}$)? $(\log 3 = 0.4771)$