$A_{(g)} \xrightarrow{\Delta} P_{(g)} + Q_{(g)} + R_{(g)}$ follows first-order kinetics with a half-life of $69.3 \ s$ at $500^{\circ}C$. Starting from the gas '$A$' enclosed in a container at $500^{\circ}C$ and at a pressure of $0.4 \ atm$,the total pressure of the system after $230 \ s$ will be (in $atm$)

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?

$A$ first order reaction has a rate constant of $1 \times 10^{-2} \ s^{-1}$. How much time will it take for $20 \ g$ of reactant to reduce to $5 \ g$ (in $s$)?

The time taken for $10 \%$ completion of a first order reaction is $20 \ min$. Then, for $19 \%$ completion, the reaction will take (in $min$)

The half-life of a first order reaction having rate constant $K = 1.7 \times 10^{-5} \ s^{-1}$ is ........ $hr$.

For a reaction $A \rightarrow$ product,the rate constant is $2 \times 10^{-2} \ s^{-1}$. The initial concentration of $A$ is $1.0 \ mol \ dm^{-3}$. What is the value of $\log \frac{1}{[A]_{t}}$ after $100 \ s$?