The gaseous reaction $A_{(g)} \to 2B_{(g)} + C_{(g)}$ is a first-order reaction. If the initial pressure $P_A = 90 \ mm \ Hg$ and the total pressure after $10 \ min$ is $180 \ mm \ Hg$,calculate the rate constant of the reaction.

$A$ first-order reaction takes $10 \ hours$ to complete $90\%$ of the reaction. How much time will it take to complete $99.9\%$ of the reaction (in $hours$)?

$N_2O_5$ decomposes to $NO_2$ and $O_2$ and follows first order kinetics. After $50 \, min$,the pressure inside the vessel increases from $50 \, mm \, Hg$ to $87.5 \, mm \, Hg$. The pressure of the gaseous mixture after $100 \, min$ at constant temperature will be ........... $mm \, Hg$

The rate constant of a first order reaction is $3 \times 10^{-6} \ s^{-1}$. If the initial concentration is $0.10 \ M$,the initial rate of reaction is:

For the decomposition of $N_2O_5$ according to the equation $2N_2O_5(g) \to 4NO_2(g) + O_2(g)$,the reaction is of first order. After $30 \, \min$ from the start of the reaction in a closed vessel,the total pressure is $305.5 \, mm \, Hg$,and at the end of complete decomposition,the total pressure is $587.5 \, mm \, Hg$. Calculate the rate constant of the reaction.

$A$ first order reaction has a rate constant of $2.303 \times 10^{-3} \; s^{-1}$. The time required for $40 \; g$ of this reactant to reduce to $10 \; g$ will be.....$s$
[Given that $\log_{10} 2 = 0.3010$]