$A ( g ) \rightarrow 2 B ( g ) + C ( g )$ is a first order reaction. The initial pressure of the system was found to be $800 \ mm \ Hg$ which increased to $1600 \ mm \ Hg$ after $10 \ min$. The total pressure of the system after $30 \ min$ will be . . . . . . $mm \ Hg$. (Nearest integer)

$A$ first order reaction has a rate constant $0.00813 \ min^{-1}$. How long will it take for $60 \%$ completion (in $min$)?

In the following first order reactions $A$ $\xrightarrow{K_1} B$ $\xrightarrow{K_2} \text{Product}$,find the ratio $K_1/K_2$ if $90\%$ of $A$ has been reacted in time $t$ while $99\%$ of $B$ has been reacted in time $2t$.

Dissociation of $N_2O_5$ dissolved in $CCl_4$ at constant temperature: $N_2O_{5(soln)} \to 2NO_{2(soln)} + \frac{1}{2}O_{2(g)}$. This is a first order reaction. The velocity constant is $5.0 \times 10^{-4} \ s^{-1}$. The initial concentration of $N_2O_5$ is $0.25 \ mol \ L^{-1}$. How much time is required to produce $0.20 \ mol \ L^{-1}$ concentration of $NO_2$ (in $s$)?

For an elementary reaction,$X_{(g)} \rightarrow Y_{(g)} + Z_{(g)}$,the $t_{1/2}$ is $10 \text{ minutes}$. In what period of time would the concentration of $X$ be reduced to $10 \%$ of its original concentration?

Azo-isopropane decomposes according to the following equation:
$((CH_3)_2CHN = NCH(CH_3)_2)_{(g)} \xrightarrow{250 - 290 ^oC} (N_2)_{(g)} + (C_6H_{14})_{(g)}$
It is a first-order reaction. If the initial pressure is $P_o$ and the total pressure of the mixture at time $t$ is $P_t$,find the rate constant $K$.