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 $2t$.

For a first order reaction with rate constant $k$,the slope of the plot of $\log(\text{reactant concentration})$ against time is

$A$ first order reaction with respect to the reactant $A$ has a rate constant of $6 \; sec^{-1}$. If we start with $[A] = 0.5 \; mol/L$,then in what time the concentration of $A$ becomes $0.05 \; mol/L$ ........... $sec$

What is the half-life of a first-order reaction if the time required to decrease the concentration of the reactant from $0.4 \ M$ to $0.1 \ M$ is $x \ \text{hours}$?

The decomposition reaction $2N_2O_{5(g)} \xrightarrow{\Delta} 2N_2O_{4(g)} + O_{2(g)}$ is started in a closed cylinder under isothermal isochoric conditions at an initial pressure of $1 \ atm$. After $Y \times 10^3 \ s$,the pressure inside the cylinder is found to be $1.45 \ atm$. If the rate constant of the reaction is $5 \times 10^{-4} \ s^{-1}$,assuming ideal gas behavior,the value of $Y$ is. . . . . . . .

$N_2O_{(g)} \to N_{2(g)} + \frac{1}{2}O_{2(g)}$
In a closed vessel,the reaction follows first-order kinetics. If starting with pure $N_2O_{(g)}$,the total pressure after time $t$ is $P_t$ and after a very long time is $P_{\infty}$,then which of the following expressions is correct?