The integrated rate equation for a first-order reaction,$A \rightarrow \text{product}$,is

Consider the first-order gas-phase decomposition reaction given below:
$A_{(g)} \longrightarrow B_{(g)} + C_{(g)}$
The initial pressure of the system before the decomposition of $A$ was $P_i$. After time $t$,the total pressure of the system increased by $x \ units$ and became $P_t$. The rate constant $k$ for the reaction is given as:

For a first order reaction,the ratio of the time for $75 \% $ completion of a reaction to the time for $50 \% $ completion is $....$ . (Integer answer)

For two first-order reactions:
$A \rightarrow \text{Products}$
$B \rightarrow \text{Products}$
If at the same time,$50\% \, B$ has reacted and $94\% \, A$ has reacted,calculate the ratio $K_1/K_2$.

Consider a certain reaction $A \rightarrow \text{Products}$ with $k = 2.0 \times 10^{-2} \ s^{-1}$. Calculate the concentration of $A$ remaining after $100 \ s$ if the initial concentration of $A$ is $1.0 \ mol \ L^{-1}$.

Calculate the time needed for a reactant to decompose $99.9 \%$ if the rate constant of a first-order reaction is $0.576 \ min^{-1}$.