For a first-order reaction,if the value of $a/(a - x)$ is $8$ after $10 \text{ minutes}$,what will be the rate constant $K$?

The reaction,$X \to$ product follows first order kinetics. In $40 \, min$ the concentration of $X$ changes from $0.1 \, M$ to $0.025 \, M$. Then the rate of reaction when concentration of $X$ is $0.01 \, M$ is:

$t_{87.5}$ is the time required for the reaction to undergo $87.5 \%$ completion and $t_{50}$ is the time required for the reaction to undergo $50 \%$ completion. The relation between $t_{87.5}$ and $t_{50}$ for a first order reaction is $t_{87.5} = x \times t_{50}$. The value of $x$ is $......$. (Nearest integer)

For the reaction ${N_2}{O_{5(g)}} \to 2N{O_{2(g)}} + \frac{1}{2}{O_{2(g)}}$,the rate constant is $2.3 \times 10^{-2} \ s^{-1}$. Which of the following equations represents the variation of $[{N_2}{O_5}]$ with time?

In a first-order reaction,the concentration of the reactant decreases from $0.80 \, mol \, L^{-1}$ to $0.06 \, mol \, L^{-1}$ in $45 \, min$. Calculate the half-life $(t_{1/2})$. (in $, min$)

The decay constant of a first-order reaction is $1.1 \times 10^{-9} \ s^{-1}$. Calculate the half-life of the reaction.