$A$ first order reaction is $50 \%$ complete in $16 \ min$. How much time is required to complete $87.5 \%$ of the reaction (in $min$)?

Consider the following two first order reactions occurring at $298 \ K$ with same initial concentration of $A$: $(1)$ $A \rightarrow B$; rate constant, $k=0.693 \ min^{-1}$ $(2)$ $A \rightarrow C$; half-life, $t_{1/2}=0.693 \ min$. Choose the correct option.

The first order reaction takes $20 \ min$ to complete $15\%$. How much time is required to complete $75\%$ of the reaction (in $min$)?

For a first-order gas-phase reaction $A(g) \to B(g) + C(g)$, let $p_i$ be the initial pressure of gas $A$ and $p_t$ be the total pressure of the reaction mixture at time $t$. The expression for the rate constant $(k)$ is:

Derive the half-life $t_{1/2}$ of a first-order reaction.

If the concentration unit decreases by a factor of $n$,what will be the value of the rate constant for a first-order reaction?