In a first order reaction $A \to B,$ if $k$ is the rate constant and the initial concentration of the reactant $A$ is $0.5 \ M,$ then the half-life is:

For a first-order reaction,if $75\%$ of the reaction is completed in $15 \ min$,then the time required for $90\%$ completion of the reaction will be ........... $min$.

Which of the following is the correct equation for a first-order reaction?

For a first order gas phase reaction:
$A_{(g)} \rightarrow 2 B_{(g)} + C_{(g)}$
Let $P_0$ be the initial pressure of $A$ and $P_t$ be the total pressure at time $t$. The integrated rate equation is:

$75\%$ of a first-order reaction was completed in $32 \text{ minutes}$. When was $50\%$ of the reaction completed? (in $\text{minutes}$)

Decomposition of $A$ is a first order reaction at $T \ K$ and is given by $A_{(g)} \rightarrow B_{(g)} + C_{(g)}$. In a closed $1 \ L$ vessel,$1 \ bar$ of $A_{(g)}$ is allowed to decompose at $T \ K$. After $100 \ minutes$,the total pressure was $1.5 \ bar$. What is the rate constant (in $min^{-1}$) of the reaction? (Given: $\log 2 = 0.3$)