The half-life values for two different first-order reactions $A$ and $B$ are $75 \ min$ and $2.5 \ h$ respectively. What is the ratio of their rate constants $\frac{k_A}{k_B}$?

The decomposition of $N_2O_5$ occurs as $2N_2O_5 \to 4NO_2 + O_2$ and follows first-order kinetics. Hence,

$A$ first-order reaction starts with a decimolar solution of the reactant. After $8$ minutes,its concentration becomes $M/100$. Calculate the rate constant of the reaction.

The first order reaction $A_{(g)} \rightarrow B_{(g)} + 2C_{(g)}$ occurs at $25^{\circ} C$. After $24 \ min$,the ratio of the concentration of products to the concentration of the reactant is $1:3$. What is the half-life of the reaction (in $min$)? $(\log 1.11 = 0.046)$

Which of the following is correct regarding $t_{1/2}$ of a reaction if we double the initial concentration of a reactant in a first-order reaction?

For the first order reaction with rate constant $k$,which expression gives the half-life period? (Initial concentration $= a$)