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:

$A$ first order reaction has a specific reaction rate of $10^{-2} \ sec^{-1}.$ How much time will it take for $20 \ g$ of the reactant to reduce to $5 \ g?$ ........ $sec$

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 $\frac{k_A}{k_B}$?

Hydrolysis of methyl acetate in aqueous solution has been studied by titrating the liberated acetic acid against sodium hydroxide. The concentration of the ester at different times is given below:

Time $(t)$ $(\min)$	$0$	$30$	$60$	$90$
Conc. of ester $(C)$ $(M)$	$0.850$	$0.800$	$0.754$	$0.710$

Show that it follows a pseudo first order reaction as the concentration of $H_{2}O$ remains nearly constant $(55 \ mol \ L^{-1})$ during the course of the reaction. What is the value of $k^{\prime}$ in this reaction?

The rate of a first-order reaction is $0.04 \ mol \ L^{-1} \ s^{-1}$ at $10 \ minutes$ and $0.03 \ mol \ L^{-1} \ s^{-1}$ at $20 \ minutes$ after initiation. The half-life of the reaction is . . . . . . minutes. (Given $\log 2 = 0.3010, \log 3 = 0.4771$)

The half-life period of a first order reaction is $15 \ minutes$. The amount of substance left after one hour will be