The reaction $X \rightarrow$ products is a first order reaction. In $40 \ min$,the concentration of $X$ changes from $1.0 \ M$ to $0.25 \ M$. What is the rate of reaction when $[X] = 0.1 \ M$? $(\log 4 = 0.60)$

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?

The reaction $L \rightarrow M$ starts with $10 \, gL^{-1}$. After $30$ and $90$ minutes,$5 \, gL^{-1}$ and $1.25 \, gL^{-1}$ remain,respectively. The order of the reaction is:

$A$ and $B$ decompose via first order kinetics with half-lives $54.0 \, min$ and $18.0 \, min$ respectively. Starting from an equimolar non-reactive mixture of $A$ and $B$,the time taken for the concentration of $A$ to become $16$ times that of $B$ is ...... $min.$ (Round off to the Nearest Integer).

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 time required for completion of $93.75 \%$ of a first order reaction is $x$ minutes. The half life of it (in minutes) is