For a $1^{st}$ order reaction $R \rightarrow P$, the concentration of reactant $R$ changes from $0.1 \text{ M}$ to $0.025 \text{ M}$ in $40 \text{ minutes}$. The rate of reaction when the concentration of $R$ is $0.01 \text{ M}$ is

$A$ first order reaction is given as $A \rightarrow \text{products}$. Its integrated rate equation is:

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?

$A$ radioactive substance decomposes such that after $100 \ min$,its concentration becomes $1/8$ of the original concentration. Calculate the rate constant $(k)$ and half-life time $(t_{1/2})$.

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

Time required to decompose $SO_{2}Cl_{2}$ to half of its initial amount is $60 \ minutes$. If the decomposition is a first order reaction,calculate the rate constant of the reaction.