For the first-order isomerization reaction $A \rightarrow B$,the rate constant is $4.5 \times 10^{-3} \ min^{-1}$. If the initial concentration of $A$ is $1 \ M$,find the rate of the reaction after $1 \ hour$.

If $75 \%$ of a first order reaction was completed in $90 \ minutes$,$60 \%$ of the same reaction would be completed in approximately (in minutes)..........
(Take: $\log 2=0.30 ; \log 2.5=0.40)$

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 $(t)$ $\text{min}$	$0$	$30$	$60$	$90$
Conc. of ester $(C)$ $\text{mol L}^{-1}$	$0.850$	$0.800$	$0.754$	$0.710$

Show that it follows a pseudo first-order reaction as the concentration of $H_2O$ remains nearly constant $(54.2 \text{ mol L}^{-1})$ during the course of the reaction. What is the value of $k'$ in this reaction?

Which is the correct relation between rate constant and half-life of a first-order reaction?

Which of the following is a first order reaction?

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