In a first order reaction,the concentration of the reactant decreases from $20 \ mmol \ dm^{-3}$ to $8 \ mmol \ dm^{-3}$ in $40 \ minute$. Find the rate constant of the reaction.

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?

The integrated rate law equation for a first-order gas-phase reaction $A(g) \rightarrow B(g) + C(g)$ is given by (where $P_i$ is the initial pressure and $P_t$ is the total pressure at time $t$):

What is a first-order reaction? Determine the integrated rate equation for a first-order reaction $R \to P$.

The plot of $\log(a - x)$ versus time $t$ is a straight line,which indicates that the reaction is of ....... order.

For a first order reaction,the concentration of reactant was reduced from $0.03 \ mol \ L^{-1}$ to $0.02 \ mol \ L^{-1}$ in $25 \ min$. What is its rate (in $mol \ L^{-1} \ s^{-1}$)?