$1{\mathrm{dm}}^3$ of $2M {\mathrm{CH}}_3\mathrm{COOH}$ mixed with $1{\mathrm{dm}}^3$ of $3\mathrm{M}$ ethanol to form ester. The initial rate if each solution is diluted with an equal volume of water, would become

This is first-order reaction with respect to both reactants.

The rate law expression can be written as-

 $r=k\left[{\mathrm{CH}}_3\mathrm{COOH}\right]\left[{\mathrm{C}}_2{\mathrm{H}}_5\mathrm{OH}\right]$.

When the solution is diluted with equal volume of water, the concentration of two reactants is reduced to half.

$$\begin{gathered} r_1=k\left[\frac{{\mathrm{CH}}_3\mathrm{COOH}}{2}\right]\left[\frac{{\mathrm{C}}_2{\mathrm{H}}_{5}OH}{2}\right] \\ =\frac{1}{4}k\left[{\mathrm{CH}}_3\mathrm{COOH}\right]\left[{\mathrm{C}}_2{\mathrm{H}}_5\mathrm{OH}\right] \end{gathered}$$