An ester on hydrolysis gave an acid which on Kolbe's electrolysis gave ethane. The ester is (a) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COO} \mathrm{CH}_{3}\) (b) (c) \(\mathrm{CH}_{3} \mathrm{COO} \mathrm{C}_{2} \mathrm{H}_{5}\) (d) \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{COO} \mathrm{C}_{2} \mathrm{H}_{5}\)

The general equation for the hydrolysis of an ester is: \(\mathrm{R}_{1} \mathrm{COOR}_{2} + \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{R}_{1} \mathrm{COOH} + \mathrm{R}_{2} \mathrm{OH}\) Where R1 and R2 are alkyl groups or hydrogen atoms. Hydrolysis produces a carboxylic acid and an alcohol, given ester as input.

Kolbe's electrolysis involves the electrolysis of a carboxylic acid salt to produce an alkane, carbon dioxide, and water. The general equation is given by: \(2 \mathrm{RCOO}^{-} + 2 \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{R-R} + 2 \mathrm{CO}_{2} + 4 \mathrm{H}^{+}\) The hydrolysis of ester will produce an acid, and Kolbe's electrolysis of that acid will result in ethane formation.

We will now go through each ester option to see if the correct series of reactions yields ethane. 1. Option (a): \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COO} \mathrm{CH}_{3}\) Hydrolysis: \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COO} \mathrm{CH}_{3} + \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COOH} + \mathrm{CH}_{3} \mathrm{OH}\) Kolbe's electrolysis (produces ethene, not ethane): \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COO}^{-} \rightarrow \mathrm{CH}_{2} = \mathrm{CH}_{2} + 2 \mathrm{CO}_{2} + 4 \mathrm{H}^{+}\) So option (a) is not the correct answer. 2. Option (c): \(\mathrm{CH}_{3} \mathrm{COO} \mathrm{C}_{2} \mathrm{H}_{5}\) Hydrolysis: \(\mathrm{CH}_{3} \mathrm{COO} \mathrm{C}_{2} \mathrm{H}_{5} + \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{CH}_{3} \mathrm{COOH} + \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) Kolbe's electrolysis (produces ethane): \(\mathrm{CH}_{3} \mathrm{COO}^{-} \rightarrow \mathrm{CH}_{3} - \mathrm{CH}_{3} + 2 \mathrm{CO}_{2} + 4 \mathrm{H}^{+}\) Thus option (c) is the correct answer. The other options are not presented.

The correct ester that produces ethane after hydrolysis and subsequent Kolbe's electrolysis is option (c) \(\mathrm{CH}_{3} \mathrm{COO} \mathrm{C}_{2} \mathrm{H}_{5}\).