A chemist added water and acid to an unknown ester of formula \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{2}\) to produce an acid \(\mathrm{X}\) and an alcohol \(\mathrm{Y}\). Oxidation of \(\mathrm{Y}\) with chromic acid produced \(\mathrm{X}\). Determine the structure of the original ester. Write equations for all reactions that occur.

An ester has the general formula \(\mathrm{R}_{1}\mathrm{COOR}_{2}\), where R1 and R2 are organic groups, possibly alkyl or aryl groups. In this case, the given formula is \(\mathrm{C}_{6}\mathrm{H}_{12}\mathrm{O}_{2}\). Therefore, we need to find possible structures with a combination of R1 and R2 groups that add up to the 6 carbons. As there are 6 carbons in total, we can have the following combinations of R1 and R2: 1. R1 = \(\mathrm{C}_{5}\mathrm{H}_{11}\) and R2 = \(\mathrm{H}\) (5 carbons in R1 and 1 carbon in R2) 2. R1 = \(\mathrm{C}_{4}\mathrm{H}_{9}\) and R2 = \(\mathrm{CH}_{3}\) (4 carbons in R1 and 2 carbons in R2) 3. R1 = \(\mathrm{C}_{3}\mathrm{H}_{7}\) and R2 = \(\mathrm{C}_{2}\mathrm{H}_{5}\) (3 carbons in R1 and 3 carbons in R2)

Ester hydrolysis is the reaction of an ester with water and acid, resulting in the breaking of the ester bond and formation of an acid (X) and an alcohol (Y). The general reaction is: \(\mathrm{R}_{1}\mathrm{COOR}_{2} + \mathrm{H}_{2}\mathrm{O} \xrightarrow[]{\text{acid}} \mathrm{R}_{1}\mathrm{COOH} + \mathrm{R}_{2}\mathrm{OH}\)

The oxidation reaction of alcohol (Y) with chromic acid produces acid (X). This means that the oxidation converts the alcohol into the same acid with the same carbon chain. Also, this implies that R1 and R2 should have the same number of carbons since both contribute to the acid formation. This observation eliminates possibilities 1 and 2 from our previous list of combinations, leaving us with the following possibility: R1 = \(\mathrm{C}_{3}\mathrm{H}_{7}\), R2 = \(\mathrm{C}_{2}\mathrm{H}_{5}\)

Since R1 and R2 are \(\mathrm{C}_{3}\mathrm{H}_{7}\) and \(\mathrm{C}_{2}\mathrm{H}_{5}\) respectively, the original ester has the following structure: \(\mathrm{C}_{3}\mathrm{H}_{7}\mathrm{COOC}_{2}\mathrm{H}_{5}\)

Hydrolysis of the ester: \(\mathrm{C}_{3}\mathrm{H}_{7}\mathrm{COOC}_{2}\mathrm{H}_{5} + \mathrm{H}_{2}\mathrm{O} \xrightarrow[]{\text{acid}} \mathrm{C}_{3}\mathrm{H}_{7}\mathrm{COOH} + \mathrm{C}_{2}\mathrm{H}_{5}\mathrm{OH}\) Oxidation of Y with chromic acid: \(\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{OH} \xrightarrow[]{\text{chromic acid}} \mathrm{C}_{3}\mathrm{H}_{7}\mathrm{COOH}\) Thus, the structure of the original ester is \(\mathrm{C}_{3}\mathrm{H}_{7}\mathrm{COOC}_{2}\mathrm{H}_{5}\), and the reactions involved are ester hydrolysis and the oxidation of alcohol in the presence of chromic acid.