An optically active compound A, C6H10O2, when dissolved in NaOH solution, consumed one equivalent of base. On acidification, compound A was slowly regenerated. Treatment of A with LiAlH4 in ether followed by protonolysis gave an optically inactive compound B that reacted with acetic anhydride to give an acetate diester derivative C. Compound B was oxidized by aqueous chromic acid to β-methylglutaric acid (3-methylpentanedioic acid), D. Identify compounds A, B, and C; do not specify stereochemistry.

A: Compound A is 2-methylcyclohexanol

B: Compound B is 2-methylcyclohexanone
C: Compound C is 2-methylcyclohexyl acetate
D: Compound D is β-methylglutaric acid (3-methylpentanedioic acid)

To solve this problem and identify compounds A, B, and C, let's analyze the steps described in the question:

1. Compound A is an optically active compound with the molecular formula C6H10O2. When dissolved in NaOH solution, it consumes one equivalent of base.

This indicates that compound A is an acidic compound. It donates a proton to NaOH, forming a salt. This suggests that compound A contains at least one carboxylic acid functional group.

2. On acidification, compound A is slowly regenerated.

When compound A is acidified, it means that an acidic environment is created. Under such conditions, the acidic compound A gets protonated and regenerates its original form. This further confirms that compound A contains a carboxylic acid functional group.

3. Treatment of compound A with LiAlH4 in ether followed by protonolysis gives an optically inactive compound B.

LiAlH4 (lithium aluminum hydride) is a strong reducing agent that converts carboxylic acids to primary alcohols. When compound A is treated with LiAlH4, it is reduced to an alcohol. Protonolysis refers to the addition of water (H2O) or an acidic proton source to the reaction mixture to convert the intermediate compound into a more stable molecule.

Therefore, compound B is the product obtained after reducing compound A, which should be a primary alcohol. Since compound B is optically inactive, it suggests there is no chiral center in compound B. This means that compound B is a compound without a stereogenic center.

4. Compound B reacts with acetic anhydride to give an acetate diester derivative C.

When compound B reacts with acetic anhydride, it undergoes an esterification reaction, resulting in the formation of an ester derivative. This ester derivative is compound C.

5. Compound B is oxidized by aqueous chromic acid to β-methylglutaric acid (3-methylpentanedioic acid), D.

When compound B undergoes oxidation with chromic acid (H2CrO4), it is converted to β-methylglutaric acid. This oxidation converts the primary alcohol in compound B to a carboxylic acid group.

Based on this information, we can now identify the compounds:

- Compound A is a carboxylic acid with the molecular formula C6H10O2.
- Compound B is a primary alcohol, which is the reduced form of compound A.
- Compound C is the ester derivative obtained by reacting compound B with acetic anhydride.
- Compound D is β-methylglutaric acid, which is the product of the oxidation of compound B.

Note: The question does not specify the stereochemistry of compounds A, B, and C, so we cannot provide information about their absolute configurations or specific isomers.

Compound A is an optically active compound with the molecular formula C6H10O2. When dissolved in NaOH solution, it consumes one equivalent of base, indicating the presence of one acidic functional group.

On acidification, compound A is regenerated slowly, suggesting that it may have formed a salt with NaOH and the acidification releases the compound as a free acid.

Treatment of compound A with LiAlH4 in ether, followed by protonolysis, reduces the compound to an optically inactive compound B. This reduction suggests that compound A contains a carbonyl group, which is reduced by LiAlH4 to an alcohol.

Compound B, being optically inactive, suggests that it does not have a chiral center, indicating that the carbonyl group in compound A was not a ketone, but an aldehyde. The reduction of an aldehyde with LiAlH4 would produce a primary alcohol, which is achiral.

Compound B is further reacted with acetic anhydride to give an acetate diester derivative C. This indicates that the hydroxyl group in compound B underwent esterification, resulting in the formation of an ester group.

Oxidation of compound B with aqueous chromic acid yields β-methylglutaric acid (3-methylpentanedioic acid), compound D. This oxidation suggests that compound B contains a primary alcohol, which can be oxidized to a carboxylic acid.

Based on these observations, we can identify the compounds as follows:

Compound A: An optically active compound that undergoes acidification to regenerate it. It has the formula C6H10O2 and contains an aldehyde group.
Compound B: An optically inactive compound formed by the reduction of compound A using LiAlH4 in ether. It contains a primary alcohol group.
Compound C: An acetate diester derivative of compound B, formed by reacting it with acetic anhydride.
Compound D: β-methylglutaric acid (3-methylpentanedioic acid), formed by oxidizing compound B with aqueous chromic acid.