A mixture containing two enantiomers in equal proportions will have zero optical rotation, as the rotation due to one isomer will be cancelled by the rotation due to the other isomer. Such a mixture is known as racemic mixture or racemic modification. The given molecular formula C₅H₁₀O, have 4 aldehyde isomers and 3 ketone isomers. Among the ketones, two ketones forms racemic mixtures with lithium aluminium hydride.

Isomeric Ketones of C5H10O

To determine the number of ketones that give a racemic product when reacted with LiAlH4, we first need to identify all the possible isomeric ketones with the molecular formula C5H10O.

The general formula for a ketone is R-CO-R', where R and R' can be any alkyl or aryl groups. In this case, we have 5 carbon atoms, so the ketone group will be attached to one of the carbon atoms, leaving 4 carbon atoms to form the alkyl or aryl groups.

Step 1: Determine the Number of Carbon Atoms Attached to the Ketone Group

To identify the possible isomers, we need to determine the number of carbon atoms attached to the ketone group. This can be done by counting the remaining carbon atoms after attaching the ketone group to one of the carbons.

In this case, we have 5 carbon atoms, so there are four possibilities for the number of carbon atoms attached to the ketone group: 1, 2, 3, or 4.

Step 2: Generate Isomeric Structures

Using the number of carbon atoms attached to the ketone group, we can now generate the isomeric structures.

Case 1: Ketone with 1 Carbon Atom Attached
In this case, the ketone will be attached to one of the four remaining carbon atoms, and the other three carbon atoms will form alkyl or aryl groups.

Possible structure: CH3-CH2-CH2-CO-CH3

Case 2: Ketone with 2 Carbon Atoms Attached
In this case, the ketone will be attached to two of the four remaining carbon atoms, and the other two carbon atoms will form alkyl or aryl groups.

Possible structures:
1. CH3-CH2-CO-CH2-CH3
2. CH3-CO-CH2-CH2-CH3

Case 3: Ketone with 3 Carbon Atoms Attached
In this case, the ketone will be attached to three of the four remaining carbon atoms, and the remaining carbon atom will form an alkyl or aryl group.

Possible structures:
1. CH3-CO-CH(CH3)-CH3
2. CH3-CH2-CO-CH(CH3)-CH2-CH3

Case 4: Ketone with 4 Carbon Atoms Attached
In this case, the ketone will be attached to all four remaining carbon atoms.

Possible structure: CH3-CH2-CO-CH2-CH2-CH3

Step 3: Reacting with LiAlH4

When the isomeric ketones are reacted with LiAlH4, they undergo reduction to form alcohols. The stereoisomers of the ketones will react independently, meaning that each stereoisomer will give a separate product.

Step 4: Identifying Racemic Products

A racemic product is one that contains equal amounts of both enantiomers. In the case of ketones, the reduction by LiAlH4 can result in the formation of a chiral center, leading to the possibility of en