Question

Upon heating a racemic mixture of \(d, l-3,4\)-dimethyl-1,5-hexadiene, three products are possible, and all three are observed. The ratios are 90,9 , and nearly 1 percent.

Short answer

Answer: Upon heating the racemic mixture of d,l-3,4-dimethyl-1,5-hexadiene, we observe three possible products with ratios 90%, 9%, and 1%, corresponding to retention of stereochemistry at both methyl groups, inversion at one methyl group, and inversion at both methyl groups, respectively.

Step-by-step solution

Understand the Racemic Mixture

A racemic mixture refers to a mixture containing equal amounts of two enantiomers (mirror image isomers) of a compound. In this case, the mixture is \(d,l-3,4\)-dimethyl-1,5-hexadiene, which means it contains both the \(d\) (dextrorotatory) and \(l\) (levorotatory) enantiomers of 3,4-dimethyl-1,5-hexadiene.

Identify the Possible Products

Upon heating a racemic mixture of a compound, we can expect the formation of several stereoisomers depending on the reaction mechanism. Let's identify the possible products: 1. Retention of stereochemistry at both methyl groups. 2. Inversion of stereochemistry at one of the methyl groups. 3. Inversion of stereochemistry at both methyl groups.

Analyze the Reaction Pathways

Now that we have identified the possible products let's analyze the possible reaction pathways: 1. For the products with retention of stereochemistry, the reaction pathway is the simplest, and thus, these products should be formed in the highest ratio. 2. For the products with inversion of stereochemistry at only one methyl group, the reaction pathway is slightly more complex, which means these products should be formed in a smaller ratio. 3. For the products with inversion of stereochemistry at both methyl groups, the reaction pathway is the most complex, and the products are formed in the least ratio.

Match the Products with the Ratios

Now that we have analyzed the reaction pathways, we can match the products with their corresponding observed ratios: 1. 90%: Products with retention of stereochemistry at both methyl groups. 2. 9%: Products with inversion of stereochemistry at only one methyl group. 3. 1%: Products with inversion of stereochemistry at both methyl groups. In conclusion, upon heating the racemic mixture of \(d,l-3,4\)-dimethyl-1,5-hexadiene, we observe three possible products with ratios 90%, 9%, and 1%, corresponding to retention of stereochemistry at both methyl groups, inversion at one methyl group, and inversion at both methyl groups, respectively.