Question

In the following reaction, 13.4 grams of aldehyde P gave a diastereomeric mixture of alcohols Q and R in a ratio of 2:1. If the yield of the reaction is 80 percent, then the amount of Q (in grams) obtained is ___________ (in integer). \begin{center} \includegraphics{59.png} \end{center}

Hint:

In reactions involving chiral centers, nucleophilic addition to a carbonyl group can lead to diastereomeric products. The ratio of these diastereomers depends on the stereochemical environment of the existing chiral center. The yield of the reaction must be taken into account when calculating the actual amount of product obtained.

Answer 1

Correct Answer: 8

The reaction involves the addition of methyl lithium (MeLi) to a chiral aldehyde (P). This nucleophilic addition to a chiral carbonyl center creates a new chiral center, leading to a mixture of two diastereomeric alcohols, Q and R. First, calculate the molecular weight of aldehyde P (C\(_{10}\)H\(_{12}\)O): MW(P) = (10 × 12.01) + (12 × 1.01) + 16.00 = 120.1 + 12.12 + 16.00 = 148.22 g/mol Moles of aldehyde P used = mass / molecular weight = 13.4 g / 148.22 g/mol \approx 0.0904 mol The reaction with MeLi will produce a 1:1 mixture of alcohols if the reaction went to completion without considering the existing chirality. However, the problem states that a diastereomeric mixture of Q and R is formed in a 2:1 ratio. This implies that the existing chiral center influences the stereochemical outcome of the nucleophilic attack. The molecular weight of the alcohols Q and R (C\(_{11}\)H\(_{16}\)O) will be: MW(Q) = MW(R) = (11 × 12.01) + (16 × 1.01) + 16.00 = 132.11 + 16.16 + 16.00 = 164.27 g/mol The theoretical yield of the mixture of Q and R (if 100% yield) would be 0.0904 mol × 164.27 g/mol ≈ 14.85 g. The actual yield of the mixture is 80% of the theoretical yield: Actual yield (Q + R) = 0.80 × 14.85 g \approx 11.88 g The diastereomers Q and R are formed in a 2:1 ratio. This means that the amount of Q is \( \frac{2}{2+1} \) of the total amount, and the amount of R is \( \frac{1}{2+1} \) of the total amount. Amount of Q = \( \frac{2}{3} \) × Actual yield (Q + R) = \( \frac{2}{3} \) × 11.88 g \approx 7.92 g Rounding to the nearest integer, the amount of Q obtained is 8 grams.