Answer:

Introduction:
In this question, we are given a solution containing 0.1 mole of acetamide in 1 L of glacial acetic acid. We need to determine the molecule(s) that form the first crystal when the solution is cooled to the freezing point.

Explanation:
When a solution is cooled to its freezing point, the solute molecules come together and arrange themselves in an ordered, crystalline structure. The first crystal that appears is typically formed by the solute molecule(s) with the highest concentration in the solution.

In this case, the solute molecules are acetamide and acetic acid. Acetamide is a polar molecule with an amide group (-CONH2) attached to a methyl group (-CH3). Acetic acid is also a polar molecule with a carboxylic acid group (-COOH) attached to a methyl group (-CH3).

Explanation of Option (a):
If acetamide were to form the first crystal, it would mean that the concentration of acetamide in the solution is higher than that of acetic acid. However, since we are given that the solution contains 0.1 mole of acetamide in 1 L of glacial acetic acid, it is highly unlikely that the concentration of acetamide is higher than that of acetic acid. Therefore, option (a) cannot be the correct answer.

Explanation of Option (b):
If acetic acid were to form the first crystal, it would mean that the concentration of acetic acid in the solution is higher than that of acetamide. Given that the solution contains 0.1 mole of acetamide in 1 L of glacial acetic acid, it is reasonable to assume that the concentration of acetic acid is higher than that of acetamide. Therefore, option (b) is the correct answer.

Explanation of Option (c):
Option (c) suggests that both acetamide and acetic acid can form the first crystal. However, since we are given that the solution contains 0.1 mole of acetamide in 1 L of glacial acetic acid, it is highly unlikely that both molecules would have the same concentration. Therefore, option (c) cannot be the correct answer.

Explanation of Option (d):
Option (d) suggests that either acetamide or acetic acid can form the first crystal depending on the condition of the experiment. However, since we are given a specific mole ratio of acetamide to acetic acid in the solution, it is unlikely that the conditions of the experiment would change this ratio. Therefore, option (d) cannot be the correct answer.

Conclusion:
Based on the given mole ratio of acetamide to acetic acid in the solution, the correct answer is option (b), which states that the first crystal that appears at the freezing point contains acetic acid molecules.