Question

The boiling point of 0.2 mol kg$^{-1}$ solution of X in water is greater than equimolal solution of Y in water. Which one of the following statements is true in this case ?

• A. Molecular mass of X is less than the molecular mass of Y
• B. X is undergoing dissociation in water while X undergoes no change.
• C. X is undergoing dissociation in water
• D. Molecular mass of X is greater then the molecular mass of Y.

Answer 1

The Correct Option is C

This question involves understanding the colligative properties of solutions, specifically boiling point elevation. The boiling point of a solution is affected by the number of particles in the solution. The formula for boiling point elevation is given by: 

\(\Delta T_b = i \cdot K_b \cdot m\)

• \(\Delta T_b\) is the boiling point elevation.
• \(i\) is the van't Hoff factor, which indicates the number of particles the solute dissociates into.
• \(K_b\) is the ebullioscopic constant of the solvent (water in this case).
• \(m\) is the molality of the solution.

In this problem, it is given that the boiling point of a 0.2 mol kg^-1 solution of X in water is greater than that of an equimolal solution of Y in water. Since both solutions are of equal molality, \(m\) and \(K_b\) are the same for both solutions. Therefore, differences in boiling point elevations must be due to differences in the van’t Hoff factor \(i\).

The statement that the boiling point of solution X is higher indicates that the van’t Hoff factor for X is larger than for Y. This means:

• For X: \(i > 1\) (indicating that X dissociates into more particles in solution).
• For Y: \(i = 1\) (indicating that Y does not dissociate or undergoes no change).

Therefore, the correct answer must explain this behavior. Among the options provided, only the statement "X is undergoing dissociation in water" accurately describes this scenario.

Hence, the correct answer is: X is undergoing dissociation in water.