A non-volatile solute 'X' completely dimerizes in water, if...

A non-volatile solute 'X' completely dimerizes in water, if the temperature is below $-3.72^{\circ} \mathrm{C}$ and the solute completely dissociates as $\mathrm{X} \rightarrow \mathrm{Y}+\mathrm{Z}$ if the temperature is above $100.26^{\circ} \mathrm{C}$. In between these two temperatures (including both temperatures), the solute is neither dissociated nor associated. One mole of ' $\mathrm{X}$ ' is dissolved in $1.0 \mathrm{~kg}$ water $\left(K_{\mathrm{b}}=0.52 \mathrm{~K}-\mathrm{kg} / \mathrm{mol}, K_{\ell}=1.86 \mathrm{~K}-\mathrm{kg} / \mathrm{mol}\right)$. Identify the incorrect information related with the solution. (a) The freezing point of solution is $-1.86^{\circ} \mathrm{C}$ (b) The boiling point of solution is $101.04^{\circ} \mathrm{C} .$ (c) When the solution is cooled to $-7.44^{\circ} \mathrm{C}, 75 \%$ of water present initially will separate as ice. (d) When the solution is heated to $102.08^{\circ} \mathrm{C}, 50 \%$ of water present initially will escape out as vapour.

A non-volatile solute 'X' completely dimerizes in water, if the temperature is below $-3.72^{\circ} \mathrm{C}$ and the solute completely dissociates as $\mathrm{X} \rightarrow \mathrm{Y}+\mathrm{Z}$ if the temperature is above $100.26^{\circ} \mathrm{C}$. In between these two temperatures (including both temperatures), the solute is neither dissociated nor associated. One mole of ' $\mathrm{X}$ ' is dissolved in $1.0 \mathrm{~kg}$ water $\left(K_{\mathrm{b}}=0.52 \mathrm{~K}-\mathrm{kg} / \mathrm{mol}, K_{\ell}=1.86 \mathrm{~K}-\mathrm{kg} / \mathrm{mol}\right)$.
Identify the incorrect information related with the solution.
(a) The freezing point of solution is $-1.86^{\circ} \mathrm{C}$
(b) The boiling point of solution is $101.04^{\circ} \mathrm{C} .$
(c) When the solution is cooled to $-7.44^{\circ} \mathrm{C}, 75 \%$ of water present initially will separate as ice.
(d) When the solution is heated to $102.08^{\circ} \mathrm{C}, 50 \%$ of water present initially will escape out as vapour.

Key Concepts

Colligative Properties

Colligative properties are characteristics of solutions that depend solely on the concentration of solute particles in a solvent, not on the identity of the solute. This principle is pivotal in understanding phenomena such as freezing point depression and boiling point elevation, where the number of dissolved particles affects the thermodynamic properties of the solution.

Van't Hoff Factor

The van't Hoff factor quantifies the number of effective particles in solution per formula unit of solute. It plays a critical role in colligative property calculations since dissociation or association (such as dimerization) alters the total particle count, thereby influencing the magnitude of freezing point depression or boiling point elevation.

Association and Dimerization

Association, and specifically dimerization, is the process by which solute molecules combine to form larger units. In the context of solutions, dimerization reduces the effective number of particles reacting in the solvent compared to complete dissociation, directly affecting colligative properties by lowering the concentration of individual solute species.

Freezing Point Depression

Freezing point depression is the phenomenon where the addition of a non-volatile solute lowers the freezing temperature of a solvent. This concept involves calculations that rely on the cryoscopic constant of the solvent and the effective concentration of solute particles, which is modified by processes such as dissociation or association.

Boiling Point Elevation

Boiling point elevation refers to the increase in the boiling temperature of a liquid when a non-volatile solute is dissolved in it. Similar to freezing point depression, this colligative property depends on the number of solute particles present, as determined by the van't Hoff factor, and the ebullioscopic constant of the solvent.

Phase Equilibrium and Fractional Phase Changes

Phase equilibrium in solutions deals with understanding how temperature changes induce phase transitions like freezing or boiling. It involves analyzing the proportion of solvent that undergoes phase change under various conditions, which is important when accounting for effects such as partial solidification or vaporization due to the presence of a solute.

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