Solution for (a) Molal Depression Constant
Step 1 (Definition): [1 Mark]
The molal depression constant ($K_f$), also known as the cryoscopic constant, is defined as the depression in freezing point produced when 1 mole of a non-volatile solute is dissolved in 1 kg (1000 g) of the solvent.
Step 2 (Relationship with Enthalpy of Fusion): [1 Mark]
The relationship between the molal depression constant ($K_f$) and the enthalpy of fusion ($\Delta_{fus}H$) is given by the following expression:
$$K_f = \frac{R \cdot M_1 \cdot T_f^2}{1000 \cdot \Delta_{fus}H}$$Where:
- $R$ = Universal gas constant
- $M_1$ = Molar mass of the solvent
- $T_f$ = Freezing point of the pure solvent
- $\Delta_{fus}H$ = Enthalpy of fusion per mole of the solvent
Solution for (b) Deviation in Ethanol and Acetone Mixture
Step 1 (Type of Deviation & Reason): [1 Mark]
The mixture of ethanol and acetone shows positive deviation from Raoult's Law. Reason: In pure ethanol, molecules are held together by strong intermolecular hydrogen bonding. When acetone is added, it disrupts these hydrogen bonds between ethanol molecules. The new solute-solvent interactions (ethanol-acetone) are weaker than the original solvent-solvent (ethanol-ethanol) interactions, leading to an increase in vapor pressure.
Step 2 (Type of Azeotrope): [1 Mark]
This mixture forms a minimum boiling azeotrope. Because the vapor pressure is higher than expected, the boiling point of the mixture is lower than the boiling points of both individual components.
💡 EL10 Concept Insight:
Think of pure ethanol as a group of friends holding hands tightly (hydrogen bonds). When you add acetone, it acts like a stranger pushing between them, making them let go of each other's hands. Because they aren't holding on as tightly anymore, it's much easier for them to "escape" into the air as vapor, which is why the pressure goes up and the boiling point drops!