Solutions

Given:
Mass of solute (Glucose), g.
Molar mass of Glucose (C H O ), g/mol.
Mass of solvent (Water), kg.
K kg mol .
Step 1: Calculate moles of glucose ( ):
mol.
Step 2: Calculate Molality ( ):
m.
Step 3: Calculate Elevation in boiling point ( ):
K.
Step 4: Calculate Boiling Point of solution ( ):
Pure water boils at 373.15 K (100 C) at 1.013 bar.
K.
(In Celsius: C).

1. Raoult's Law: Ideal solutions obey Raoult's law ( ) over the entire range of concentration. Non-ideal solutions deviate (positively or negatively) from Raoult's law.
2. Thermodynamics of Mixing: For an ideal solution, the enthalpy of mixing ( ) is zero, and the volume of mixing ( ) is zero. For a non-ideal solution, and .

Given:
Molality of solution, molal.
Boiling point of solution, C.
Boiling point of pure water, C.
Calculate elevation in boiling point ( ):
C (or 0.052 K).
Formula for elevation in boiling point:

Rearrange to solve for :


K kg mol .

Reverse osmosis requires a semi-permeable membrane that allows solvent to pass but blocks solute.
The most common material used for this membrane is Cellulose Acetate.
Option (A) says "Cellulose acetone", which appears to be a typo for Cellulose Acetate found in the original exam paper (confirmed by Hindi version "Cellulose Acetate").
Options B, C, and D are chemical salts or carbohydrates not typically used as membrane films for RO.
Therefore, (A) is the intended correct answer.

The ebullioscopic constant ( ) relates the elevation in boiling point ( ) to the molality ( ) of the solution: .
Rearranging for , we get .
The unit of temperature change ( ) is Kelvin (K).
The unit of molality ( ) is mol kg .
Therefore, the unit of is .

Let the total mass of the solution be 100 g.
Mass of Benzene (C H ) = 30 g. Mass of Carbon tetrachloride (CCl ) = 100 - 30 = 70 g.
Molar mass of Benzene (C H ) = g/mol.
Molar mass of CCl = g/mol.
Moles of Benzene ( ) = mol.
Moles of CCl ( ) = mol.
Total moles = mol.
Mole fraction of Benzene ( ) = .
This value is closest to 0.459.

Concept: Depression in freezing point is a colligative property and is calculated using the formula: where is the depression in freezing point, is the cryoscopic constant, and is the molality of the solution.
Answer:
To calculate the depression in freezing point:

• First, calculate molality ( ):
• Then apply the formula:

Example:
If and , then: Thus, the freezing point decreases by .

Concept: Molarity and molality are concentration terms, but they differ in how they depend on volume and mass, which affects temperature dependence.
Answer:
Molarity (M): Molality (m): Differences:

• Basis: Molarity depends on volume; Molality depends on mass.
• Temperature Effect: Molarity changes with temperature (volume expands or contracts), whereas molality remains constant (mass unaffected).
• Usage: Molality is preferred in colligative properties due to temperature independence.

Temperature Dependence:
As temperature increases, the volume of solution increases, causing molarity to decrease. However, molality remains unchanged because mass does not vary with temperature.