Colligative Properties

Step 1: Definition.
Molal elevation constant (also called ebullioscopic constant, ) is defined as the elevation in boiling point of a solvent when 1 mole of a non-volatile solute is dissolved in 1 kg of the solvent.
where, = elevation in boiling point,
= molality of the solution.
Step 2: Explanation.
It depends only on the nature of the solvent, not on the solute. The constant has units of K·kg·mol .
Step 3: Relation with molality.
Since the formula involves molality, the rise in boiling point of a solution is directly proportional to its molality.
Step 4: Distinction from molarity.
- Molality is defined per kg of solvent and is temperature-independent.
- Molarity is defined per liter of solution and is temperature-dependent.
Thus, molal elevation constant is connected with molality of the solution, not with molarity.

Step 1: Normal molecular mass.
Molecular mass of a solute is generally calculated from colligative properties (elevation of boiling point, depression of freezing point, osmotic pressure, relative lowering of vapor pressure). Ideally, this gives the correct molecular mass.
Step 2: Abnormal case.
Sometimes, the molecular mass determined experimentally using colligative properties differs from the theoretical (expected) value. This is called abnormal molecular mass.
Step 3: Causes of abnormal molecular mass.
- Association of molecules: Solute molecules combine to form aggregates (e.g., acetic acid in benzene). This leads to a molecular mass higher than expected.
- Dissociation of molecules: Solute molecules dissociate into ions (e.g., electrolytes like KCl in water). This leads to a molecular mass lower than expected.
Step 4: Explanation using van’t Hoff factor.
To correct this abnormal behavior, van’t Hoff introduced a factor : Then, modified formula: Step 5: Conclusion.
Abnormal molecular mass occurs due to association or dissociation of solute molecules in solution. It is corrected using the van’t Hoff factor.

Step 1: Concept of osmosis.
Semi-permeable membranes allow only solvent molecules (commonly water) to pass through, but not solute particles.
Step 2: Analyze options.
(A) Solvent molecules: Correct — these can move across the membrane.
(B) Solute molecules: Blocked.
(C) Complex ions: Too large to pass.
(D) Simple ions: Generally do not cross without special ion channels.
Step 3: Conclusion.
Thus, solvent molecules can pass through semi-permeable membranes.

Step 1: Use colligative property (boiling point elevation).
Boiling point elevation depends on van’t Hoff factor (number of particles).
Step 2: Compare for solutes.
Glucose, sucrose, urea are non-electrolytes .
NaCl dissociates into Na +Cl .
Step 3: Conclusion.
Greater gives larger . Hence 1% NaCl(aq) has the highest boiling point.

Step 1: Definition.
Two or more solutions having the same osmotic pressure at a given temperature are called isotonic solutions.
Step 2: Explanation.
When two isotonic solutions are separated by a semipermeable membrane, there is no net movement of solvent molecules across the membrane, because both have equal osmotic pressure.
Step 3: Example.
- 0.9% NaCl solution (saline) is isotonic with human blood and tears.
Step 4: Relation.
Osmotic pressure ( ) = , where = concentration, = gas constant, and = temperature. For isotonic solutions, .

Step 1: Definition.
Mole fraction is a way to express the concentration of a component in a mixture. It is defined as the ratio of the number of moles of a component to the total number of moles of all components in the mixture.
Step 2: Calculation.
For a solution containing two components, A and B, the mole fraction of A, , is given by: where and are the number of moles of A and B, respectively.

Step 1: Raoult’s Law.
Raoult's law states that the relative lowering of the vapour pressure of a solvent in a solution is equal to the mole fraction of the solute in the solution. where:
- is the lowering of vapour pressure,
- is the vapour pressure of the pure solvent,
- is the mole fraction of the solute.
Step 2: Explanation.
This law is valid for ideal solutions where there is no significant interaction between the solute and solvent molecules. It shows that as the amount of solute increases, the vapour pressure of the solvent decreases.

Step 1: Understanding isotonic solutions.
Isotonic solutions are solutions that have the same osmotic pressure. This means the molar concentration of solute in both solutions is the same. Step 2: Analysis of options.
(A) Density: Density may not be the same in isotonic solutions as it depends on the composition of the solvent.
(B) Normality: Normality depends on the equivalent weight of solute, so it may vary between solutions.
(C) Strength: Strength is not the property that defines isotonic solutions.
(D) Molar concentration: Correct — Isotonic solutions have the same molar concentration of solute.
Step 3: Conclusion.
The correct answer is (D) because isotonic solutions have the same molar concentration.

Step 1: Understanding osmotic pressure.
Osmotic pressure ( ) is a colligative property and is related to the concentration of the solute. It is given by the equation: where is the concentration, is the gas constant, and is the temperature in Kelvin. Step 2: Analysis of options.
(A) : Correct — This is the correct equation for osmotic pressure.
(B) : This is incorrect because it does not include temperature, which is required for the correct calculation.
(C) : This is incorrect because the units of osmotic pressure are not balanced in this form.
(D) : This is incorrect because it reverses the correct equation.
Step 3: Conclusion.
The correct answer is (A) because it is the proper equation for osmotic pressure.