Time: 2 Hours | Max Marks: 50

Section A: Multiple Choice Questions (10 x 1 Mark)

1. Which of the following concentration terms is independent of temperature? a) Molarity b) Normality c) Molality d) Formality

2. An amalgam of mercury with sodium is an example of which type of solution? a) Solid in liquid b) Liquid in solid c) Liquid in gas d) Gas in solid

3. The value of Henry’s law constant ($K_H$): a) Increases with an increase in temperature b) Decreases with an increase in temperature c) Is independent of temperature d) Is the same for all gases

4. For an ideal solution, the enthalpy of mixing ($\Delta H_{mix}$) is: a) $\Delta H_{mix} > 0$ b) \Delta H_{mix} < 0 c) $\Delta H_{mix} = 0$ d) Not defined

5. Which of the following is NOT a colligative property? a) Osmotic pressure b) Elevation of boiling point c) Vapor pressure d) Depression of freezing point

6. A solution of ethanol and acetone shows: a) Ideal behavior b) Negative deviation from Raoult's Law c) Positive deviation from Raoult's Law d) No vapor pressure

7. The unit of the molal elevation constant ($K_b$) is: a) K mol/kg b) K kg/mol b) K/mol d) kg/mol

8. The spontaneous flow of solvent molecules through a semipermeable membrane is called: a) Diffusion b) Reverse osmosis c) Osmosis d) Plasmolysis

9. If a solute undergoes association in a solvent, its van’t Hoff factor ($i$) will be: a) $i = 1$ b) $i > 1$ c) i < 1 d) $i = 0$

10. The relative lowering of vapor pressure is equal to the: a) Molarity of the solution b) Mole fraction of the solvent c) Mole fraction of the solute d) Molality of the solution

Section B: Short Answer Questions (8 x 2 Marks)

1. Define a binary solution and distinguish between the solute and the solvent.

2. State Henry’s Law and write its mathematical expression.

3. Why does the solubility of a gas in a liquid typically decrease with an increase in temperature?.

4. Define "Molarity" and "Molality." Which one is preferred for studies at varying temperatures and why?.

5. What are azeotropes? Give one example.

6. Explain why the vapor pressure of a solvent decreases when a non-volatile solute is added.

7. Define "Isotonic solutions".

8. What is the van’t Hoff factor ($i$)? Write its formula in terms of observed and calculated colligative properties.

Section C: Long Answer Questions (3 x 5 Marks)

1. Raoult’s Law and Deviations: State Raoult’s Law for a solution of volatile liquids. Explain the molecular reasons for positive and negative deviations from this law with examples.

2. Colligative Properties: Derive the relationship between the elevation of boiling point and the molality of the solution. Why is the boiling point of a solution always higher than that of a pure solvent?.

3. Osmotic Pressure and Reverse Osmosis: Define osmotic pressure. Describe the process of reverse osmosis and its application in the desalination of seawater.

Section D: Numerical Problems (3 x 3 Marks)

1. Concentration Calculation: Calculate the mole fraction of ethylene glycol ($\text{C}_2\text{H}_6\text{O}_2$) in a solution containing 20% of $\text{C}_2\text{H}_6\text{O}_2$ by mass.

2. Boiling Point Elevation: $18\text{ g}$ of glucose ($\text{C}_6\text{H}_{12}\text{O}_6$) is dissolved in $1\text{ kg}$ of water in a saucepan. At what temperature will water boil at $1.013\text{ bar}$? ($K_b$ for water is $0.52\text{ K kg/mol}$) .

3. Osmotic Pressure: Calculate the osmotic pressure of a solution prepared by dissolving $2.5\text{ g}$ of $\text{K}_2\text{SO}_4$ in $2\text{ L}$ of water at $25^\circ\text{C}$, assuming it is completely dissociated.

Solutions

Section A: Multiple Choice Questions (Answers)

1. [cite_start]c) Molality (It is based on mass, which does not change with temperature [cite: 46, 256]).
2. [cite_start]b) Liquid in solid (Mercury is liquid, sodium is solid [cite: 44, 45]).
3. [cite_start]a) Increases with an increase in temperature (This results in decreased gas solubility [cite: 48, 151]).
4. [cite_start]c) $\Delta H_{mix} = 0$ (Ideal solutions have no heat change upon mixing [cite: 49, 91]).
5. [cite_start]c) Vapor pressure (Only the relative lowering of vapor pressure is a colligative property [cite: 51, 186]).
6. [cite_start]c) Positive deviation from Raoult's Law (Intermolecular forces become weaker after mixing [cite: 50, 184]).
7. [cite_start]b) K kg/mol[cite: 52, 267].
8. [cite_start]c) Osmosis[cite: 52, 98].
9. [cite_start]c) i < 1 (Association reduces the total number of particles [cite: 54, 233]).
10. [cite_start]c) Mole fraction of the solute[cite: 51, 186].

---

Section B: Short Answer Questions (Answers)

1. [cite_start]Binary Solution: A solution consisting of only two components[cite: 77]. [cite_start]The solvent is the component in the larger proportion, while the solute is the component in the smaller proportion[cite: 60, 77].
2. [cite_start]Henry’s Law: At a constant temperature, the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid[cite: 64, 116]. [cite_start]Formula: $P = K_H \cdot \chi$[cite: 117].
3. [cite_start]Gas Solubility & Temperature: Dissolving gas in a liquid is usually an exothermic process[cite: 119]. [cite_start]According to Le Chatelier's principle, increasing temperature shifts the equilibrium back toward the gas phase, decreasing solubility[cite: 120].
4. Molarity vs. Molality: Molarity (M) is moles per liter of solution; [cite_start]Molality (m) is moles per kg of solvent[cite: 81, 82]. [cite_start]Molality is preferred because it is temperature-independent, whereas molarity changes as the volume of the solution expands or contracts with temperature[cite: 256].
5. [cite_start]Azeotropes: Liquid mixtures that boil at a constant temperature and have the same composition in both liquid and vapor phases[cite: 50]. Example: Ethanol-water mixture (95% ethanol by volume).
6. [cite_start]Vapor Pressure Decrease: Non-volatile solute particles occupy space on the liquid surface, reducing the number of solvent molecules that can escape into the vapor phase[cite: 171, 181].
7. [cite_start]Isotonic Solutions: Two solutions that have the same osmotic pressure at a given temperature[cite: 52, 230].
8. [cite_start]van’t Hoff Factor ($i$): A ratio used to account for the extent of solute association or dissociation[cite: 71, 100].
   • [cite_start]$i = \frac{\text{Observed colligative property}}{\text{Calculated colligative property}}$[cite: 102, 236].

---

Section C: Long Answer Questions (Hints)

1. [cite_start]Raoult’s Law: $P_A = P_A^\circ \cdot \chi_A$[cite: 172].
   • [cite_start]Positive Deviation: $A-B$ interactions are weaker than $A-A$ and $B-B$ (e.g., Ethanol + Acetone)[cite: 92, 184].
   • [cite_start]Negative Deviation: $A-B$ interactions are stronger (e.g., Phenol + Aniline)[cite: 93, 185].
2. [cite_start]Boiling Point Elevation: $\Delta T_b = K_b \cdot m$[cite: 266]. [cite_start]The boiling point increases because the addition of a non-volatile solute lowers the vapor pressure; therefore, a higher temperature is required for the vapor pressure to equal atmospheric pressure[cite: 170, 215].
3. [cite_start]Osmotic Pressure: The excess pressure applied to a solution to prevent the inward flow of solvent through a semi-permeable membrane[cite: 98, 229]. [cite_start]Reverse Osmosis: Applying pressure greater than osmotic pressure to force solvent from the solution into the pure solvent, used to remove salt from seawater[cite: 53, 229].

---

Section D: Numerical Solutions

1. Mole Fraction of Ethylene Glycol ($\text{C}_2\text{H}_6\text{O}_2$):
   • Mass of glycol = $20\text{ g}$, Mass of water = $80\text{ g}$.
   • Moles of glycol = $20 / 62 \approx 0.322\text{ mol}$.
   • Moles of water = $80 / 18 \approx 4.444\text{ mol}$.
   • $\chi_{glycol} = \frac{0.322}{0.322 + 4.444} \approx \mathbf{0.068}$.
2. Boiling Point Elevation:
   • Moles of glucose = $18 / 180 = 0.1\text{ mol}$.
   • Molality ($m$) = $0.1\text{ mol} / 1\text{ kg} = 0.1\text{ m}$.
   • $\Delta T_b = K_b \cdot m = 0.52 \times 0.1 = 0.052\text{ K}$.
   • Boiling Point = $373.15\text{ K} + 0.052\text{ K} = \mathbf{373.202\text{ K}}$.
3. Osmotic Pressure:
   • $\text{K}_2\text{SO}_4 \rightarrow 2\text{K}^+ + \text{SO}_4^{2-}$, so $i = 3$.
   • Moles of solute = $2.5 / 174 \approx 0.0143\text{ mol}$.
   • Molarity ($C$) = $0.0143 / 2 = 0.00715\text{ M}$.
   • $\pi = iCRT = 3 \times 0.00715 \times 0.0821 \times 298 \approx \mathbf{0.525\text{ atm}}$.