Correct Option: (d)

Explanation: Gold (22 carat) is an alloy composed of gold combined with copper or silver. Alloys represent uniform mixtures of crystalline solids, which are classic examples of solid-in-solid solutions.

Correct Option: (c)

Explanation: Molarity $M$ is defined as the number of moles of solute dissolved in 1 Liter of solution. Because volume expands or contracts with temperature variations, molarity is temperature-dependent, rendering Assertion (A) true. However, molarity is a concentration term, not a colligative property, making Reason (R) false.

Correct Option: (d)

Explanation: Molality $m$ is defined as moles of solute per kilogram of solvent. Since mass is unaffected by temperature changes, molality remains completely constant with temperature, making Assertion (A) false. On the other hand, the volume of a liquid expansion is temperature-dependent, making Reason (R) true.

Definition: Molality is defined as the number of moles of solute dissolved per kilogram $(1000 \text{ g})$ of the solvent.

Where:

• $w_B$ = mass of solute (g)
• $M_B$ = molar mass of solute ($\text{g mol}^{-1}$)
• $w_A$ = mass of solvent (g)

Unit: $\text{mol kg}^{-1}$ (or molal, $m$).

Step 1: Interpret the weight percentage.

$9.8\% \, (w/w)$ means $9.8 \text{ g}$ of solute $\text{H}_2\text{SO}_4$ is dissolved in $100 \text{ g}$ of total solution.

• Mass of solute $(w_B) = 9.8 \text{ g}$
• Mass of solution $= 100 \text{ g}$

Step 2: Calculate the volume of the solution ($V$) using its density.

Step 3: Calculate moles of solute ($n_B$).

Step 4: Solve for Molarity ($M$).

Answer: The molarity of the solution is $1.02 \text{ M}$.

Step 1: Extract quantities from mass percentage.

• Mass of glucose (solute, $w_B$) = $10 \text{ g}$
• Mass of water (solvent, $w_A$) = $100 \text{ g} - 10 \text{ g} = 90 \text{ g} = 0.09 \text{ kg}$

Step 2: Compute Molality ($m$).

Step 3: Compute Molarity ($M$). First, find volume of the $100 \text{ g}$ solution.

Answer: Molality is $0.62 \text{ m}$ and Molarity is $0.67 \text{ M}$.

Correct Option: (b)

Explanation: The dissolution of gas molecules in a liquid is an exothermic process (releasing heat, $\Delta H \lt 0$). According to Le Chatelier's principle, when temperature increases, a reversible exothermic reaction shifts in the backward direction. Hence, gaseous solubility decreases as temperature increases.

Correct Option: (a)

Explanation: Acetone and chloroform show a negative deviation from Raoult's law. This is because intermolecular hydrogen bonds establish between the oxygen atom of acetone and the polar hydrogen atom of chloroform:

As the new interactions are significantly stronger than pure solute-solute or solvent-solvent interactions, the molecules pull closer together, leading to contraction in volume ($\Delta V_{\text{mix}} \lt 0$).

Henry's Law: This law states that at a constant temperature, the partial pressure of a gas in the vapour phase $p$ is directly proportional to the mole fraction of the gas $X$ dissolved in the solution.

Where $K_H$ is the Henry's law constant.

Scuba Diving Application: Divers breathe gases at high pressures deep underwater, causing nitrogen to highly dissolve in blood. Upon coming back to low pressures at the surface, dissolved nitrogen is rapidly expelled, creating painful bubbles in blood capillaries—a clinical condition called "the bends". To prevent this, divers use cylinders diluted with helium ($11.7\% \text{ He}$, $56.2\% \text{ N}_2$, and $32.1\% \text{ O}_2$) because helium exhibits extremely low solubility in blood lipids and aqueous environments.

Henry's Law Relation:

Calculation:

• Partial pressure of $\text{CO}_2 \, (p) = 760 \text{ mm Hg}$
• $K_H = 1.25 \times 10^6 \text{ mm Hg}$

Answer: The solubility of $\text{CO}_2$ in terms of mole fraction is $6.08 \times 10^{-4}$.

Step 1: Find mole fractions of component A ($X_A$) and component B ($X_B$).

Since equal moles are mixed ($n_A = n_B$):

Step 2: Apply Raoult's Law to calculate total pressure ($P_{\text{total}}$).

Answer: Vapour pressure of the ideal solution is $140 \text{ mm Hg}$.

Correct Option: (c)

Explanation: Isotonic solutions are defined as solutions having identical osmotic pressures ($\pi_1 = \pi_2$) at the exact same temperature. When separated by a semipermeable membrane, no net osmosis occurs between isotonic solutions.

Correct Option: (c)

Calculation:

Apply the elevation in boiling point formula:

Since the boiling point of pure water is $100^\circ\text{C}$:

Step 1: Find depression of freezing point for sucrose ($\Delta T_{f1}$).

Step 2: Compute molality of the sucrose solution ($m_1$).

$10\%$ mass solution = $10 \text{ g}$ sucrose in $90 \text{ g}$ water.

Step 3: Express the relation using the cryoscopic constant ($K_f$).

Step 4: Compute molality of the glucose solution ($m_2$).

Step 5: Compute the freezing point depression for glucose ($\Delta T_{f2}$).

Step 6: Calculate glucose solution's freezing point ($T_{f2}$).

Answer: The freezing point of the glucose solution is $265.55 \text{ K}$.

Step 1: Apply Raoult's law for relative lowering of vapour pressure.

Given parameters:

• $P^\circ = 32 \text{ mm Hg}$
• $P = 31.84 \text{ mm Hg}$
• $w_B = 5 \text{ g}$
• $w_A = 200 \text{ g}$

Step 2: Compute the mole fraction of the solvent ($X_{\text{solvent}}$).

Step 3: Relate molecular fractions to moles. Let molar mass of solute be $M_B$.

Step 4: Solve for $M_B$.

Answer: The molar mass of the non-volatile solute is $89.64 \text{ g/mol}$.

Correct Option: (b)

Explanation: Water of crystallization behaves as part of the solvent system. On dissolving, the salt dissociates fully as follows:

Because complete ionization produces 3 moles of ions from 1 mole of salt, the Van't Hoff factor is:

Step 1: Determine the Van't Hoff factor ($i$) for $\text{CaCl}_2$.

Since $\text{CaCl}_2$ undergoes complete ionization, its chemical reaction is:

Yielding 3 total ions, hence $i = 3$.

Step 2: State the colligative freezing depression relation.

Substitute given values: $\Delta T_f = 2\text{ K}$, $K_f = 1.86$, and solvent mass $w_A = 500\text{ g} = 0.5\text{ kg}$.

Step 3: Calculate mass of solute ($w_B$).

Answer: The mass of $\text{CaCl}_2$ required is $19.87 \text{ g}$.

Step 1: Set up the dissociation equation.

Total particles generated $(n) = 3 + 1 = 4$.

Step 2: Compute the Van't Hoff factor ($i$).

Step 3: Calculate the elevation in boiling point ($\Delta T_b$) at $1 \, m$.

Step 4: Determine the boiling point of the solution ($T_b$).

Answer: The Van't Hoff factor is $3.556$ and the boiling point is $101.85^\circ\text{C}$.

Step 1: Find calculated molality ($m$) of benzoic acid.

Step 2: Compute the theoretical freezing point depression ($\Delta T_{f,\text{calc}}$).

Step 3: Find the Van't Hoff factor ($i$).

Step 4: Establish dimerization association. Let degree of association be $\beta$.

For dimerization, the system particles at equilibrium are:

Substitute value of $i$:

Answer: The percentage association of benzoic acid is $97.56\%$ (dimerization).

Step 1: Calculate the calculated molality of the solution.

Step 2: Compute the calculated freezing point depression ($\Delta T_{f,\text{calc}}$).

Step 3: Solve for the Van't Hoff factor ($i$).

Step 4: Establish dissociation equilibrium. Let degree of dissociation be $\alpha$.

Since it yields 2 particles:

Answer: The degree of dissociation of fluoroacetic acid is $0.0753$ (or $7.53\%$).