Match List I with List II:

Choose the correct answer from the options given below:

A-III, B-IV, C-I, D-II

The correct answer is option 4. A-III, B-IV, C-I, D-II.

Let us go through each concept from List I and match it with the correct equation or expression from List II, providing a detailed explanation for each.

A. Raoult's Law: III. \(p = \chi_ 1p_1^0 + \chi _2p_2^0\)

Raoult's Law is a fundamental principle in the study of solutions, particularly dealing with the vapor pressure of ideal solutions. It states that the partial vapor pressure of each volatile component in a solution is directly proportional to its mole fraction in the solution. Mathematically, for a two-component system, Raoult's law is expressed as:

\(p_i = \chi_i \times p_i^0\)

Where:

\( p_i \) is the partial vapor pressure of component \( i \) in the solution.

\( \chi_i \) is the mole fraction of component \( i \) in the solution.

\( p_i^0 \) is the vapor pressure of the pure component \( i \).

For a solution with two components (1 and 2):

\(p_{\text{total}} = \chi_1 \times p_1^0 + \chi_2 \times p_2^0\)

B. Henry's Law: IV. \(P = K_H \times \chi \)

Henry's Law describes the relationship between the partial pressure of a gas above a liquid and its concentration in the liquid. It is particularly important for gases dissolving in liquids. Henry's law is expressed as:

\(P = K_H \times \chi\)

Where:

\( P \) is the partial pressure of the gas above the solution.

\( K_H \) is Henry's law constant, which depends on the gas and the solvent.

\( \chi \) is the mole fraction of the gas dissolved in the liquid.

C. Elevation in Boiling Point: I. \(\Delta T_b = k_b \times m\)

The Elevation in Boiling Point is a colligative property, meaning it depends on the number of solute particles in a solution rather than the identity of the solute. When a non-volatile solute is added to a solvent, the boiling point of the solution is higher than that of the pure solvent. The increase in boiling point is given by:

\(\Delta T_b = k_b \times m\)

Where:

\( \Delta T_b \) is the elevation in boiling point.

\( k_b \) is the ebullioscopic constant (boiling point elevation constant) of the solvent.

\( m \) is the molality of the solution (moles of solute per kilogram of solvent).

D. Depression in Freezing Point: II. \(\Delta T_f = k_f \times m\)

The Depression in Freezing Point is another colligative property. When a solute is dissolved in a solvent, the freezing point of the solution decreases compared to that of the pure solvent. The decrease in freezing point is expressed by:

\(\Delta T_f = k_f \times m\)

Where:

\( \Delta T_f \) is the depression in freezing point.

\( k_f \) is the cryoscopic constant (freezing point depression constant) of the solvent.

\( m \) is the molality of the solution.

Conclusion:

The correct answer is Option 4: A-III, B-IV, C-I, D-II. Each of these laws and their corresponding equations explains different aspects of solution chemistry, from vapor pressures to the effects of solutes on boiling and freezing points.