Statement I: Relative lowering of vapour pressure is independent of temperature

Statement II: Relative lowering of vapour pressure is nothing but the mole fraction of solution.

Both Statement I and Statement II are correct and Statement II is the correct explanation of Statement I

The correct answer is option 1. Both Statement I and Statement II are correct and Statement II is the correct explanation of Statement I.

Let us delve into the concepts of relative lowering of vapor pressure and how they relate to the statements provided:

Relative Lowering of Vapor Pressure:

Relative lowering of vapor pressure (\(\Delta P/P_{\text{0}}\)) is a colligative property that measures the decrease in vapor pressure of a solvent in the presence of a non-volatile solute. It is defined as:

\(\Delta P = P_{\text{0}} - P\)

where \( P_{\text{0}} \) is the vapor pressure of the pure solvent and \( P \) is the vapor pressure of the solvent in the solution.

Temperature Independence: The relative lowering of vapor pressure is independent of temperature. This means that at a given temperature, the amount by which the vapor pressure of the solvent is reduced due to the presence of a solute is solely determined by the concentration (mole fraction) of the solute in the solution. The mathematical expression for relative lowering of vapor pressure is:

\(\frac{\Delta P}{P_{\text{0}}} = \frac{n_{\text{solute}}}{n_{\text{solvent}} + n_{\text{solute}}}\)

where \( n_{\text{solute}} \) and \( n_{\text{solvent}} \) are the number of moles of solute and solvent, respectively.

Mole Fraction Relation: According to Raoult's Law for ideal solutions, the relative lowering of vapor pressure (\(\Delta P/P_{\text{0}}\)) is directly proportional to the mole fraction of the solute (\( x_{\text{solute}} \)) in the solution:

\(\frac{\Delta P}{P_{\text{0}}} = x_{\text{solute}}\)

This means that as the mole fraction of the solute increases, the relative lowering of vapor pressure also increases proportionally.

Analysis of Statements:

Statement I: Relative lowering of vapor pressure is independent of temperature

This statement is correct. The relative lowering of vapor pressure depends solely on the presence and amount of solute particles in the solution. It does not change with variations in temperature, assuming the solution remains ideal and non-electrolytic.

Statement II: Relative lowering of vapor pressure is nothing but the mole fraction of solution.

This statement is also correct. The relative lowering of vapor pressure (\(\Delta P/P_{\text{0}}\)) is indeed equal to the mole fraction of the solute (\( x_{\text{solute}} \)) in the solution, as per Raoult's Law for ideal solutions. This relationship holds true at a constant temperature.

Relationship Between Statements: Both statements I and II are correct:

Statement I correctly identifies that the relative lowering of vapor pressure is independent of temperature. Statement II correctly defines the relative lowering of vapor pressure as directly proportional to the mole fraction of the solute in the solution.

Statement II provides a correct explanation for Statement I. The mole fraction of the solute determines the extent of the relative lowering of vapor pressure, regardless of temperature changes.

Conclusion: Both Statement I and Statement II are correct and Statement II is the correct explanation of Statement I. This conclusion emphasizes that the understanding of relative lowering of vapor pressure relies on the concept that it is primarily governed by the mole fraction of the solute in the solution and is not influenced by temperature variations under ideal conditions. Thus, both statements are accurate, and Statement II logically explains why Statement I is true.