The correct answer is option 'A': the relative lowering of vapor pressure is equal to the mole fraction of solute. Let's break down the explanation into several points:

1. Definition of Relative Lowering of Vapor Pressure:
The relative lowering of vapor pressure is a measure of the decrease in the partial pressure of the solvent caused by the presence of a non-volatile solute. It is defined as the ratio of the decrease in vapor pressure to the vapor pressure of the pure solvent.

2. Raoult's Law:
Raoult's Law states that the vapor pressure of a solvent in a solution is directly proportional to its mole fraction. Mathematically, the vapor pressure of the solvent in the solution (P_solvent) is given by P_solvent = X_solvent * P°_solvent, where X_solvent is the mole fraction of the solvent and P°_solvent is the vapor pressure of the pure solvent.

3. Effect of Non-volatile Solute on Vapor Pressure:
When a non-volatile solute is dissolved in a solvent, the vapor pressure of the solvent decreases. This is because the solute particles occupy some of the space at the surface of the solvent, reducing the number of solvent particles available to escape into the vapor phase. As a result, the vapor pressure of the solvent in the solution becomes lower than the vapor pressure of the pure solvent.

4. Relationship between Relative Lowering of Vapor Pressure and Mole Fraction of Solute:
The relative lowering of vapor pressure (ΔP/P°_solvent) is directly proportional to the mole fraction of solute (X_solute) in the solution. Mathematically, it can be expressed as ΔP/P°_solvent = X_solute.

5. Justification of Option 'A':
Since the relative lowering of vapor pressure is equal to the mole fraction of solute, option 'A' is the correct answer. The other options (b) molality of solution, (c) mole fraction of solvent, and (d) molarity of solution, do not accurately represent the relationship between the relative lowering of vapor pressure and the solute concentration in the solution.

In conclusion, when a non-volatile solute is dissolved in a solvent, the relative lowering of vapor pressure is equal to the mole fraction of solute. This relationship is based on Raoult's Law and the effect of solute particles on the vapor pressure of the solvent.