Raoult's Law is a principle that relates the vapor pressure of a solvent in a solution to the mole fraction of the solvent in the solution. It is applicable to ideal solutions, where the solute-solute and solute-solvent interactions are similar to the solvent-solvent interactions.

According to Raoult's Law, the relative lowering of vapor pressure (ΔP) of a solution is equal to the mole fraction of the solute (χsolute) in the solution. Mathematically, it can be expressed as:

ΔP = χsolute

Let's understand this concept in detail:

1. The Ideal Solution:
- An ideal solution is a homogeneous mixture of two or more components that obeys Raoult's Law.
- In an ideal solution, the vapor pressure of each component is directly proportional to its mole fraction in the solution.
- The solute-solute and solute-solvent interactions are similar to the solvent-solvent interactions.

2. Vapor Pressure:
- The vapor pressure of a liquid is the pressure exerted by its vapor when it is in equilibrium with its liquid phase at a given temperature.
- In a pure solvent, the vapor pressure is solely determined by the properties of the solvent.

3. Lowering of Vapor Pressure:
- When a solute is added to a solvent, the vapor pressure of the solvent is reduced.
- This is because the solute particles occupy some of the surface area of the solvent, reducing the number of solvent particles available to escape into the vapor phase.
- The extent of vapor pressure lowering depends on the concentration of the solute in the solution.

4. Relative Lowering of Vapor Pressure:
- The relative lowering of vapor pressure is defined as the ratio of the decrease in vapor pressure to the vapor pressure of the pure solvent.
- It is calculated by dividing the decrease in vapor pressure (ΔP) by the vapor pressure of the pure solvent (P0).
- Mathematically, it can be expressed as: ΔP/P0.
- According to Raoult's Law, this relative lowering of vapor pressure is equal to the mole fraction of the solute in the solution.

5. The Mole Fraction:
- The mole fraction of a component in a solution is the ratio of the number of moles of that component to the total number of moles of all components in the solution.
- It is denoted by χ and is calculated by dividing the number of moles of a component by the total number of moles.
- In the case of Raoult's Law, the mole fraction of the solute (χsolute) is equal to the relative lowering of vapor pressure (ΔP).

Therefore, based on the above explanation, the correct answer to the question is option 'C', which states that the relative lowering of vapor pressure for a solution is equal to the mole fraction of the solute.