The relative lowering in vapour pressure is proportional to the ratio ...
The relative lowering in vapor pressure is a concept in colligative properties of solutions, which refers to the decrease in the vapor pressure of a solvent when a solute is added to it. This phenomenon can be explained by Raoult's law, which states that the vapor pressure of a solvent above a solution is directly proportional to the mole fraction of the solvent in the solution.
Raoult's law can be mathematically represented as:
P(solvent) = X(solvent) * P°(solvent)
where P(solvent) is the vapor pressure of the solvent above the solution, X(solvent) is the mole fraction of the solvent in the solution, and P°(solvent) is the vapor pressure of the pure solvent.
Now, let's consider a solution where a solute is dissolved in a solvent. The presence of solute molecules reduces the number of solvent molecules at the surface, leading to a decrease in the mole fraction of the solvent (X(solvent)). As a result, the vapor pressure of the solvent above the solution is lowered.
The relative lowering in vapor pressure (ΔP/P°) can be defined as the ratio of the decrease in vapor pressure (ΔP) to the vapor pressure of the pure solvent (P°):
ΔP/P° = (P° - P(solvent))/P° = 1 - X(solvent)
This equation shows that the relative lowering in vapor pressure is directly related to the mole fraction of the solvent in the solution (X(solvent)).
Now, let's consider the options given in the question:
a) Solute molecules to solvent molecules: This ratio does not directly affect the vapor pressure of the solvent. Therefore, it is not the correct answer.
b) Solvent molecules to solute molecules: This ratio also does not directly affect the vapor pressure of the solvent. Therefore, it is not the correct answer.
c) Solute molecules to the total number of molecules in solution: This ratio represents the mole fraction of the solute (X(solute)), which is not directly related to the vapor pressure of the solvent. Therefore, it is not the correct answer.
d) Solvent molecules to the total number of molecules in solution: This ratio represents the mole fraction of the solvent (X(solvent)), which is directly related to the vapor pressure of the solvent. Therefore, it is the correct answer.
In conclusion, the correct answer is option 'C': Solute molecules to the total number of molecules in solution.
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