The relative lowering of vapour pressure is equal to the ratio between the number of

Options

A. solute molecules to the solvent molecules
B. solute molecules to the total molecules in solution
C. solvent molecules to the total molecules in the solution
D. solvent molecules to the total number of ions of the solute

Explanation

To solve the question regarding the relative lowering of vapor pressure, we will follow these steps:

### Step 1: Understand Raoult's Law
According to Raoult's Law, the vapor pressure of a solvent in a solution (P_A) is directly proportional to the mole fraction of the solvent (X_A) in the solution. The equation can be expressed as:
\[ P_A = P_{A0} \cdot X_A \]
where \( P_{A0} \) is the vapor pressure of the pure solvent.

### Step 2: Relate Vapor Pressures to Mole Fractions
We can manipulate the equation to find the relationship between the vapor pressures and mole fractions. Dividing both sides by \( P_{A0} \):
\[ \frac{P_A}{P_{A0}} = X_A \]

### Step 3: Express Mole Fraction of Solute
Since the mole fraction of solute (X_B) can be expressed as:
\[ X_B = 1 - X_A \]
we can substitute this into our equation. Therefore, we can express the relative lowering of vapor pressure as:
\[ \frac{P_{A0} - P_A}{P_{A0}} = X_B \]

### Step 4: Define Relative Lowering of Vapor Pressure
The left side of the equation represents the relative lowering of vapor pressure:
\[ \text{Relative Lowering of Vapor Pressure} = \frac{P_{A0} - P_A}{P_{A0}} = X_B \]

### Step 5: Express Mole Fraction in Terms of Moles
The mole fraction of solute (X_B) can also be defined in terms of the number of moles of solute (N_B) and the total number of moles in the solution (N_A + N_B):
\[ X_B = \frac{N_B}{N_A + N_B} \]

### Step 6: Conclude the Relationship
From the above steps, we conclude that the relative lowering of vapor pressure is equal to the mole fraction of solute:
\[ \text{Relative Lowering of Vapor Pressure} = \frac{N_B}{N_A + N_B} \]

### Final Answer
Thus, the relative lowering of vapor pressure is equal to the ratio between the number of solute molecules (N_B) to the total number of molecules in the solution (N_A + N_B).