**Given Data:**
- Mass of solute = 45 g
- Mass of solvent (water) = 900 g
- Initial vapor pressure of water = 30 mm
- Final vapor pressure of water = 24 mm

**Calculating Moles of Solute:**
To calculate the mole fraction of the solvent in the solution, we first need to determine the number of moles of the solute.

The molar mass of the solute can be calculated using the periodic table or other reliable sources. Let's assume the molar mass of the solute is M g/mol.

The number of moles of the solute can be calculated using the formula:

Moles of solute = Mass of solute / Molar mass of solute

**Calculating Moles of Solvent:**
Next, we need to calculate the number of moles of the solvent (water). The molar mass of water is 18 g/mol.

The number of moles of the solvent can be calculated using the formula:

Moles of solvent = Mass of solvent / Molar mass of solvent

**Calculating Mole Fraction:**
The mole fraction of the solvent in the solution can be calculated using the formula:

Mole fraction of solvent = Moles of solvent / (Moles of solute + Moles of solvent)

Substituting the values we calculated earlier:

Mole fraction of solvent = Moles of solvent / (Moles of solute + Moles of solvent)

**Calculating Moles of Solute:**
Using the given mass of solute (45 g) and assuming the molar mass of the solute is X g/mol, we can calculate the moles of the solute:

Moles of solute = 45 g / X g/mol

**Calculating Moles of Solvent:**
Using the given mass of solvent (900 g) and the molar mass of water (18 g/mol), we can calculate the moles of the solvent:

Moles of solvent = 900 g / 18 g/mol

**Calculating Mole Fraction:**
Substituting the calculated values, we can find the mole fraction of the solvent:

Mole fraction of solvent = (900 g / 18 g/mol) / [(45 g / X g/mol) + (900 g / 18 g/mol)]

Simplifying the expression:

Mole fraction of solvent = (50 / X) / (1 + (50 / X))

Therefore, the mole fraction of the solvent in the solution is (50 / X) / (1 + (50 / X)), where X is the molar mass of the solute.