A solution is made by dissolving 1.0 gurea and 2.0g sucrose in 100 g water at 298 K. predict the vapour pressure of solution if the vapour pressure of water at 298 Kis 23.756 torr.

Explanation

To solve the problem of predicting the vapor pressure of a solution made by dissolving 1.0 g of urea and 2.0 g of sucrose in 100 g of water at 298 K, we will follow these steps:

### Step 1: Calculate the number of moles of urea and sucrose

1. **Molar mass of urea (NH₂CONH₂)**:
- Molar mass = 14 (N) + 2*1 (H) + 12 (C) + 16 (O) = 60 g/mol
- Moles of urea = mass / molar mass = 1 g / 60 g/mol = 0.0167 mol

2. **Molar mass of sucrose (C₁₂H₂₂O₁₁)**:
- Molar mass = 12*12 (C) + 22*1 (H) + 11*16 (O) = 342 g/mol
- Moles of sucrose = mass / molar mass = 2 g / 342 g/mol = 0.0058 mol

### Step 2: Calculate the total number of moles of solute

- Total moles of solute = moles of urea + moles of sucrose
- Total moles of solute = 0.0167 mol + 0.0058 mol = 0.0225 mol

### Step 3: Calculate the number of moles of solvent (water)

- Molar mass of water (H₂O) = 18 g/mol
- Moles of water = mass / molar mass = 100 g / 18 g/mol = 5.55 mol

### Step 4: Calculate the mole fraction of the solvent

- Mole fraction of solvent (χ_solvent) = moles of solvent / (moles of solvent + moles of solute)
- χ_solvent = 5.55 mol / (5.55 mol + 0.0225 mol) = 5.55 mol / 5.5725 mol ≈ 0.996

### Step 5: Apply Raoult's Law to find the vapor pressure of the solution

- According to Raoult's Law, the vapor pressure of the solution (P_solution) is given by:
\[ P_{\text{solution}} = P^{\circ}_{\text{solvent}} \times \chi_{\text{solvent}} \]
- Given that the vapor pressure of pure water at 298 K (P°_solvent) is 23.756 torr:
\[ P_{\text{solution}} = 23.756 \, \text{torr} \times 0.996 \approx 23.661 \, \text{torr} \]

### Final Answer:
The vapor pressure of the solution is approximately **23.661 torr**.

---