(a) Calculate the vapor pressure of water above a solution prepared by adding 22.5 g of lactose (C12H22O11) to 200.0 g of water at 338 K. (Vapor–pressure data for water are given in Appendix B.)

Verified step by step guidance

1. Step 1: Determine the molar mass of lactose (C_{12}H_{22}O_{11}) by adding the atomic masses of its constituent elements: 12 carbon atoms, 22 hydrogen atoms, and 11 oxygen atoms.
2. Step 2: Calculate the number of moles of lactose using the formula: \( \text{moles of lactose} = \frac{\text{mass of lactose}}{\text{molar mass of lactose}} \).
3. Step 3: Calculate the number of moles of water using its molar mass (approximately 18.02 g/mol) and the given mass of water (200.0 g).
4. Step 4: Determine the mole fraction of water in the solution using the formula: \( \text{mole fraction of water} = \frac{\text{moles of water}}{\text{moles of water} + \text{moles of lactose}} \).
5. Step 5: Use Raoult's Law to calculate the vapor pressure of water above the solution: \( P_{\text{solution}} = \chi_{\text{water}} \times P^0_{\text{water}} \), where \( P^0_{\text{water}} \) is the vapor pressure of pure water at 338 K.