(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

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.

Step 2: Calculate the number of moles of lactose using the formula: \( \text{moles of lactose} = \frac{\text{mass of lactose}}{\text{molar mass of lactose}} \).

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).

Step 4: Determine the mole fraction of water in the solution using the formula: \( \text{mole fraction of water} = \frac{\text{moles of water}}{\text{moles of water} + \text{moles of lactose}} \).

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.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid phase at a given temperature. It reflects the tendency of particles to escape from the liquid phase into the vapor phase. The vapor pressure of a solvent decreases when a non-volatile solute, like lactose, is added, due to the solute particles occupying space at the surface and reducing the number of solvent molecules that can escape.

Raoult's Law

Raoult's Law states that the vapor pressure of a solvent in a solution is directly proportional to the mole fraction of the solvent. This law is crucial for calculating the vapor pressure of a solution, as it allows us to determine how the addition of a solute affects the overall vapor pressure. In this case, the mole fraction of water must be calculated to apply Raoult's Law effectively.

Mole Fraction

Mole fraction is a way of expressing the concentration of a component in a mixture, defined as the number of moles of that component divided by the total number of moles of all components in the mixture. It is a dimensionless quantity and is essential for applying Raoult's Law, as it helps quantify the proportion of solvent present in the solution after the solute is added.

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Textbook Question

You make a solution of a nonvolatile solute with a liquid solvent. Indicate if each of the following statements is true or false. (d) The boiling point of the solution increases in proportion to the concentration of the solute. (e) At any temperature, the vapor pressure of the solvent over the solution is lower than what it would be for the pure solvent.

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Textbook Question

The vapor pressure of pure water at 60 °C is 149 torr. The vapor pressure of water over a solution at 60 °C containing equal numbers of moles of water and ethylene glycol (a nonvolatile solute) is 67 torr. Is the solution ideal according to Raoult's law?

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Textbook Question

At 63.5 °C, the vapor pressure of H₂O is 175 torr, and that of ethanol (C₂H₅OH) is 400 torr. A solution is made by mixing equal masses of H₂O and C₂H₅OH. (a) What is the mole fraction of ethanol in the solution?

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Textbook Question

At 63.5 °C, the vapor pressure of H₂O is 175 torr, and that of ethanol (C₂H₅OH) is 400 torr. A solution is made by mixing equal masses of H₂O and C₂H₅OH. (b) Assuming ideal solution behavior, what is the vapor pressure of the solution at 63.5 °C?

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