a. The vapor pressure of pure water at 60°C is 149 torr. What vapor pressure is predicted by Raoult’s law for a solution at 60°C that is 50 mol% water and 50 mol% ethylene glycol (a nonvolatile solute)?

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Identify the components of the solution: water (solvent) and ethylene glycol (nonvolatile solute).

Recognize that Raoult's law applies to the vapor pressure of the solvent in a solution: \( P_{solution} = \chi_{solvent} \times P^0_{solvent} \), where \( \chi_{solvent} \) is the mole fraction of the solvent and \( P^0_{solvent} \) is the vapor pressure of the pure solvent.

Determine the mole fraction of water (solvent) in the solution. Given that the solution is 50 mol% water, \( \chi_{water} = 0.50 \).

Use the given vapor pressure of pure water at 60°C, which is 149 torr, as \( P^0_{water} \).

Calculate the vapor pressure of the solution using Raoult's law: \( P_{solution} = 0.50 \times 149 \text{ torr} \).

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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 higher the vapor pressure, the more volatile the substance. In this context, understanding vapor pressure is crucial for applying Raoult's law to predict the vapor pressure of a solution.

Raoult's Law

Raoult's law states that the vapor pressure of a solvent in a solution is equal to the vapor pressure of the pure solvent multiplied by its mole fraction in the solution. This law applies to ideal solutions and helps predict how the presence of a nonvolatile solute, like ethylene glycol, affects the vapor pressure of the solvent, in this case, water.

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. In this question, calculating the mole fraction of water and ethylene glycol is essential for applying Raoult's law to determine the vapor pressure of the solution at 60°C.

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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.

a. The solid that forms as the solution freezes is nearly pure solute.

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.

b. The freezing point of the solution is independent of the concentration of the solute.

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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