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Ch.14 - Solutions
All textbooksTro 5th EditionCh.14 - SolutionsProblem 76
Chapter 14, Problem 76

A solution of methanol and water has a mole fraction of water of 0.312 and a total vapor pressure of 211 torr at 39.9 °C. The vapor pressures of pure methanol and pure water at this temperature are 256 torr and 55.3 torr, respectively. Is the solution ideal? If not, what can be inferred about the relative strengths of the solute–solvent interactions compared to the solute–solute and solvent–solvent interactions?

Verified step by step guidance
1
Identify the components of the solution: methanol and water.
Use Raoult's Law to calculate the expected vapor pressure of the solution if it were ideal. Raoult's Law states that the partial vapor pressure of each component in an ideal solution is equal to the vapor pressure of the pure component multiplied by its mole fraction in the solution.
Calculate the partial vapor pressure of methanol: \( P_{\text{methanol}} = X_{\text{methanol}} \times P^0_{\text{methanol}} \), where \( X_{\text{methanol}} = 1 - X_{\text{water}} \).
Calculate the partial vapor pressure of water: \( P_{\text{water}} = X_{\text{water}} \times P^0_{\text{water}} \).
Add the partial pressures of methanol and water to find the total vapor pressure of the ideal solution and compare it to the given total vapor pressure to determine if the solution is ideal. If the calculated total vapor pressure is different from the given total vapor pressure, the solution is not ideal, indicating that the solute-solvent interactions differ in strength from the solute-solute and solvent-solvent interactions.

Key Concepts

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

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, where the interactions between different molecules are similar to those between like molecules. Deviations from Raoult's Law can indicate non-ideal behavior, which is crucial for analyzing the vapor pressure of the methanol-water solution.
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Ideal vs. Non-Ideal Solutions

An ideal solution is one where the solute-solvent interactions are similar in strength to the solvent-solvent and solute-solute interactions, leading to predictable behavior according to Raoult's Law. Non-ideal solutions exhibit deviations from this behavior, often due to stronger or weaker interactions between solute and solvent molecules compared to their respective pure states. Understanding these differences helps in assessing the nature of the solution in question.
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Vapor Pressure and Intermolecular Forces

Vapor pressure is influenced by the strength of intermolecular forces within a liquid. Stronger intermolecular forces result in lower vapor pressures, as more energy is required for molecules to escape into the vapor phase. In the context of the methanol-water solution, comparing the observed vapor pressure to the expected value from Raoult's Law can provide insights into the relative strengths of solute-solvent interactions versus solvent-solvent and solute-solute interactions.
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Related Practice
Textbook Question

A solution contains 50.0 g of heptane (C7H16) and 50.0 g of octane (C8H18) at 25 °C. The vapor pressures of pure heptane and pure octane at 25 °C are 45.8 torr and 10.9 torr, respectively. Assuming ideal behavior, answer the following: d. Why is the composition of the vapor different from the composition of the solution?

Textbook Question

A solution contains a mixture of pentane and hexane at room temperature. The solution has a vapor pressure of 258 torr. Pure pentane and hexane have vapor pressures of 425 torr and 151 torr, respectively, at room temperature. What is the mole fraction composition of the mixture? (Assume ideal behavior.)

Textbook Question

A glucose solution contains 55.8 g of glucose (C6H12O6) in 455 g of water. Determine the freezing point and boiling point of the solution.