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Ch.13 - Properties of Solutions
All textbooksBrown 14th EditionCh.13 - Properties of SolutionsProblem 66
Chapter 13, Problem 66

(b) Calculate the mass of ethylene glycol (C2H6O2) that must be added to 1.00 kg of ethanol (C2H5OH) to reduce its vapor pressure by 10.0 torr at 35 °C. The vapor pressure of pure ethanol at 35 °C is 1.00 x 10^2 torr.

Verified step by step guidance
1
Step 1: Use Raoult's Law to determine the change in vapor pressure. Raoult's Law states that the vapor pressure of a solvent in a solution (P_solution) is equal to the mole fraction of the solvent (X_solvent) times the vapor pressure of the pure solvent (P_pure). The change in vapor pressure (ΔP) is given by ΔP = P_pure - P_solution.
Step 2: Calculate the vapor pressure of the ethanol solution. Since the vapor pressure is reduced by 10.0 torr, the vapor pressure of the solution is P_solution = P_pure - 10.0 torr, where P_pure is 1.00 x 10^2 torr.
Step 3: Determine the mole fraction of ethanol in the solution. Rearrange Raoult's Law to find the mole fraction: X_ethanol = P_solution / P_pure.
Step 4: Calculate the moles of ethanol. Use the molar mass of ethanol (C2H5OH), which is approximately 46.08 g/mol, to convert the mass of ethanol (1.00 kg) to moles.
Step 5: Use the mole fraction to find the moles of ethylene glycol needed. The mole fraction of ethanol is related to the moles of ethanol and ethylene glycol by X_ethanol = moles_ethanol / (moles_ethanol + moles_ethylene_glycol). Solve for moles_ethylene_glycol and then convert to mass using the molar mass of ethylene glycol (C2H6O2), which is approximately 62.07 g/mol.

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 directly proportional to the mole fraction of the solvent present. This principle is crucial for understanding how the addition of a solute, like ethylene glycol, affects the vapor pressure of a solvent, such as ethanol. By applying this law, one can calculate the change in vapor pressure when a non-volatile solute is added.
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Raoult's Law and Vapor Pressure

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 this context, calculating the mole fraction of ethanol and ethylene glycol is essential to determine how much ethylene glycol needs to be added to achieve the desired reduction in vapor pressure.
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Colligative Properties

Colligative properties are properties of solutions that depend on the number of solute particles in a given amount of solvent, rather than the identity of the solute. Vapor pressure lowering is one such property, and understanding it helps in predicting how the addition of ethylene glycol will affect the vapor pressure of ethanol, allowing for the calculation of the required mass of solute.
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Related Practice
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?
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?

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?