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?
Ch.13 - Properties of Solutions
Chapter 13, Problem 68
At 20 °C, the vapor pressure of benzene (C6H6) is 75 torr, and that of toluene (C7H8) is 22 torr. Assume that benzene and toluene form an ideal solution. (a) What is the composition in mole fraction of a solution that has a vapor pressure of 35 torr at 20 °C?
Verified step by step guidance1
Identify the given data: The vapor pressure of pure benzene (P°_benzene) is 75 torr, and the vapor pressure of pure toluene (P°_toluene) is 22 torr. The total vapor pressure of the solution (P_solution) is 35 torr.
Apply Raoult's Law for an ideal solution, which states that the partial vapor pressure of each component in the solution is equal to the vapor pressure of the pure component multiplied by its mole fraction in the solution. Mathematically, this is expressed as: P_benzene = x_benzene * P°_benzene and P_toluene = x_toluene * P°_toluene, where x_benzene and x_toluene are the mole fractions of benzene and toluene, respectively.
Since the solution is composed of only benzene and toluene, the sum of their mole fractions must equal 1: x_benzene + x_toluene = 1.
Express the total vapor pressure of the solution using the sum of the partial pressures: P_solution = P_benzene + P_toluene. Substitute the expressions from Raoult's Law: 35 torr = (x_benzene * 75 torr) + (x_toluene * 22 torr).
Use the equation x_benzene + x_toluene = 1 to express x_toluene in terms of x_benzene: x_toluene = 1 - x_benzene. Substitute this into the total vapor pressure equation and solve for x_benzene. Once x_benzene is found, use x_toluene = 1 - x_benzene to find x_toluene.
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. In this context, the vapor pressures of benzene and toluene indicate how much of each substance will evaporate into the air at 20 °C.
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Raoult's Law and Vapor Pressure
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 in the solution. For an ideal solution, the total vapor pressure can be calculated by summing the contributions of each component, which is determined by their respective mole fractions and pure component vapor pressures.
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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 problem, calculating the mole fractions of benzene and toluene is essential to determine the composition of the solution that results in a specific vapor pressure.
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Related Practice
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?
Textbook Question
At 20 °C, the vapor pressure of benzene (C6H6) is 75 torr, and that of toluene (C7H8) is 22 torr. Assume that benzene and toluene form an ideal solution. (b) What is the mole fraction of benzene in the vapor above the solution described in part (a)?
Textbook Question
(a) Does a 0.10 m aqueous solution of NaCl have a higher boiling point, a lower boiling point, or the same boiling point as a 0.10 m aqueous solution of C6H12O6?