Air conditioners not only cool air, but dry it as well. A room in a home measures 6.0 m × 10.0 m × 2.2 m. If the outdoor temperature is 30 °C and the partial pressure of water in the air is 85% of the vapor pressure of water at this temperature, what mass of water must be removed from the air each time the volume of air in the room is cycled through the air conditioner? (Assume that all of the water must be removed from the air.) The vapor pressure for water at 30 °C is 31.8 torr.
Ch.12 - Liquids, Solids & Intermolecular Forces
Chapter 12, Problem 86
The vapor pressure of CCl3F at 300 K is 856 torr. If 11.5 g of CCl3F is enclosed in a 1.0-L container, will any liquid be present? If so, what mass of liquid?
Verified step by step guidance1
Calculate the number of moles of CCl_3F using its molar mass.
Use the ideal gas law, PV = nRT, to calculate the pressure exerted by the gas if all the CCl_3F were in the gaseous state.
Compare the calculated pressure with the given vapor pressure of CCl_3F at 300 K.
If the calculated pressure is greater than the vapor pressure, some liquid will be present. Calculate the moles of gas that would exert the vapor pressure using the ideal gas law.
Subtract the moles of gas from the total moles to find the moles of liquid, then convert this to mass using the molar mass.

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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 indicates the tendency of a substance to evaporate; higher vapor pressure means a greater tendency to vaporize. In this context, the vapor pressure of CCl3F at 300 K is 856 torr, which serves as a critical threshold for determining whether liquid will remain in the container.
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Ideal Gas Law
The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law helps in calculating the number of moles of CCl3F present in the container, which is essential for comparing it to the vapor pressure. Understanding this relationship allows us to determine if the conditions favor the presence of liquid or if all the substance will be in the gaseous state.
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Phase Equilibrium
Phase equilibrium occurs when the rates of evaporation and condensation of a substance are equal, resulting in a stable mixture of liquid and vapor. In this scenario, if the number of moles of CCl3F exceeds what can exist as vapor at the given vapor pressure, some of it will remain as liquid. Analyzing the mass of CCl3F and its vapor pressure helps in assessing whether liquid will be present in the container.
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Related Practice
Textbook Question
Textbook Question
A sample of steam with a mass of 0.552 g and at a temperature of 100 °C condenses into an insulated container holding 4.25 g of water at 5.0 °C. Assuming that no heat is lost to the surroundings, what is the final temperature of the mixture?
Textbook Question
Explain the observed trend in the melting points of the hydrogen halides.
HI -50.8 °C
HBr -88.5 °C
HCl -114.8 °C
HF -83.1 °C
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Textbook Question
Explain the observed trend in the boiling points of these compounds.
H2Te -2 °C
H2Se -41.5 °C
H2S -60.7 °C
H2O 100 °C
Textbook Question
The vapor pressure of water at 25 °C is 23.76 torr. If 1.25 g of water is enclosed in a 1.5-L container, will any liquid be present? If so, what mass of liquid?
