Phase Equilibrium: Single Condensable Component Part 1 Contributions by: John L. Falconer & Will Medlin Department of Chemical and Biological Engineering University of Colorado Boulder, CO 80309-0424 Supported by the National Science Foundation

A container has liquid water (50% of the volume) and water vapor (50% of the volume) in equilibrium. It is sealed so the volume is fixed. When the temperature is raised, the ___________. liquid evaporates and the pressure increases vapor condenses and the pressure increases liquid and vapor both remain and pressure increases Vapor ANSWER: A. liquid evaporates and the pressure increases. Assume that the specific volume for the water in the container is above the critical volume. Water

Liquid water is in VLE at 1.2 bar with water vapor and air in a piston-cylinder. Half the air is removed through a selective membrane; no water leaves. Pressure and temperature are constant. What happens? Vapor/air 1.2 bar Air Water 1 kg All of the water vaporizes All of the water condenses Some of the water vaporizes Some of the water condenses ANSWER: D. Some of the water condenses. The partial pressure of water does not change, and the partial pressure of air must stay the same, so when the volume of the gas decreases less water can remain in the gas phase.

Liquid water is in VLE at 1.2 bar with water vapor and air in a piston-cylinder. All the air is removed through a selective membrane and half the water vapor is also removed. Pressure and temperature are constant. What happens? Vapor 1.2 bar Air Water 1 kg Water Vapor All of the water vaporizes All of the water condenses Some of the water vaporizes Some of the water condenses ANSWER: A. All of the water vaporizes.

Liquid water is in VLE at 1.2 bar with water vapor and air in a piston-cylinder. Half the air and half the water vapor are removed. Pressure and temperature are constant. What happens? Vapor 1.2 bar Air Water 1 kg Water Vapor All of the water vaporizes All of the water condenses Some of the water vaporizes Some of the water condenses No water vaporizes ANSWER: E. No water vaporizes.

Liquid water is in VLE at 1.2 bar with water vapor and air in a fixed-volume container. Half the air is removed through a selective membrane; no water leaves. Temperature is constant. What happens? All of the water vaporizes All of the water condenses Some of the water vaporizes Some of the water condenses No water changes phase Vapor 1.2 bar Air ANSWER: E. No water changes phase. The partial pressure of the water doesn’t change, so no water changes phase. Water

Liquid water is in equilibrium at 50°C with air in a piston-cylinder at 1 bar. The pressure is isothermally raised to 2 bar by pushing down on the piston. The amount of water in the vapor phase __________. Vapor Water increases decreases remains the same Not enough information ANSWER: B. decreases. Less vapor volume and same saturation pressure of water, so there is less water in the vapor.

Liquid water is in equilibrium at 50°C with air in a piston-cylinder at 1 bar. The pressure is isothermally raised to 2 bar by pushing down on the piston. The water partial pressure ________. Vapor Water increases decreases remains the same Not enough information ANSWER: C. remains the same. The saturation pressure doesn’t change because there’s no change in temperature.

A piston-cylinder at 45°C and 0 A piston-cylinder at 45°C and 0.5 bar contains hexane in vapor-liquid equilibrium. You push down on the piston until the vapor volume is half its original volume. The system is at constant temperature. What is the pressure at the new equilibrium? Hexane Vapor Liquid 0.25 bar 0.5 bar 1.0 bar Cannot be determined ANSWER B. 0.5 bar. Still at VLE, so saturation pressure remains the same.

Liquid water is in equilibrium at 50°C with air in a piston-cylinder at 1 bar. The temperature is lowered to 40°C. The partial pressure of the air ___________. Vapor Water 1 kg increases decreases remains the same Not enough information ANSWER: A. increases. Because the total pressure is fixed and partial pressure of water decreases with the change in temperature (saturation pressure lowers), the partial pressure of air increases.

Liquid water is in equilibrium at 50°C with air in a piston-cylinder at 1 bar. The temperature is lowered to 40°C. What happens to the water vapor? Vapor Water Some of it condenses All of it condenses None of it condenses More water evaporates 1 kg ANSWER: A. Some of it condenses. The saturation pressure decreases with the decrease in temperature, so some water must condense to lower the water partial pressure.

A piston and cylinder at 45oC and below atmospheric pressure contains 0.9 mol of n-hexane liquid and 0.1 mol of n-hexane vapor in equilibrium. Weights are removed from the piston to decrease the pressure to 99% of its original value at constant temperature. What happens? Vapor Liquid 1 kg Some of the liquid evaporates Most of the liquid evaporates All the liquid evaporates All the vapor condenses Some of the vapor condenses ANSWER: C. All the liquid evaporates Since the temperature is constant and the system was originally at the saturation pressure for 45oC, if the pressure is decreased the system try to reach equilibrium by getting back to its vapor pressure by evaporating liquid, but it will never get back to the original pressure since the pressure of the piston is lower than saturation pressure.

Liquid water is in equilibrium at 50°C with air in a fixed-volume container at 1 bar. The temperature is lowered to 40°C. The partial pressure of the air ___________. increases decreases remains the same Not enough information Vapor 1 bar ANSWER: A. Increases. The saturation pressure of water decreases so the partial pressure of air increases to keep total pressure constant. Water

Liquid water is equilibrium with air in a fixed volume container at 1 Liquid water is equilibrium with air in a fixed volume container at 1.2 bar. Half the air and half the water vapor are removed. Temperature is constant. What happens? All of the water vaporizes All of the water condenses Some of the water vaporizes Some of the water condenses No water changes phase Vapor 1.2 bar ANSWER: C. Some of the water vaporizes. Water vaporizes as the partial pressure becomes lower in order to maintain saturation pressure (because the temperature is constant). Water

Liquid water is equilibrium with air in a fixed volume container at 1 Liquid water is equilibrium with air in a fixed volume container at 1.2 bar. Half the air and half the water vapor are removed. Temperature is constant. The partial pressures of air and water __________. decrease increase remain the same Need more information. Vapor 1.2 bar ANSWER: C. remain the same. Water

Water is in VLE at 1. 2 bar in a fixed-volume container Water is in VLE at 1.2 bar in a fixed-volume container. You inject 5 cm3 of air into the system, but keep the temperature constant. What happens? All of the water vaporizes All of the water condenses Some of the water vaporizes Some of the water condenses No water changes phase Vapor 1.2 bar Air ANSWER: E. No water changes phase. The saturation pressure doesn’t change (constant temperature), and the partial pressure of the water doesn’t change, so no water changes phase. Just the air partial pressure increases to account for the overall increase in pressure. Water

Liquid water is in equilibrium at 50°C with air in a piston-cylinder at 1 bar. The temperature is raised to 60°C. What happens? Vapor Water Some liquid evaporates All liquid evaporates No liquid evaporates Some vapor condenses 1 kg ANSWER: A. Some liquid evaporates. When the temperature is increased, the saturation pressure of water also increases so some liquid water evaporates.

Liquid water is in equilibrium at 50°C with air in a piston-cylinder at 1 bar. The temperature is raised to 60°C. The partial pressure of the air ______________. Vapor Water 1 kg increases decreases remains the same Not enough information. ANSWER: B. decreases. Air partial pressure decreases because the water partial pressure increases with the increase in temperature (some water vaporizes as the saturation pressure increases with the increase in temperature).

The partial pressure of air ________. Liquid water is in equilibrium at 30°C with air in a piston-cylinder at 1 bar. The pressure is isothermally lowered to 0.85 bar by removing weights from the piston. The partial pressure of air ________. Vapor Water 1 kg increases decreases remains the same Not enough information. ANSWER: B. decreases. The saturation pressure of the water doesn’t change because the temperature is constant, so the air partial pressure decreases as the overall pressure decreases.

The partial pressure of water ________. Liquid water is in equilibrium at 30°C with air in a piston-cylinder at 1 bar. The pressure is isothermally lowered to 0.85 bar by removing weights from the piston. The partial pressure of water ________. Vapor Water 1 kg increases decreases remains the same Not enough information. ANSWER: C. remains the same. The partial pressure of water does not change because the temperature is constant and the saturation pressure doesn’t change.

Liquid water is in equilibrium at 30°C with air in a piston-cylinder at 1 bar. The pressure is isothermally lowered to 0.85 bar by removing weights from the piston. What happens? Vapor Water Some of the water vaporizes. All of the water vaporizes. No water vaporizes. Not enough information. 1 kg ANSWER: A. Some of the water vaporizes. The partial pressure of H2O stays the same, T stays same, V must increase to lower system P, therefore number of moles of water in vapor phase must go up.

What happens to the injected water? A piston-cylinder contains liquid water in equilibrium with air at 1 bar and 40°C. You inject water vapor into the system and let it equilibrate to 40°C. What happens to the injected water? All of it condenses All of it stays in the vapor phase Some of it condenses 1 kg Water vapor Vapor ANSWER: A. All of it condenses. The temperature doesn’t change, so the saturation pressure stays the same and the all the added water vapor condenses to return to the saturation pressure by the time the system equilibrates. Water

What happens to the injected water? A piston-cylinder contains liquid water in equilibrium with air at 1 bar and 40°C. You inject water liquid water into the system and let it equilibrate to 40°C. What happens to the injected water? All of it vaporizes All of it stays in the liquid phase Some of it vaporizes 1 kg Water Vapor ANSWER: B. All of it stays in the liquid phase. The temperature doesn’t change, so the saturation pressure stays the same and the all the added liquid water stays as liquid. Water

Water is in VLE at 1.2 bar in a piston-cylinder. You inject 5 cm3 of air into the system, but keep pressure and temperature constant. What happens? All of the water vaporizes All of the water condenses Some of the water vaporizes Some of the water condenses 1 kg Air Vapor ANSWER: A. All the water vaporizes. The total pressure is 1.2 bar and the saturation pressure of water is 1.2 bar so once air is present the partial pressure of water is less than 1.2 bar so no liquid water will be present at equilibrium. Water

Water is in VLE at 1. 2 bar in a piston-cylinder Water is in VLE at 1.2 bar in a piston-cylinder. The system contains 3 mol of liquid water. You inject 5 cm3 of air into the system at the same temperature. The system is adiabatic. What happens? All of the water vaporizes All of the water condenses Some of the water vaporizes Some of the water condenses Air Vapor ANSWER: C. Some of the water vaporizes. As water vaporizes, the temperature decreases as energy for heat of vaporization is supplied from the sensible heat. As the temperature decreases, the saturation pressure of water decreases, so not all of the water will vaporize, just some will. Water 3.0 mol

Water is in VLE at 1. 2 bar in a piston-cylinder Water is in VLE at 1.2 bar in a piston-cylinder. The system contains 3 mol of liquid water. You inject 5 cm3 of air into the system at the same temperature. The system is adiabatic. The system temperature ____________. increases decreases remains the same Air ANSWER: B. decreases. Water evaporates to try to maintain vapor-liquid equilibrium. Because the system is adiabatic, the temperature decreases as energy for heat of vaporization is supplied from the sensible heat. Vapor Water 3.0 mol

An insulated container of water is in VLE at 250°C. When the valve is opened at the top of the container, the pressure __________ and the ___________? stays the same; liquid level drops at constant temperature decreases; temperature drops decreases; temperature stays the same stays the same; temperature drops. Vapor ANSWER: B. decreases; temperature drops. Evaporative cooling lowers the temperature and thus the saturation pressure. Energy for evaporating comes from sensible heat since the container is insulated. Water

An isothermal container of water is in VLE at 250°C. When the valve at the top of the container is opened to the atmosphere, the pressure __________ and the ___________? stays the same; liquid level drops at constant temperature decreases; temperature drops decreases; temperature stays the same stays the same; temperature drops. Vapor ANSWER: A. stays the same; liquid level drops at constant temperature. Since the temperature is constant, the saturation pressure constant. Water

Liquid water is in VLE with air at 1. 2 bar in a piston-cylinder Liquid water is in VLE with air at 1.2 bar in a piston-cylinder. The vapor volume is 3 cm3. You inject 1 cm3 of air, but keep pressure and temperature constant. The mole fraction of air in the gas ________. increases decreases remains the same 1 kg Air ANSWER: C. remains the same. Partial pressure of water remains same (the saturation pressure remains the same because the temperature stays constant) so partial pressure of air remains the same because total pressure constant. Vapor Water 3.0 mol

A fixed volume tank contains water in VLE A fixed volume tank contains water in VLE. One mole of air is added to the system. All gases are ideal. The partial pressure of air ___________. increases decreases stays the same Air + H2O Vapor Liquid 1 mol Air ANSWER: A. increases. There are more moles of air in the same volume, which results in a higher partial pressure of air.

A fixed-volume tank contains liquid water and water vapor in VLE A fixed-volume tank contains liquid water and water vapor in VLE. One mole of air is added to the system. All gases are ideal. The partial pressure of water ____________. Air + H2O Vapor Liquid 1 mol Air increases decreases stays the same ANSWER: C. stays the same. Ideal gases, the air does not change the water pressure.

This piston-cylinder contains air and water vapor (10% relative humidity). Which is the correct plot of partial pressure of water versus total pressure, as the total pressure on the gas increases? Air & Water Vapor (10% RH) Ptotal PH2O Ptotal PH2O A B ANSWER: A. As total pressure increases, the partial pressure of water increases until the saturation pressure is reached. The water partial pressure then remains constant. Ptotal PH2O Ptotal PH2O C D

This piston-cylinder contains air and water vapor (50% relative humidity). Which is the correct plot of partial pressure of water versus temperature, as the temperature decreases? Air & Water Vapor (50% RH) 1 kg PH2O PH2O A B T T ANSWER: A Once condensation occurs, the pressure continues to drop exponentially as the temperature drops. PH2O PH2O C D T T

A 500 cm3 fixed-volume container has air at 100°C and 1 bar A 500 cm3 fixed-volume container has air at 100°C and 1 bar. You inject 2 cm3 of liquid water that is at 25°C and let the system reach equilibrium at 100°C. What is the approximate final pressure? 1 bar 1.004 bar 1.05 bar 2 bar None of the above Air 100°C 1 bar Water 25°C ANSWER: D. The water will vaporize until it reaches VLE at 100°C, so 1 bar partial pressure water, so total 2 bar pressure.