Air conditioners not only cool air but dry it as well. A...

Air conditioners not only cool air but dry it as well. A room in a home measures $6.0 \mathrm{~m} \times 10.0 \mathrm{~m} \times 2.2 \mathrm{~m} .$ If the outdoor tem- perature is $30^{\circ} \mathrm{C}$ 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 vol- ume 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 $30^{\circ} \mathrm{C}$ is 31.8 torr.

Air conditioners not only cool air but dry it as well. A room in a home measures $6.0 \mathrm{~m} \times 10.0 \mathrm{~m} \times 2.2 \mathrm{~m} .$ If the outdoor tem-
perature is $30^{\circ} \mathrm{C}$ 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 vol-
ume 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 $30^{\circ} \mathrm{C}$ is 31.8 torr.

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Key Concepts

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its liquid at a given temperature. It is a crucial property in determining how much of the substance can exist as vapor, and it plays a significant role in phase change and humidity calculations.

Relative Humidity

Relative humidity is a measure of how much water vapor is in the air compared to the maximum amount of water vapor the air can hold at a given temperature, expressed as a percentage. It indicates the degree of saturation of the air and is essential for understanding condensation and drying processes.

Partial Pressure

Partial pressure represents the pressure contributed by a single component in a mixture of gases. In the context of water vapor in air, it quantifies the pressure due solely to the water molecules, and is used in conjunction with the total pressure to determine humidity and condensation phenomena.

Ideal Gas Law

The Ideal Gas Law is an equation of state that relates pressure, volume, temperature, and the number of moles of a gas (PV = nRT). It provides a fundamental framework for calculating the amount of gas present under certain conditions and is widely used in analyzing processes involving gaseous mixtures, such as the removal of water vapor.

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