Question

Under the same conditions of temperature and pressure, why does \(1 \mathrm{~L}\) of moist air weigh less than \(1 \mathrm{~L}\) of dry air?

Short answer

Moist air is lighter because water vapor replaces heavier nitrogen and oxygen molecules, reducing its density.

Step-by-step solution

Understanding the Concept

To figure out why moist air weighs less than dry air under the same conditions, we need to understand the concept of gases and vapor pressures. Dry air is composed mostly of nitrogen and oxygen. Moist air has water vapor in addition to these gases.

Analyzing Molecular Weights

The molecular weight of water (H₂O) is approximately 18 ext{ g/mol}, oxygen (O₂) is 32 ext{ g/mol}, and nitrogen (N₂) is 28 ext{ g/mol}. Thus, water, being lighter, reduces the overall average molecular weight of the air mixture.

Quantifying the Mixture

When air is moist, some of the heavier nitrogen and oxygen molecules are replaced by lighter water molecules. Since water vapor has a lower molecular weight, the average density of the gas mixture decreases.

Calculating Density

Density is defined as mass per unit volume. With some molecules of water vapor replacing heavier nitrogen and oxygen molecules, the mass of 1 L of this mixture is less, leading to a lower density compared to dry air.

Key concepts

Molecular Weight

Molecular weight is the sum of the masses of all the atoms in a molecule. This is often expressed in units called grams per mole (g/mol). Each molecule has a specific molecular weight depending on the types and numbers of atoms it contains.
In the context of air, different gases have their own molecular weights. For dry air, the principal components are nitrogen and oxygen. Nitrogen, which constitutes nearly 78% of the atmosphere, has a molecular weight of 28 g/mol. Oxygen, making up about 21% of the atmosphere, is slightly heavier with a molecular weight of 32 g/mol. Water vapor, an additional component in moist air, is much lighter with a molecular weight of 18 g/mol.

• Nitrogen (N₂) = 28 g/mol
• Oxygen (O₂) = 32 g/mol
• Water (H₂O) = 18 g/mol

Because the molecular weight of water is lower, it impacts the overall molecular weight of the air when water vapor is present. This means that moist air, having lighter water molecules, has a lower average molecular weight than dry air.

Gas Mixture

Air is a mixture of different gases, primarily nitrogen and oxygen, with trace amounts of other gases, including carbon dioxide and argon. In the context of atmospheric science, understanding gas mixtures is crucial because air behaves differently based on its composition.
When water vapor enters this mix, it influences the density and molecular weight of the air. This is particularly important as it allows us to understand why moist air is lighter than dry air. As water vapor is mixed into the air, it displaces heavier nitrogen and oxygen molecules due to its lighter molecular weight of 18 g/mol.
Thus, the dynamic mixing of these gases alters the overall characteristics of air at any given moment. This dynamic can be visualized as "lighter" water molecules taking up space in the air, reducing the mass of that particular volume.

• Air is a mix of gases: mostly nitrogen and oxygen.
• Water vapor lightens the mix by displacing heavier gases.

This influence of water vapor is significant in meteorology, where the understanding of moist and dry air impacts weather predictions and climate studies.

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its liquid phase at a given temperature. It's a concept that illustrates how easily molecules evaporate from a liquid and enter the vapor phase.
In the context of moist air, vapor pressure is crucial because it determines how much water vapor the air can hold before it begins to condense. When air is humid, its vapor pressure increases because there is more water vapor present.
The presence of this water vapor affects the density and, consequently, the weight of the air. Since water molecules are less massive than nitrogen and oxygen molecules, the introduction of water vapor reduces the overall weight of the air.

• Vapor pressure helps measure how saturated the air is with water vapor.
• Higher vapor pressure indicates more water vapor presence.

This understanding of vapor pressure and the interaction of gases in a vapor-liquid equilibrium is vital for explaining why the weight of a given volume of air changes when it contains differing amounts of moisture.

Water Vapor

Water vapor is the gaseous state of water, present in the air around us. It is invisible, unlike liquid water, and forms through the process of evaporation.
As a crucial component of moist air, water vapor is key to understanding atmospheric processes. When air contains more water vapor, it is said to be humid. The introduction of water vapor into the air decreases its overall density and weight. This is why, under the same conditions, a liter of moist air is lighter than a liter of dry air.
Considering water's molecular weight (H₂O = 18 g/mol) is less than that of either nitrogen or oxygen, it is understandable why its presence lightens the air. When air is humid, water vapor replaces some of the heavier molecules, reducing the mass per volume.

• Water vapor is lighter than other air molecules.
• It affects air density and weight.

Understanding water vapor's role clarifies many atmospheric phenomena, such as weather changes, humidity levels, and atmospheric pressure variations.