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Chapter 5: Problem 40

Why is moist air less dense than dry air?

Short Answer

Expert verified
Moist air is less dense than dry air because water vapor has a lower molecular mass than the major components of dry air, nitrogen, and oxygen.

Step by step solution

01

Understand the Composition of Air

Air is composed of various gases, primarily nitrogen (78%), oxygen (21%), and small amounts of other gases, including water vapor.
02

Analyze Molecular Mass

Dry air is mostly nitrogen (N_2) and oxygen (O_2), which have molecular masses of approximately 28 u and 32 u, respectively. Water vapor (H_2O), on the other hand, has a molecular mass of about 18 u.
03

Compare Molecular Masses

Since water vapor has a lower molecular mass than both nitrogen and oxygen, when water vapor replaces these gases in the air, the overall molecular mass of the air mixture decreases.
04

Density and Molecular Mass Relationship

Density is directly proportional to molecular mass for a given volume. Therefore, when air contains more water vapor (lower molecular mass), it becomes less dense compared to dry air.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

composition of air
Air is a mixture of gases surrounding our planet. The most abundant components are nitrogen and oxygen. To be specific, about 78% of air is nitrogen and 21% is oxygen. The remaining 1% includes various gases like argon, carbon dioxide, and traces of others.
However, another significant component of air is water vapor. The amount of water vapor in the air can vary greatly, from almost zero up to about 4% by volume. This variation in water vapor changes the overall composition of air, which impacts its properties such as density.
In dry air, the composition is fixed with negligible water vapor. In contrast, moist air includes a higher percentage of water vapor, which alters its overall makeup.
molecular mass
Molecular mass is a concept that plays a crucial role in understanding the density of air. It is the mass of a molecule, usually measured in atomic mass units (u).
Dry air is primarily made up of nitrogen (N₂) and oxygen (O₂), with molecular masses of around 28 u for nitrogen and 32 u for oxygen. When comparing these with water vapor (H₂O), which has a molecular mass of approximately 18 u, the difference becomes evident.
Because water vapor has a lower molecular mass than both nitrogen and oxygen, any increase in water vapor content in the air lowers the overall average molecular mass of the air mixture.
air density
Density is a measure of how much mass is packed into a given volume. For air, density depends directly on its molecular mass in a specific volume.
When water vapor, which has a lower molecular mass, replaces some of the nitrogen and oxygen in the air, the overall molecular mass of the air decreases. This decrease leads to a lower air density because the same volume of air now contains lighter molecules.
Hence, moist air, which contains a higher percentage of water vapor, is less dense than dry air. This can be illustrated by the proportional relationship:density = (mass/volume)Therefore, if the mass is reduced due to lighter water vapor replacing heavier nitrogen and oxygen, the density of air decreases.

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Most popular questions from this chapter

In the average adult male, the residual volume (RV) of the lungs, the volume of air remaining after a forced exhalation, is \(1200 \mathrm{~mL}\). (a) How many moles of air are present in the \(\mathrm{RV}\) at \(1.0 \mathrm{~atm}\) and \(37^{\circ} \mathrm{C} ?\) (b) How many molecules of gas are present under these conditions?

The air in a hot-air balloon at 744 torr is heated from \(17^{\circ} \mathrm{C}\) to \(60.0^{\circ} \mathrm{C}\). Assuming that the amount (mol) of air and the pressure remain constant, what is the density of the air at each temperature? (The average molar mass of air is \(28.8 \mathrm{~g} / \mathrm{mol} .)\)

An atmospheric chemist studying the pollutant \(\mathrm{SO}_{2}\) places a mixture of \(\mathrm{SO}_{2}\) and \(\mathrm{O}_{2}\) in a 2.00 -L container at \(800 . \mathrm{K}\) and \(1.90 \mathrm{~atm}\). When the reaction occurs, gaseous \(\mathrm{SO}_{3}\) forms, and the pressure falls to 1.65 atm. How many moles of \(\mathrm{SO}_{3}\) form?

When an evacuated 63.8 -mL glass bulb is filled with a gas at \(22^{\circ} \mathrm{C}\) and \(747 \mathrm{mmHg}\), the bulb gains \(0.103 \mathrm{~g}\) in mass. Is the gas \(\mathrm{N}_{2}, \mathrm{Ne},\) or \(\mathrm{Ar} ?\)

A mixture of gaseous disulfur difluoride, dinitrogen tetrafluoride, and sulfur tetrafluoride is placed in an effusion apparatus. (a) Rank the gases in order of increasing effusion rate. (b) Find the ratio of effusion rates of disulfur difluoride and dinitrogen tetrafluoride. (c) If gas \(\mathrm{X}\) is added, and it effuses at 0.935 times the rate of sulfur tetrafluoride, find the molar mass of X.
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