Chapter 11: Gases – Properties, Laws, and Applications

Gases

Gas Pressure and Molecular Motion

Gases are composed of molecules that are constantly in motion. As these molecules move and collide with surfaces, they exert a force known as pressure. Pressure is defined as the force per unit area exerted by gas molecules on the surfaces they contact.

• Pressure: The result of gas molecules striking surfaces.

• Formula: $\text{Pressure} = \frac{\text{Force}}{\text{Area}}$

• Gas flow: Gases move from areas of high pressure to low pressure, pushing objects in their path.

Example: When drinking through a straw, the pressure difference between the inside and outside of the straw causes liquid to move.

Atmospheric Pressure

The atmosphere exerts pressure on all objects it contacts. At sea level, atmospheric pressure averages 14.7 psi (pounds per square inch), equivalent to 1 atm (atmosphere). Most atmospheric mass is concentrated within the first 10 miles above Earth's surface.

• Atmospheric pressure: 14.7 psi = 1 atm = 760 mmHg

• Pressure equivalence: This is the same as the pressure exerted by a 10.3 m column of water.

Properties of Gases

Gases exhibit several unique properties due to the freedom of their molecules:

• Expansion: Gases expand to fill their container.

• Shape: Gases take the shape of their container.

• Low density: Gases have much lower density than solids or liquids due to large spaces between molecules.

• Compressibility: Gases can be compressed because of the empty space between molecules.

• Homogeneous mixtures: Mixtures of gases are always homogeneous.

Kinetic Molecular Theory

The kinetic molecular theory explains the behavior of gases:

• Gas particles are in constant motion.

• Attractions between particles are negligible.

• Collisions are elastic; particles bounce off without sticking.

• There is a lot of empty space between particles compared to their size.

• The average kinetic energy of particles is directly proportional to the Kelvin temperature.

Indefinite Shape and Volume

Because gas molecules have enough kinetic energy to overcome attractions, they spread out and fill the container, taking both its shape and volume.

Compressibility of Gases

Gases are highly compressible due to the large amount of unoccupied space between molecules. When pressure is applied, gas molecules can be squeezed closer together.

Low Density of Gases

Gases have low density because of the large spaces between molecules. For example, converting the water in a can of soda to steam would fill the space of 1700 cans.

Factors Affecting Gas Pressure

The pressure of a gas depends on:

• Number of gas particles in a given volume

• Volume of the container

• Average speed of gas particles

Measuring Air Pressure

Air pressure is measured using a barometer, which relies on a column of mercury supported by atmospheric pressure. The force of air on the mercury is balanced by gravity pulling down on the mercury column.

Pressure Imbalance and the Ear

Rapid changes in atmospheric pressure can cause discomfort or "popping" in the ears due to pressure imbalances across the eardrum.

Boyle’s Law: Pressure and Volume Relationship

Boyle’s Law states that the pressure of a gas is inversely proportional to its volume, provided temperature and amount of gas are constant.

• Equation: $P \times V = \text{constant}$

• Equation (two states): $P_1 \times V_1 = P_2 \times V_2$

• As pressure increases, volume decreases by the same factor.

Example: If pressure on a gas is doubled, its volume is halved (at constant temperature and amount).

Boyle’s Law and Breathing

Boyle’s Law explains the mechanics of breathing:

• Inhalation: Chest cavity expands, volume increases, pressure drops, air flows in.

• Exhalation: Chest cavity contracts, volume decreases, pressure rises, air flows out.

Charles’ Law: Volume and Temperature Relationship

Charles’ Law states that the volume of a gas is directly proportional to its temperature (in Kelvin), at constant pressure and amount of gas.

• Equation: $V = \text{constant} \times T$

• Graph of volume vs. temperature is a straight line.

• Kelvin temperature: $T_{\text{Kelvin}} = T_{\text{Celsius}} + 273$

Absolute Zero

Absolute zero is the theoretical temperature at which a gas would have zero volume and no pressure. It is calculated by extrapolating the volume vs. temperature graph.

• 0 K = -273.15 °C = -459 °F

• Absolute zero is unattainable, but all gas law calculations use the Kelvin scale.

Avogadro’s Law: Volume and Number of Molecules

Avogadro’s Law states that the volume of a gas is directly proportional to the number of gas molecules (moles), at constant pressure and temperature.

• Equation: $V = \text{constant} \times n$

• Equal volumes of gases contain equal numbers of molecules.

• 1 mole of gas at STP occupies 22.4 L.

Ideal Gas Law

The Ideal Gas Law combines Boyle’s, Charles’, and Avogadro’s laws into a single equation:

• Equation: $P V = n R T$

• R (Gas Constant): 0.0821 L·atm/(mol·K)

• Use this law for gases at one condition; use the Combined Gas Law for changing conditions.

Molar Mass of a Gas

Chemists can determine the molar mass of an unknown gas by measuring its mass, volume, temperature, and pressure, then applying the Ideal Gas Law.

• Equation: $\text{Molar Mass} = \frac{\text{mass}}{\text{moles}}$

Ideal vs. Real Gases

Real gases deviate from ideal behavior at high pressure or low temperature. The Ideal Gas Law assumes no attractions between molecules and negligible molecular volume, which is not valid under these conditions.

Mixtures of Gases and Partial Pressure

In a mixture, each gas behaves independently and exerts its own partial pressure. The total pressure is the sum of all partial pressures (Dalton’s Law).

• Equation: $P_{\text{total}} = P_{\text{gas A}} + P_{\text{gas B}} + P_{\text{gas C}} + \ldots$

• Partial pressure is calculated by multiplying the total pressure by the fractional composition of the gas.

Partial Pressure in Biological and Environmental Contexts

Partial pressure of oxygen is critical for human health. Low partial pressures can cause hypoxia, while high partial pressures can cause oxygen toxicity. Deep-sea divers must manage partial pressures to avoid nitrogen narcosis and the bends.

Collecting Gases and Vapor Pressure

When gases are collected over water, water vapor mixes with the gas. The partial pressure of water vapor depends on temperature and must be subtracted to find the pressure of the dry gas.

Molar Volume of Gases

At STP, 1 mole of any ideal gas occupies 22.4 L. This molar volume is used as a conversion factor in stoichiometric calculations involving gases.

Stoichiometry of Gas Reactions

Gas laws are combined with reaction stoichiometry to calculate volumes, masses, or moles of gases involved in chemical reactions. The Ideal Gas Law allows conversion between volume and moles, facilitating stoichiometric calculations.

• Always specify pressure and temperature when reporting gas volumes.

• Use molar volume (22.4 L at STP) for conversions at standard conditions.