Study Notes: Properties and Laws of Gases (General Chemistry, Chapter 10)

Gases: Properties, Laws, and Theories

Introduction to Gases

Gases are one of the fundamental states of matter, characterized by their ability to expand and fill any container, high compressibility, and low density compared to liquids and solids. The study of gases is essential in understanding atmospheric phenomena, chemical reactions, and industrial processes.

• Atmospheric Composition: Air is a mixture of gases, primarily nitrogen (N2) and oxygen (O2).

• Key Properties: Volume, composition, density, temperature, and pressure are used to describe gases.

Characteristics of Gases

• Compressibility: Gases can be compressed much more than liquids or solids due to the large distances between molecules.

• Low Density: Gases have much lower densities than liquids and solids.

• Expansion: Gases expand to fill the volume of their container.

• Mixing: Multiple gases mix to form homogeneous mixtures (e.g., air).

Example: The air in a room can be described by its volume (e.g., 1 L, 5 mL), composition (N2, O2, CO2), density, temperature (e.g., steam at 100°C), and pressure.

Pressure

Definition and Units

Pressure is the force exerted by gas molecules per unit area on the surfaces they contact.

• Formula: $P = \frac{F}{A}$, where P is pressure, F is force, and A is area.

• Units: Pascal (Pa), Bar, Atmosphere (atm), Torr, mm Hg.

• 1 Pa = 1 N/m2; 1 bar = 105 Pa = 100 kPa; 1 atm = 101325 Pa = 760 mm Hg = 760 Torr = 1.01325 bar.

Example: A basketball, syringe, or insect exerts pressure on a surface due to the force distributed over an area.

Origin of Pressure in Gases

• Pressure results from gas molecules colliding with the walls of their container.

• More molecules or higher speed increases pressure.

• Smaller volume or higher temperature also increases pressure.

Measurement of Pressure

• Barometer: Invented by Torricelli, measures atmospheric pressure using a column of mercury (Hg).

• Formula: $P = h \rho g$, where h is height of mercury column, \rho is density of mercury, g is acceleration due to gravity.

• Standard atmospheric pressure: 760 mm Hg (Torr), 101325 Pa, 1 atm.

Example: If water is used instead of mercury, the column height changes due to lower density.

Gas Laws

Boyle's Law (Pressure-Volume Relationship)

Boyle's Law describes how the volume of a fixed amount of gas varies inversely with pressure at constant temperature.

• Formula: $V \propto \frac{1}{P}$ or $PV = \text{constant}$

• As pressure increases, volume decreases (and vice versa).

Example: Balloons shrink at higher pressure and expand at lower pressure.

Charles's Law (Temperature-Volume Relationship)

Charles's Law states that the volume of a fixed amount of gas at constant pressure is directly proportional to its absolute temperature.

• Formula: $V \propto T$

• Absolute temperature is measured in Kelvin: $T(K) = T(°C) + 273.15$

• At 0 K (absolute zero), volume theoretically becomes zero.

Example: Heating a balloon at constant pressure causes it to expand.

Avogadro's Law (Quantity-Volume Relationship)

Avogadro's Law states that the volume of a gas at constant temperature and pressure is directly proportional to the number of moles of gas.

• Formula: $V \propto n$

• Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.

Example: 1 mole of any ideal gas occupies 22.414 L at STP.

Ideal Gas Equation

The ideal gas law combines Boyle's, Charles's, and Avogadro's laws into a single equation describing the state of an ideal gas.

• Formula: $PV = nRT$

• R: Universal gas constant (varies by units, e.g., 0.08206 L·atm/mol·K, 8.314 J/mol·K)

• Standard Temperature and Pressure (STP): 1 atm, 0°C (273.15 K)

Gas Density and Molar Mass

The ideal gas law can be rearranged to calculate the density and molar mass of a gas.

• Formula: $d = \frac{m}{V} = \frac{PM}{RT}$

• Density increases with pressure and molar mass, decreases with temperature.

Example: Hot-air and helium balloons rise because the density of the gas inside is less than the surrounding air.

Kinetic-Molecular Theory of Gases

Postulates of the Theory

The kinetic-molecular theory explains the behavior of gases based on the motion of their molecules.

• Gases consist of large numbers of molecules in continuous, random motion.

• The volume occupied by gas molecules is negligible compared to the container.

• Intermolecular forces (attractive and repulsive) are negligible.

• Energy is transferred during collisions, but total energy is conserved.

Kinetic Energy and Temperature

The average kinetic energy of gas molecules is proportional to the absolute temperature.

• Formula: $\text{Average K.E.} = \frac{3}{2}kT$

• k: Boltzmann constant ($1.381 \times 10^{-23}$ J·K-1)

• At a given temperature, all gases have the same average kinetic energy, regardless of molecular mass.

Example: Hydrogen molecules move faster than oxygen molecules at the same temperature due to lower mass.

Summary Table: Gas Laws

Law	Relationship	Formula	Constant Parameters
Boyle's Law	Pressure vs. Volume	$PV = \text{constant}$	n, T
Charles's Law	Volume vs. Temperature	$V \propto T$	n, P
Avogadro's Law	Volume vs. Moles	$V \propto n$	P, T
Ideal Gas Law	State Equation	$PV = nRT$	None

Additional info:

• Absolute zero (0 K) is the theoretical temperature at which molecular motion ceases.

• Barometers and manometers are used to measure atmospheric and gas pressures, respectively.

• Gas laws are foundational for understanding chemical reactions, stoichiometry, and thermodynamics in chemistry.