Gases: Physical Characteristics and Properties

Physical Characteristics of Gases

Gases exhibit unique physical properties that distinguish them from solids and liquids. They are primarily composed of nonmetallic elements with simple formulas and low molar masses.

• Expansion: Gases expand to fill their containers.

• Compressibility: Gases are highly compressible.

• Low Density: Gases have extremely low densities compared to solids and liquids.

• Homogeneous Mixtures: Two or more gases can form homogeneous mixtures.

Common Gases at Room Temperature

Several compounds exist as gases at room temperature, each with distinct properties.

Pressure and Measurement

Definition of Pressure

Pressure is defined as the amount of force applied to a given area. All gases exert pressure on surfaces they contact, and atmospheric pressure is the weight of air per unit area.

• Formula:

Units of Pressure

Pressure can be measured in various units, each with specific applications.

Measurement of Pressure: Barometer and Manometer

Pressure is commonly measured using barometers and manometers. A barometer measures atmospheric pressure, while a manometer measures the pressure of a gas in a vessel relative to atmospheric pressure.

• Manometer Equation:

Standard Pressure

Standard atmospheric pressure at sea level is defined as:

• 1 atm = 760 torr = 760 mmHg = 101.325 kPa = 1.01325 bar

The Gas Laws

Variables Defining Gas State

Four variables are required to describe the state of a gas:

• Temperature (T)

• Pressure (P)

• Volume (V)

• Amount of gas (n, in moles)

The relationships between these variables are described by the gas laws.

Boyle’s Law: Pressure–Volume Relationship

Boyle’s Law states that the volume of a fixed quantity of gas at constant temperature is inversely proportional to the pressure.

• Mathematical Relationship:

• Two Conditions:

• A graph of V versus P is not linear, but V versus is linear.

Charles’s Law: Volume–Temperature Relationship

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

• Mathematical Relationship:

• Two Conditions:

• A graph of V versus T is linear.

Avogadro’s Law: Volume–Amount 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 the gas.

• Mathematical Relationship:

• At STP, one mole of any gas occupies 22.4 L.

• Two Conditions:

The Ideal Gas Equation

Derivation and Formula

The ideal gas equation combines Boyle’s, Charles’s, and Avogadro’s laws:

• Formula:

• R is the ideal gas constant.

Values of the Gas Constant R

Standard temperature and pressure (STP) is 0°C and 1 atm. At STP, one mole of an ideal gas occupies 22.4 L.

Using the Ideal Gas Equation

To solve gas law problems:

1. Tabulate the information.

2. Convert to consistent units.

3. Pick the correct equation and solve for the unknown.

4. Use dimensional analysis.

Gas Densities and Molar Mass

Calculating Density and Molar Mass

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

• Density Formula:

• Molar Mass Formula:

To calculate density, molecular mass, pressure, and temperature are needed. To calculate molar mass, mass, volume, and temperature are required.

Volume of Gases in Chemical Reactions

Stoichiometry with Gases

Balanced chemical equations indicate the relative amounts of moles in a reaction. Unknowns can be determined using stoichiometry:

• If given volume, use the stoichiometric ratio to determine the unknown.

• If given pressure, volume, and temperature:

  • Solve for n using

  • Multiply by the mole ratio

  • Convert to grams or other desired unit

Gas Mixtures and Partial Pressures

Dalton’s Law of Partial Pressures

When two non-reacting gases are combined, each behaves as if it is alone in the container. Dalton’s Law states that the total pressure is the sum of the partial pressures of each gas.

• Formula:

• For n moles of gas:

Mole Fraction and Partial Pressure

The mole fraction (χ) is used to determine the partial pressure of a component in a mixture.

• Mole Fraction:

• Partial Pressure:

Kinetic-Molecular Theory of Gases

Fundamental Statements

The kinetic-molecular theory explains the behavior of gases and the gas laws.

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

• The combined volume of all molecules is negligible relative to the container volume.

• Attractive and repulsive forces between molecules are negligible.

• Energy can be transferred during collisions, but average kinetic energy remains constant if temperature is constant.

• Average kinetic energy is proportional to absolute temperature; at the same temperature, all gases have equal average kinetic energy.

Distribution of Molecular Speeds

Temperature relates to the average kinetic energy, but individual molecules have different speeds. Three speeds are defined:

• Most probable speed (ump)

• Average speed (uav)

• Root-mean-square speed (urms)

Application to Gas Laws

Kinetic-molecular theory explains gas law observations:

• Increasing volume at constant temperature decreases pressure (fewer collisions).

• Increasing temperature at constant volume increases pressure (more forceful collisions).

Molecular Speeds, Effusion, and Diffusion

Root-Mean-Square Speed

At a given temperature, the average kinetic energy is the same for all gases. The root-mean-square speed is given by:

• Formula:

Effusion and Diffusion

Effusion is the escape of gas molecules through a tiny hole into an evacuated space. Diffusion is the spread of one substance throughout a space or another substance.

Graham’s Law

Graham’s Law relates the molar mass of two gases to their rates of effusion or diffusion. The lighter gas always moves faster.

• Formula:

Real Gases: Deviations from Ideal Behavior

Deviations from Ideal Gas Law

Gases behave ideally only at high temperature and low pressure. At high pressure or low temperature, the assumptions of the kinetic-molecular theory break down.

• Molecules occupy volume.

• Attractive forces become significant.

Van der Waals Equation

The van der Waals equation corrects for nonideal behavior by adjusting for molecular volume and intermolecular forces.

• Formula:

Example: The van der Waals equation is used to calculate the behavior of real gases under nonideal conditions, such as high pressure or low temperature.