Gases: Characteristics and Properties

Physical Properties of Gases

Gases exhibit unique physical properties that distinguish them from liquids and solids. 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 a homogeneous mixture.

Properties Defining the State of a Gas

State Variables

The state of a gas sample is defined by four key properties:

• Temperature (T)

• Pressure (P)

• Volume (V)

• Amount of gas (n), usually expressed in moles

Pressure is a fundamental property that requires precise definition.

Pressure and Its Measurement

Definition of Pressure

Pressure is the amount of force applied to a given area. Atmospheric pressure is the weight of air per unit area at Earth's surface.

Units of Pressure

Pressure can be measured in several units:

• Pascals (Pa): SI unit of pressure

• Bar: 1 bar = 100 kPa

• mm Hg or Torr: Based on the height difference in a mercury column

• Atmosphere (atm): 1 atm = 760 torr = 760 mm Hg = 101.325 kPa = 1.01325 bar

Manometer

A manometer is used to measure the difference in pressure between atmospheric pressure and the pressure of a gas in a vessel.

Standard Pressure

Normal atmospheric pressure at sea level is referred to as standard atmospheric pressure and is equal to:

• 1 atm

• 760 torr (760 mmHg)

• 101.325 kPa

Gas Laws

Boyle’s Law

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

• Mathematical Relationship:

• For two conditions:

A graph of volume versus pressure is not linear, but volume versus the inverse of pressure is linear.

Charles’s Law

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:

• For two conditions:

Gay-Lussac’s Law of Combining Volumes

At a given temperature and pressure, the volumes of gases that react are in small whole-number ratios. For example, two volumes of hydrogen gas and one volume of oxygen gas produce two volumes of water vapor.

• Stoichiometry: This law is foundational for stoichiometric calculations involving gases.

Avogadro’s Law

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.

• At STP: One mole of any gas occupies 22.4 L.

• Mathematical Relationship:

Ideal-Gas Equation

The ideal-gas equation combines the relationships from Boyle’s, Charles’s, and Avogadro’s laws:

• Equation:

• R: The ideal gas constant, with values depending on units used

Density and Molar Mass of Gases

Calculating Density

The density of a gas can be calculated using the ideal-gas equation:

• Where d is density, P is pressure, M is molar mass, R is the gas constant, and T is temperature.

Calculating Molar Mass

If the mass, volume, and temperature of a gas are known, its molar mass can be determined.

Volume and Chemical Reactions

Stoichiometry with Gases

Balanced chemical equations indicate the relative amounts of moles in a reaction. The ideal-gas equation allows for the calculation of gas volumes involved in reactions.

Mixtures of Gases

Dalton’s Law of Partial Pressures

Dalton’s Law states that the total pressure of a mixture of non-reacting gases equals the sum of the partial pressures each would exert if alone:

Mole Fraction

The mole fraction is the ratio of moles of a substance to the total moles in a mixture. Partial pressure is related to mole fraction:

• Where is the mole fraction of component

Kinetic-Molecular Theory

Explanation of Gas Laws

The kinetic-molecular theory explains the observed gas laws by describing the behavior of gas molecules.

Main Tenets of Kinetic-Molecular Theory

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

• The combined volume of all molecules is negligible compared 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.

Speed of Gas Molecules

Distribution of Molecular Speeds

Temperature is related to the average kinetic energy of gas molecules. Individual molecules have different speeds, characterized by:

• ump: Most probable speed

• uav: Average speed

• urms: Root-mean-square speed, related to average kinetic energy

Effect of Molecular Mass

At a given temperature, lighter gas molecules move faster than heavier ones. The root-mean-square speed is given by:

• Where M is molar mass in kg/mol

Effusion and Diffusion

Effusion

Effusion is the escape of gas molecules through a tiny hole into an evacuated space.

Diffusion

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 effuses or diffuses faster:

Real Gases and Deviations from Ideal Behavior

Behavior of Real Gases

Gases behave ideally only at high temperature and low pressure. At high pressure or low temperature, deviations from ideal behavior occur.

Causes of Deviations

Deviations arise because the assumptions of the kinetic-molecular theory break down:

• Gas molecules have finite volume.

• Intermolecular forces become significant.

van der Waals Equation

The van der Waals equation corrects the ideal-gas equation for real gases by accounting for molecular volume and intermolecular forces:

• Where a and b are van der Waals constants specific to each gas

Summary

This chapter provides a comprehensive overview of the properties, laws, and theoretical models of gases, including their behavior under ideal and real conditions. Understanding these concepts is essential for predicting and explaining the behavior of gases in chemical reactions and various applications.