Gases: Properties, Laws, and Applications

Introduction to Gases

Gases are one of the fundamental states of matter, characterized by their ability to expand and fill any container. Their behavior is governed by several physical laws and can be described both macroscopically and microscopically.

• Macroscopic properties: Pressure (P), Volume (V), Temperature (T), and Amount in moles (n).

• Microscopic properties: Position, velocity, and mass of individual molecules.

Units and Measurement of Pressure

Pressure is a key property of gases, defined as the force exerted per unit area by gas molecules colliding with surfaces.

• Definition:

• Common units:

  • Pascal (Pa):

  • Kilopascal (kPa):

  • Bar:

  • Atmosphere (atm):

  • Millimeter of mercury (mmHg):

  • Torr:

  • Pounds per square inch (psi):

• Metric prefixes: μ (micro), m (milli), k (kilo), M (mega), G (giga).

Measuring Gas Pressure

Gas pressure can be measured using devices such as barometers and manometers.

• Barometer: Measures atmospheric pressure using a column of mercury. The height of the mercury column is proportional to the atmospheric pressure.

• Manometer: Measures the pressure of a gas sample by comparing it to atmospheric pressure, often using a liquid column.

• Equation for liquid column pressure: where is the height, is the density of the liquid, and is the acceleration due to gravity.

Gas Laws

The behavior of gases is described by several empirical laws:

• Boyle's Law: At constant temperature and amount, pressure and volume are inversely proportional.

• Charles's Law: At constant pressure and amount, volume and temperature are directly proportional.

• Avogadro's Law: At constant temperature and pressure, volume is directly proportional to the number of moles.

• Combined Gas Law: Combines Boyle's, Charles's, and Avogadro's laws.

• Ideal Gas Law: Relates all four variables. where is the gas constant (varies with units, e.g., or ).

Applications of Gas Laws

Gas laws are used to solve problems involving changes in pressure, volume, temperature, and amount of gas. They are also essential in stoichiometry involving gases.

• Calculating molar mass:

• Calculating gas density:

• Standard molar volume: At STP (273 K, 1 atm), $1 L.

Mixtures of Gases and Partial Pressures

Gases in a mixture behave independently, and the total pressure is the sum of the partial pressures of each component (Dalton's Law).

• Dalton's Law of Partial Pressures:

• Mole fraction:

• Partial pressure:

Gases Collected Over Water

When gases are collected over water, the total pressure includes both the gas and water vapor. The partial pressure of the gas is found by subtracting the vapor pressure of water.

• Equation:

Kinetic Molecular Theory (KMT)

KMT explains the behavior of gases at the molecular level.

• Gases consist of tiny particles in constant, random motion.

• The volume of gas particles is negligible compared to the container.

• Collisions between particles and with container walls are elastic.

• The average kinetic energy is proportional to temperature in Kelvin.

Molecular Velocities and Kinetic Energy

The speed of gas molecules depends on temperature and molar mass.

• Average kinetic energy per molecule:

• Root mean square velocity: where is the molar mass in kg/mol.

• Higher temperature or lower molar mass leads to higher molecular speeds.

Diffusion and Effusion

Gases spread out (diffusion) and escape through small holes (effusion). The rates depend on molecular speed and molar mass.

• Graham's Law of Effusion:

• Lower molar mass gases effuse and diffuse faster.

Real Gases and Deviations from Ideality

Real gases deviate from ideal behavior at high pressures and low temperatures due to finite molecular volume and intermolecular forces.

• Van der Waals Equation: where corrects for intermolecular forces and for molecular volume.

• At low pressure and high temperature, gases behave more ideally.

Summary Table: Common Units of Pressure

Examples of Gas Applications

• Oxygen generation:

• Airbag deployment:

Practice Problems

• Convert between pressure units.

• Calculate the pressure exerted by a given mass over a specific area.

• Apply Boyle's, Charles's, and Avogadro's laws to solve for unknown variables.

• Use Dalton's Law to find partial pressures in gas mixtures.

• Calculate effusion rates using Graham's Law.

• Apply the van der Waals equation to real gases.

Additional info: These notes expand on the provided slides and text, filling in missing definitions, equations, and context for a comprehensive study guide suitable for General Chemistry students.