Chapter 6: Gases

Introduction to Gases and Their Importance

Gases are a fundamental state of matter characterized by their ability to expand and fill any container. Understanding gas behavior is crucial in many scientific and practical contexts, such as scuba diving, atmospheric science, and industrial applications. The study of gases involves examining their properties, laws governing their behavior, and deviations from ideality.

Pressure: The Result of Molecular Collisions

Definition and Origin of Pressure

Pressure is defined as the force exerted per unit area by gas molecules as they collide with surfaces. The continuous motion and collisions of gas molecules create pressure within a container.

• Pressure Formula:

• Key Point: The greater the number of collisions or the force of collisions, the higher the pressure.

• Example: Increasing the number of gas molecules in a container increases the frequency of collisions, thus increasing pressure.

Pressure and Density

Pressure is closely related to the density of gas molecules. Higher density means more molecules per unit volume, resulting in more frequent collisions and higher pressure.

• Lower Pressure: Fewer molecules, less frequent collisions.

• Higher Pressure: More molecules, more frequent collisions.

Units and Measurement of Pressure

Common Units of Pressure

Pressure can be measured in several units, each with specific applications:

• Pascal (Pa): SI unit, 1 Pa = 1 N/m2

• Pounds per square inch (psi): Common in engineering

• Torr (mmHg): Originates from mercury barometer measurements

• Inches of mercury (in Hg): Used in meteorology

• Atmosphere (atm): Average pressure at sea level

Measuring Pressure: Barometers and Manometers

Pressure is measured using devices such as barometers and manometers:

• Mercury Barometer: Measures atmospheric pressure by the height of mercury in a glass tube.

• Manometer: Measures the pressure of enclosed gases by comparing the height difference in a U-shaped tube.

Variables Affecting Gas Pressure

Three Key Variables

The pressure of a gas in a container is affected by:

• Volume of the container (V): Decreasing volume increases pressure.

• Temperature of the gas (T): Increasing temperature increases pressure.

• Number of gas molecules (n): Increasing the number of molecules increases pressure.

The Gas Laws

Boyle's Law

Boyle's Law describes the relationship between pressure and volume at constant temperature and number of moles:

• Formula:

• Application: Compressing a balloon decreases its volume and increases its pressure.

Charles's Law

Charles's Law relates volume and temperature at constant pressure and number of moles. Temperature must be in Kelvin.

• Formula:

• Application: Heating a balloon causes it to expand.

Avogadro's Law

Avogadro's Law relates volume and number of moles at constant temperature and pressure.

• Formula:

• Application: Adding more gas to a balloon increases its volume.

Combined Gas Law

The combined gas law incorporates Boyle's, Charles's, and Avogadro's laws, relating pressure, volume, and temperature:

• Formula:

The Ideal Gas Law

Definition and Formula

The ideal gas law relates pressure, volume, number of moles, and temperature for an ideal gas:

• Formula:

• R: Ideal gas constant, L·atm/(mol·K)

• Application: Used to calculate unknown properties of gases under various conditions.

Applications: Molar Volume

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

Applications: Density and Molar Mass

The ideal gas law can be rearranged to calculate the density and molar mass of gases:

• Density Formula:

• Molar Mass Calculation: Combine mass measurement with ideal gas law to determine molar mass.

Mixtures of Gases and Partial Pressures

Dalton's Law of Partial Pressures

In a mixture of ideal gases, each gas exerts its own partial pressure independently. The total pressure is the sum of all partial pressures:

• Formula:

• Mole Fraction:

Collecting Gases Over Water

When gases are collected over water, the total pressure includes both the gas and water vapor. The partial pressure of water vapor depends on temperature.

• Formula:

Kinetic Molecular Theory

Postulates of Kinetic Molecular Theory

Kinetic molecular theory explains the behavior of gases based on molecular motion:

• Particle size is negligibly small.

• Average kinetic energy is proportional to temperature (in Kelvin).

• Collisions are completely elastic.

Mean Free Path, Diffusion, and Effusion

Definitions and Differences

Gas molecules move randomly, and their behavior can be described by:

• Mean Free Path: Average distance a molecule travels between collisions.

• Diffusion: Spread of gas molecules in response to a concentration gradient.

• Effusion: Escape of gas molecules through a small hole into a vacuum.

Real Gases: Deviations from Ideal Behavior

Effect of Particle Volume and Intermolecular Forces

Real gases deviate from ideal behavior at high pressures and low temperatures due to:

• Finite volume of gas particles: At high pressure, particle size becomes significant.

• Intermolecular forces: At low temperature, attractive forces lower the pressure.

The Van Der Waals Equation

The van der Waals equation modifies the ideal gas law to account for real gas behavior:

• Formula:

• a: Correction for intermolecular forces

• b: Correction for particle volume

Real Gases Deviate from Ideal Gas Behavior

The combined effects of particle volume and intermolecular forces cause real gases to deviate from ideal gas predictions, especially at high pressures and low temperatures.

Summary Table: Key Gas Laws and Equations