Kinetic Theory of Gases

Introduction

The kinetic theory of gases provides a molecular-level explanation for the macroscopic properties of gases. It is based on a set of assumptions about the nature and behavior of gas particles, which help explain phenomena such as pressure, temperature, and volume.

Properties of States of Matter

Comparison of Gases, Liquids, and Solids

The three classical states of matter—gases, liquids, and solids—differ in their physical properties due to the arrangement and movement of their particles.

Volume

Definition and Units

Volume is the quantity used to describe the space that a substance occupies. It is a fundamental measurement in chemistry, especially for gases.

• Common units of volume: Litre (L), millilitre (mL), cubic metre (m3), cubic centimetre (cm3).

• 1 L = 1000 mL

• 1 m3 = 1,000,000 cm3 = 1000 L

• Volumes of gas are typically measured in mL or L; very large volumes are measured in m3.

Pressure

Definition and Units

Pressure is defined as the force exerted per unit area. In the context of gases, it results from collisions of gas particles with the walls of their container.

• Mathematically: , where P is pressure, F is force, and A is area.

• The SI unit for force is the Newton (N), and for area is the square metre (m2), so the SI unit for pressure is the Pascal (Pa): .

Summary of Pressure Units

There are several units commonly used to measure gas pressure. The following table summarizes these units and their conversions:

Partial Pressure

Definition and Application

Partial pressure is the individual pressure exerted by a single gas in a mixture of gases. The total pressure of a mixture is the sum of the partial pressures of each component gas.

• For a mixture of gases:

• Example: If a container has oxygen at 20 kPa and nitrogen at 80 kPa, the total pressure is .

Kinetic Molecular Theory of Gases

Postulates of the Theory

The kinetic molecular theory explains the behavior of ideal gases based on the following assumptions:

• Gases are composed of small particles (atoms or molecules) in constant, random, straight-line motion.

• The volume of the individual gas particles is negligible compared to the total volume occupied by the gas.

• There are negligible attractive or repulsive forces between particles.

• Collisions between gas particles and with the container walls are perfectly elastic (no loss of kinetic energy).

• The average kinetic energy of gas particles is proportional to the absolute temperature (in Kelvin): .

Implications and Properties

• Gases take the shape and volume of their container due to negligible intermolecular forces and random motion.

• Gases have low density because particles are far apart.

• Gases are compressible because there is much empty space between particles.

• Gases diffuse rapidly due to constant motion and large intermolecular distances.

• Pressure is caused by collisions of gas particles with the container walls; it increases with the number of particles, temperature, and decreases with increasing volume.

Deviations from Ideal Behavior

Real gases deviate from ideal behavior under high pressure and low temperature because:

• Gas particles do occupy space, so their volume is not negligible.

• There are intermolecular forces of attraction, which become significant at high pressures and low temperatures.

• Real gases can condense to liquids, while ideal gases cannot.

Temperature and Kinetic Energy

Relationship

The average kinetic energy of gas particles is directly proportional to the absolute temperature:

• (in Kelvin)

• At a given temperature, all gases have the same average kinetic energy, regardless of their chemical identity.

Maxwell-Boltzmann Distribution

Distribution of Molecular Energies

The Maxwell-Boltzmann distribution describes the spread of kinetic energies among molecules in a gas sample at a given temperature.

• Most molecules have intermediate kinetic energies; few have very low or very high energies.

• As temperature increases, the distribution broadens and the average kinetic energy increases.

Heating Curves

Phase Changes and Temperature

A heating curve shows how the temperature of a substance changes as it is heated, illustrating phase changes such as melting and boiling.

• Pure substances have clearly defined melting and boiling points.

• Mixtures do not have sharp melting or boiling points.

Summary

• The kinetic theory of gases provides a framework for understanding the properties and behavior of gases.

• Key properties such as pressure, volume, and temperature are interrelated and can be explained by the motion and interactions of gas particles.

• Real gases deviate from ideal behavior under certain conditions, but the kinetic theory remains a useful model for most practical purposes.