Cambridge A-Level Chemistry 9701

Physical Chemistry

States of Matter: Arrangement, Motion, Energies of Particles, Changes of State, Gas Laws

This section explores the fundamental properties of matter in its different states – solid, liquid, and gas. We will delve into the arrangement and motion of particles within these states, the associated energies, the processes of changing between states, and the relationships governing the behaviour of gases.

Particle Arrangement and Motion

The state of matter is determined by the arrangement and motion of its constituent particles (atoms, ions, or molecules). Different states exhibit distinct characteristics in these aspects.

Solid

• Particles are tightly packed in a fixed, regular arrangement (crystal lattice).
• Particles vibrate about their fixed positions.
• Strong intermolecular forces hold particles together.

Liquid

• Particles are close together but not in a fixed arrangement.
• Particles can move past each other.
• Intermolecular forces are weaker than in solids.

Gas

• Particles are widely separated and move randomly.
• Particles move with high speeds and undergo random collisions.
• Intermolecular forces are negligible.

Kinetic Theory of Gases

The kinetic theory provides a model for understanding the macroscopic properties of gases based on the microscopic behaviour of their particles. Key assumptions include:

1. Gases consist of a large number of particles in constant, random motion.
2. The volume occupied by the particles is negligible compared to the total volume of the container.
3. There are no intermolecular forces between the particles (except during collisions).
4. Collisions between particles and with the walls of the container are perfectly elastic.

Energy of Particles

The kinetic energy of particles in a substance is related to its temperature. The average kinetic energy of particles in a gas is directly proportional to the absolute temperature (in Kelvin).

$$KE_{avg} = \frac{3}{2} k T$$

where:

• $KE_{avg}$ is the average kinetic energy per particle.
• $k$ is the Boltzmann constant ($1.38 \times 10^{-23} \, J/K$).
• $T$ is the absolute temperature in Kelvin.

Changes of State

Changes of state involve the absorption or release of heat energy. These processes are accompanied by a change in the arrangement and motion of particles.

Melting (Solid to Liquid)

Melting occurs at a specific temperature called the melting point. Heat energy is absorbed to overcome the intermolecular forces holding the solid together.

Freezing (Liquid to Solid)

Freezing occurs at the melting point. Heat energy is released as intermolecular forces become stronger and particles arrange into a crystalline structure.

Boiling (Liquid to Gas)

Boiling occurs at a specific temperature called the boiling point. Heat energy is absorbed to overcome the remaining intermolecular forces and allow particles to escape into the gaseous phase.

Condensation (Gas to Liquid)

Condensation occurs at the boiling point. Heat energy is released as particles slow down and intermolecular forces become dominant, causing them to cluster together in a liquid state.

Sublimation (Solid to Gas)

Sublimation occurs when a solid directly changes into a gas without passing through the liquid phase. This happens when the particles in the solid have enough kinetic energy to overcome the intermolecular forces.

Deposition (Gas to Solid)

Deposition occurs when a gas directly changes into a solid without passing through the liquid phase. This happens when the particles in the gas lose enough kinetic energy to form a crystalline structure.

Gas Laws

Gas laws describe the relationship between the macroscopic properties of gases – pressure (P), volume (V), temperature (T), and number of moles (n).

Boyle's Law

At constant temperature and number of moles, the pressure of a gas is inversely proportional to its volume.

$$P \propto \frac{1}{V}$$

or

$$P_1 V_1 = P_2 V_2$$

Charles's Law

At constant pressure and number of moles, the volume of a gas is directly proportional to its absolute temperature.

$$V \propto T$$

or

$$\frac{V_1}{T_1} = \frac{V_2}{T_2}$$

Gay-Lussac's Law

At constant volume and number of moles, the pressure of a gas is directly proportional to its absolute temperature.

$$P \propto T$$

or

$$\frac{P_1}{T_1} = \frac{P_2}{T_2}$$

Combined Gas Law

Combines Boyle's Law, Charles's Law, and Gay-Lussac's Law.

$$\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$$

Ideal Gas Law

Relates pressure, volume, temperature, and the number of moles of a gas through the ideal gas constant (R).

$$PV = nRT$$

where:

• $P$ is the pressure.
• $V$ is the volume.
• $n$ is the number of moles.
• $R$ is the ideal gas constant ($8.314 \, J/mol \cdot K$).
• $T$ is the absolute temperature in Kelvin.