When the volume of a closed container of gas is decreased, the gas particles are forced into a smaller space. Since the number of particles and the temperature (and therefore average kinetic energy) remain constant, the particles have less space to move and therefore collide with the container walls more frequently. This increased frequency of collisions results in a greater total force exerted on the container walls. Because pressure is defined as force per unit area, the increased force on the walls leads to an increase in pressure. In essence, the same number of particles colliding with the same area, but in a smaller volume, means more frequent collisions and thus higher pressure.

The random motion of particles in a suspension is a direct consequence of the kinetic theory of matter, which postulates that all matter is composed of particles in constant, random motion. The kinetic theory states that the average kinetic energy of the particles in a substance is directly proportional to the absolute temperature of the substance. This means that as the temperature increases, the particles move faster and their random motion becomes more vigorous.

The concept of collisions is central to the kinetic theory and is directly relevant to the observed random motion. As particles move randomly, they constantly collide with each other and with the walls of the container. These collisions cause the particles to change direction and speed, resulting in the erratic, unpredictable paths that we observe. The frequency of collisions is also dependent on the particle size and the density of the substance. Smaller particles experience more frequent collisions relative to their size, contributing to the overall random motion. The collisions are not perfectly elastic; some kinetic energy is lost to heat during each collision.

As a substance is heated, the particles within it gain kinetic energy. This increased kinetic energy manifests as increased random motion. Initially, in a solid, the particles vibrate about fixed positions. As the temperature rises, the vibrational energy increases, and the particles vibrate with greater amplitude. At a certain temperature (the melting point), the particles gain enough energy to overcome the intermolecular forces holding them in a fixed lattice, transitioning to a liquid state.

In a liquid, the particles have more freedom of movement than in a solid, but they are still relatively close together. As the temperature continues to rise, the particles gain even more kinetic energy, moving faster and further apart. At a certain temperature (the boiling point), the particles gain enough energy to overcome the intermolecular forces holding them in the liquid, transitioning to a gaseous state. In a gas, the particles move randomly and independently, with minimal intermolecular forces.

The relationship between temperature, particle speed, and state is directly linked to the kinetic molecular theory. Higher temperatures mean higher average particle speeds. The state of a substance is determined by the strength of the intermolecular forces and the amount of kinetic energy the particles possess. At absolute zero (-273.15°C), all particle motion ceases (except for quantum effects), and the substance exists in a solid state. Above absolute zero, the substance can exist as a solid, liquid, or gas, depending on the temperature and the strength of the intermolecular forces.