Particle Motion in Solids, Liquids, and Gases

Particle motion describes how the particles of a substance move: in solids they vibrate about fixed positions, in liquids they slide past each other while staying in contact, and in gases they move quickly and randomly in straight lines until they collide. In brief: at room temperature the particles of air move at several hundred meters per second, but they collide so often that they travel only a very short distance before changing direction.

The way particles move accounts for the properties that we observe: whether a substance flows, how it fills a container and how it responds to pressure. This article describes each type of motion, explains pressure in terms of collisions, compares typical speeds in a table, works through speed calculations and gives the history of the kinetic theory.

How do particles move in solids?

Particles in a solid are held in fixed positions by strong attractive forces. They cannot change places, but they vibrate rapidly back and forth around their positions. The vibrations become bigger when the solid is heated. If the vibrations become big enough to overcome the attractions between neighbors, the solid melts.

Because the particles do not change positions, a solid has a definite shape and volume. It cannot flow and cannot be compressed easily.

How do particles move in liquids?

In a liquid, particles are close together and in contact, but they have enough energy to move past each other. They vibrate, rotate and move short distances, constantly exchanging neighbors. This explains why liquids flow and take the shape of the bottom of the container.

Because the particles stay in contact, liquids have a definite volume and are almost incompressible. At the surface, some particles with high energy escape as vapor, which is evaporation.

How do particles move in gases?

In a gas, particles are far apart compared with their size and move rapidly in straight lines until they collide with each other or the container walls. After a collision, the direction and speed change. The motion is random and different particles have different speeds, but the average speed depends on the temperature.

Gas particles exert almost no force on each other except during collisions, so a gas expands to fill any container. The large gaps allow gases to be compressed.

How do moving particles cause gas pressure?

Each time a gas particle hits the wall of its container, it exerts a tiny force. Billions of collisions every second add up to a steady push, which we measure as pressure. Three results follow from this explanation.

• Squeezing the gas into a smaller volume makes particles hit the walls more often, so the pressure rises.
• Heating the gas in a fixed container makes particles faster, so they hit harder and more often and the pressure rises.
• Adding more gas increases the number of particles and so the number of collisions.

Comparing particle motion

Worked example: speeds of gas particles

The root-mean-square speed of gas particles is v = √(3RT ÷ M), where R = 8.314 J/(mol·K), T is the temperature in kelvin and M is the molar mass in kg/mol. This formula is used in more advanced courses, and here it shows the order of magnitude of the speeds.

1. Nitrogen at 300 K. M = 0.028 kg/mol. v = √(3 × 8.314 × 300 ÷ 0.028) = √267,000 ≈ 517 m/s.
2. Oxygen at 300 K. M = 0.032 kg/mol. v = √(3 × 8.314 × 300 ÷ 0.032) = √233,800 ≈ 484 m/s.
3. Hydrogen at 300 K. M = 0.002016 kg/mol. v ≈ 1,926 m/s. Lighter particles move faster at the same temperature.
4. Conversion. 517 m/s is 517 × 3.6 ≈ 1,860 km/h, which is faster than the speed of sound in air (about 343 m/s).

Although the speeds are high, a gas particle collides about several billion times per second at normal pressure, so a smell takes seconds or minutes to cross a room.

How did scientists develop the kinetic theory?

The idea that gas pressure is caused by moving particles was proposed by Daniel Bernoulli in 1738. In the middle of the 19th century, James Clerk Maxwell and Ludwig Boltzmann developed the mathematical theory of the distribution of speeds in a gas. Their work, known as kinetic theory, explained heat as the motion of particles and became the base of statistical mechanics.

Which mistakes are common?

Mistake 1: Assuming that all particles in a gas have the same speed

They have a range of speeds. Only the average depends on temperature.

Mistake 2: Saying that gas particles settle at the bottom of a container

Their speeds are so large that gravity has little effect on small molecules, and they spread through the whole volume.

Mistake 3: Believing that liquid particles are stationary

They are constantly moving and changing neighbors.

Mistake 4: Thinking that particles stop moving when a substance is cold

Particles keep moving at all temperatures above absolute zero.