The Kinetic Molecular Theory and Ideal Gases

A model you cannot see

Open a bottle of vanilla across the kitchen and, a little later, someone at the table smells it. Pump up a bike tire and it gets firm. Leave a helium balloon from a birthday party overnight and it sags. All of these are explained by one model: the kinetic molecular theory (KMT).

Kinetic means "related to motion". The KMT says that the behaviour of a gas that we can measure (its pressure, volume and temperature) comes from the motion of particles we cannot see.

The postulates of the kinetic molecular theory

Chemists describe an ideal gas, an imaginary gas that follows the model perfectly:

1. A gas is made of a huge number of tiny particles (atoms or molecules). The particles' own volume is negligible compared with the space between them.
2. The particles are in constant, random, straight-line motion. They change direction only when they collide.
3. Collisions with each other and with the container walls are elastic: no kinetic energy is lost overall.
4. There are no attractive or repulsive forces between particles except during collisions.
5. The average kinetic energy of the particles is directly proportional to the absolute (Kelvin) temperature. (To change °C to kelvins, add 273. You'll work with this much more in the next lesson.)

Real gases are not perfectly ideal, but at room temperature and normal pressure most gases (N₂, O₂, He, CO₂) come very close.

Explaining gas properties with the KMT

• Gases are compressible because most of a gas is empty space (postulate 1).
• Gases fill their containers and mix because the particles move randomly and freely, with no attractions to hold them together (postulates 2 and 4).
• Gases exert pressure because particles constantly hit the walls. Pressure depends on how often and how hard they hit.
• Heating a gas raises the average kinetic energy (postulate 5), so the particles move faster and hit the walls more often and harder.

Kinetic energy and speed. For one particle, Eₖ = ½mv². At the same temperature, all gases have the same average kinetic energy. So a light molecule must move faster than a heavy one. At 25 °C, nitrogen molecules move at roughly 500 m/s on average (faster than a passenger jet), and hydrogen molecules much faster still.

Not every particle has the same speed

At any instant, some particles are slow, most are near the average, and a few are very fast. When the temperature rises, the whole distribution shifts to higher speeds and spreads out. The average kinetic energy rises in proportion to the Kelvin temperature.

Diffusion

Diffusion is the spreading of one substance through another because of random particle motion. Lighter gases diffuse faster, because their particles move faster at the same temperature. (Effusion is the escape of gas through a tiny hole; a helium balloon goes flat sooner than an air-filled one partly because the small, fast helium atoms escape through the rubber more quickly.)

A classic school demonstration (done in a fume hood, never at home) puts cotton soaked in concentrated ammonia solution at one end of a long glass tube and cotton soaked in concentrated hydrochloric acid at the other. The two gases diffuse toward each other and react to form a white ring of solid ammonium chloride: NH₃(g) + HCl(g) → NH₄Cl(s). The ring forms closer to the HCl end, because the lighter NH₃ molecules move faster and travel farther in the same time.

When real gases are not ideal

Postulates 1 and 4 are approximations. Real gases deviate from ideal behaviour when:

• the pressure is very high: particles are squeezed so close that their own volume is no longer negligible;
• the temperature is very low: particles move slowly, so intermolecular attractions (from the last lesson) start to matter. Eventually the gas condenses into a liquid, which an ideal gas would never do.

So: gases behave most ideally at high temperature and low pressure. Gases with weak IMFs (He, H₂, N₂) are closest to ideal; polar gases with stronger IMFs (NH₃, H₂O vapour) deviate more.