Kinetic theory and real gases

MDCAT Chemistry · Chemistry · Gases. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

The kinetic molecular theory pictures a gas as tiny molecules that are far apart and move fast in straight lines in all directions. Pressure comes from their collisions with the walls. The hotter the gas, the faster the molecules move.

An ideal gas follows this picture exactly. A real gas does not, because two postulates are not quite true: real molecules attract one another, and they take up some space. Both matter most when the molecules are pushed close together or are moving slowly.

Plasma is the fourth state of matter. It is a very hot, ionised gas made of positive ions and free electrons. It is neutral overall but conducts electricity.

Rules to remember

Postulates: the volume of the molecules is negligible; there are no forces between them; collisions are perfectly elastic; motion is random
average kinetic energy ∝ absolute temperature (in K), and it is the same for all gases at the same temperature
root mean square speed = √(3RT/M), so lighter molecules move faster at the same temperature
Real gases are most ideal at low pressure and high temperature; they deviate most at high pressure and low temperature
van der Waals equation: (P + n²a/V²)(V − nb) = nRT; a corrects for attractions, b for the volume of the molecules
PV/nRT < 1: attractions dominate; PV/nRT > 1: the volume of the molecules dominates (very high pressure)
Plasma examples: the Sun and stars, lightning, neon signs, fluorescent tubes

Common mistake

Students say that doubling the temperature in °C doubles the kinetic energy. Kinetic energy follows the kelvin temperature, and speed follows only its square root.

Worked example

A gas is heated from 27 °C to 927 °C. By what factor does the root mean square speed of its molecules increase?

Change to kelvin: 27 °C = 300 K and 927 °C = 1200 K.
The absolute temperature rises by a factor of 1200 ÷ 300 = 4.
Root mean square speed ∝ √T, so the speed rises by √4 = 2.

Answer: The speed doubles (factor of 2), while the average kinetic energy becomes 4 times as great

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