Kinetic Molecular Theory: MDCAT Chemistry notes

Postulates of the kinetic molecular theory

The kinetic molecular theory of gases (Bernoulli, later Clausius, Maxwell and Boltzmann) explains gas behaviour by assuming the molecules are in constant motion. For an ideal gas:

1. A gas consists of a very large number of tiny particles (molecules) that are far apart; their actual volume is negligible compared with the volume of the container.
2. Molecules are in continuous, random, straight-line motion, colliding with each other and with the container walls.
3. Collisions are perfectly elastic: there is no change in total kinetic energy (energy may be transferred between molecules, but none is lost).
4. Pressure is caused by molecules colliding with the walls of the container.
5. There are no attractive or repulsive forces between the molecules of an ideal gas.
6. Gravity has negligible effect on the molecules. Because collisions are elastic and motion never stops, the molecules of air do not settle down.
7. The average kinetic energy of the molecules is directly proportional to the absolute temperature.

Ideal vs real gases

Property	Ideal gas	Real gas
Random motion	Yes	Yes
Intermolecular forces	Absent	Present (weak attractions)
Molecular volume	Negligible	Significant at high pressure

Key formulas

Kinetic equation of gases:

$$PV=\frac{1}{3}mN\overline{c^2}$$

Average translational kinetic energy of one molecule and of one mole:

$$\overline{E_k}=\frac{3}{2}\frac{RT}{N_A}=\frac{3}{2}kT\qquad E_k(\text{per mole})=\frac{3}{2}RT$$

Root mean square speed:

$$c_{rms}=\sqrt{\frac{3RT}{M}}$$

So speed increases with temperature and decreases with molar mass. At the same temperature, all gases have the same average kinetic energy.

Temperature and heat flow

Temperature is a measure of the average translational kinetic energy of the molecules. When a hot gas and a cold gas are in contact, heat flows until both have equal average translational kinetic energy, i.e. equal temperature. The total kinetic energy of a molecule is the sum of translational, rotational and vibrational energies, but temperature relates to the translational part.

Explaining gas behaviour

• Heating at constant pressure (movable piston): molecules move faster and hit the piston harder, so the volume increases (Charles's law).
• Diffusion: gases mix spontaneously to form a uniform mixture because of random motion, e.g. scent spreading through a room. Effusion is escape through a tiny hole.
• Plasma: a gas heated until its atoms ionise; it is called the fourth state of matter.

Common MDCAT traps

• Molecules do exert pressure by colliding with the walls; any option denying this is not a postulate.
• Elastic means no change in total kinetic energy, not no change in velocity.
• Intermolecular forces in an ideal gas are absent, not merely weak.
• $\overline{E_k}=\frac{3}{2}RT/N_A$, not $\frac{2}{3}$.
• Only random motion is common to both ideal and real gases.

Quick revision

• Pressure comes from wall collisions.
• Average KE ∝ absolute temperature.
• $c_{rms}=\sqrt{3RT/M}$.
• Diffusion explains spreading of smells.
• Plasma is the fourth state of matter.