1.1 Ideal Gases

The Ideal Gas Law

The behavior of an ideal gas is described by PV = nRT, where P is pressure, V is volume, n is moles, R is the gas constant, and T is absolute temperature (in Kelvin). This law links pressure, volume, and temperature for a fixed amount of gas, assuming particles have negligible volume and no intermolecular forces except brief elastic collisions.

Kinetic Molecular Theory

Gas pressure arises from collisions of gas particles with container walls. Average kinetic energy of particles is directly proportional to absolute temperature: KE_avg = (3/2)kT. Faster particles (higher T) hit walls harder and more often, increasing pressure. This microscopic model explains the macroscopic PV = nRT relationship.

Combined Gas Behavior

Using PV = nRT, if one variable is held constant, you can predict how the others change. At constant temperature, P and V are inversely related (Boyle's Law); at constant pressure, V and T are directly related (Charles's Law). These are special cases of the same underlying ideal gas law.

Key terms

Ideal Gas Law

PV = nRT; relates pressure, volume, moles, and absolute temperature of an ideal gas.

Kinetic Molecular Theory

Model explaining gas pressure as resulting from particle collisions with container walls; assumes negligible particle volume and elastic collisions.

Average kinetic energy formula

KE_avg = (3/2)kT, where k is Boltzmann's constant and T is absolute temperature.

Boyle's Law

At constant temperature, pressure and volume are inversely proportional (a special case of PV = nRT).

Why use Kelvin for gas laws?

Kelvin is an absolute scale starting at 0, ensuring temperature (and thus kinetic energy) is never negative.

Try an AP-style question

An ideal gas in a rigid container has its absolute temperature doubled. What happens to its pressure?

1. It doubles
2. It stays the same
3. It halves
4. It quadruples