AP Chemistry Unit 3 Gases: Linking Macroscopic Laws, Particle Motion, and Real-World Behavior

Gas (state of matter)

A state where particles are far apart, move rapidly, and expand to fill any container; bulk behavior is described by relationships among P, V, T, and n.

Pressure (P)

Force per unit area caused by gas particles colliding with container walls; more frequent or more forceful collisions increase pressure.

Standard atmosphere (atm)

A common pressure unit; 1 atm = 760 mmHg and 1 atm = 101.325 kPa.

Millimeters of mercury (mmHg) / torr

Pressure units commonly used for gases; 760 mmHg = 760 torr = 1 atm.

Kilopascal (kPa)

SI-related pressure unit used in gas laws; 101.325 kPa = 1 atm.

Volume (V)

The space a gas occupies, commonly measured in liters (L) in gas-law problems.

Kelvin temperature (K)

The required temperature scale for gas-law calculations because it is directly proportional to average kinetic energy.

Celsius-to-Kelvin conversion

$T(K) = T(°C) + 273.15$; using $°C$ in gas laws produces incorrect results.

Amount of gas (n)

Number of moles of gas; connects macroscopic measurements (P, V, T) to particle-level quantity.

Ideal Gas Law

PV = nRT; relates pressure, volume, moles, and Kelvin temperature for an ideal gas model.

Gas constant (R)

The proportionality constant in PV = nRT; its numerical value depends on the chosen P and V units.

R = 0.082057 L·atm·mol⁻¹·K⁻¹

Gas constant value used when pressure is in atm and volume is in liters.

R = 8.314 L·kPa·mol⁻¹·K⁻¹

Gas constant value used when pressure is in kPa and volume is in liters.

Unit consistency (gas laws)

Requirement that P, V, T, and R units match (e.g., don’t use kPa with L·atm R), or results will be wrong by large factors.

Moles from lab data (ideal gas rearrangement)

$n = \frac{PV}{RT}$; common use of the ideal gas law to determine moles from measured $P$, $V$, and $T$.

Molar mass from ideal gas measurements

Using n = m/M in PV = nRT gives M = (mRT)/(PV), allowing molar mass to be found from mass, P, V, and T.

Density form of ideal gas law

From $d = \frac{m}{V}$ and $PV = \frac{m}{M}RT$, one obtains $PM = dRT$ (or $M = \frac{dRT}{P}$).

Combined Gas Law

For constant n: (P1V1)/T1 = (P2V2)/T2; compares two states of the same sample of gas.

Dalton’s Law of Partial Pressures

In a mixture of nonreacting gases, total pressure equals the sum of partial pressures: P_{total} = \SigmaP_i.

Mole fraction (X_i)

Fraction of total moles contributed by component $i$; for ideal mixtures, $P_i = X_i \times P_{total}$.

Kinetic Molecular Theory (KMT)

Particle-level model explaining gas behavior: links macroscopic variables (P, T) to molecular motion and collisions.

Elastic collision (KMT postulate)

A collision in which there is no net loss of kinetic energy; assumed for ideal gas particles colliding with each other or walls.

Average kinetic energy of an ideal gas

$KE_{avg} = \frac{3}{2}RT$ (per mole); depends only on Kelvin temperature, not on gas identity or molar mass.

Graham’s law (effusion/diffusion rate)

For gases at the same conditions: $\frac{r_1}{r_2} = \sqrt\frac{M_2}{M_1}$; lighter gases effuse/diffuse faster.

Compressibility factor (Z)

$Z = \frac{PV}{nRT}$; $Z = 1$ indicates ideal behavior, $Z < 1$ suggests attractions dominate, and $Z > 1$ suggests finite volume/repulsions dominate.