Ideal Gas Law Worked Examples Cheat Sheet

Key Facts

• The ideal gas law is $PV = nRT$, and it relates pressure, volume, moles, and absolute temperature for an ideal gas.
• Temperature must be converted to kelvin before using the ideal gas law, so $T_K = T_C + 273.15$.
• Use $R = 0.08206\ \frac{\text{L}\cdot\text{atm}}{\text{mol}\cdot\text{K}}$ when pressure is in atmospheres and volume is in liters.
• Use $R = 8.314\ \frac{\text{J}}{\text{mol}\cdot\text{K}}$ when pressure is in pascals and volume is in cubic meters, since $1\ \text{J} = 1\ \text{Pa}\cdot\text{m}^3$.
• To solve for moles, rearrange the ideal gas law as $n = \frac{PV}{RT}$.
• To connect mass to gas amount, use $n = \frac{m}{M}$, where $m$ is mass and $M$ is molar mass.
• Gas density can be found from the ideal gas law using $\rho = \frac{PM}{RT}$.
• At standard temperature and pressure for many classroom problems, $T = 273.15\ \text{K}$, $P = 1\ \text{atm}$, and one mole of ideal gas occupies about $22.4\ \text{L}$.

Vocabulary

Ideal gas

An ideal gas is a model gas whose particles have negligible volume and no intermolecular attractions.

Pressure

Pressure is the force per unit area caused by gas particles colliding with the walls of a container.

Absolute temperature

Absolute temperature is temperature measured in kelvin, where $0\ \text{K}$ represents absolute zero.

Mole

A mole is an amount of substance equal to $6.022 \times 10^{23}$ particles.

Gas constant

The gas constant $R$ is the proportionality constant in $PV = nRT$ and its numerical value depends on the units used.

Molar mass

Molar mass $M$ is the mass of one mole of a substance, usually measured in $\text{g/mol}$.