Gas law

Ideal Gas Law Glossary

• Absolute Pressure: Actual pressure of gas inside a container, no reference to outside pressure.

• Gauge Pressure: Difference between absolute pressure and atmospheric pressure.

Key Gas Laws

• Boyle’s Law: $P<em>1 V</em>1 = P<em>2 V</em>2$ (Pressure and volume at different states)

• Charles’s Law: $\frac{V<em>1}{T</em>1} = \frac{V<em>2}{T</em>2}$ (Volume and temperature relation)

• Avogadro’s Law: $\frac{V<em>1}{n</em>1} = \frac{V<em>2}{n</em>2}$ (Volume and number of moles)

Ideal Gas Law Formula

• $PV = nRT$

  • P: Pressure

  • V: Volume

  • n: Number of moles

  • R: Ideal gas constant = 8.314 L kPa mol K or L atm mol K

  • T: Temperature (must be in Kelvin)

Using the Ideal Gas Law

• Calculate unknown if three variables are known: Rearrangement gives $n = \frac{PV}{RT}$

• Ensure units match those of the ideal gas constant:

  • Volume: L

  • Pressure: atm or kPa

  • Temperature: K

Application Examples

1. Pressure and moles calculation from a gas sample given values.

2. Conversion of temperature from Celsius to Kelvin: $K = °C + 273.15$

3. Calculation of gauge pressure when given absolute and atmospheric pressures.

Mixtures of Gases

• Each gas in a mixture can be treated individually.

• Total pressure is the sum of partial pressures: $P<em>{total} = P</em>1 + P<em>2 + … + P</em>n$

Important Rearrangements of the Ideal Gas Law

• To solve for pressure (P): $P = \frac{nRT}{V}$

• To solve for volume (V): $V = \frac{nRT}{P}$

• To solve for number of moles (n): $n = \frac{PV}{RT}$

• To solve for temperature (T): $T = \frac{PV}{nR}$