Gas Laws

Discovered by Robert Boyle in 1662, this law states that at constant temperature and amount of gas, the pressure of a gas is inversely proportional to its volume: P ∝ 1/V, or equivalently P₁V₁ = P₂V₂. Physically, compressing a gas into a smaller volume forces molecules to collide with the container walls more frequently, raising the pressure. A bicycle pump illustrates this perfectly — pushing the handle in decreases the volume and forces air out at higher pressure.

Jacques Charles formulated this law in 1787 (published by Gay-Lussac in 1802): at constant pressure and fixed amount of gas, volume is directly proportional to absolute temperature: V ∝ T, or V₁/T₁ = V₂/T₂. Temperature must always be in Kelvin (K = °C + 273.15). As temperature rises, gas molecules move faster, exert more force, and push the container walls outward, increasing volume. A balloon shrinks in cold water and expands in warm water because of this relationship.

Joseph Louis Gay-Lussac established in 1809 that at constant volume and fixed amount of gas, pressure is directly proportional to absolute temperature: P ∝ T, or P₁/T₁ = P₂/T₂. Heating a sealed, rigid container raises molecular kinetic energy and collision frequency with the walls, increasing pressure. This is why aerosol cans carry warnings about heat exposure — the pressure inside rises dangerously as temperature increases.

Amedeo Avogadro proposed in 1811 that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules, regardless of the gas's identity: V ∝ n, or V₁/n₁ = V₂/n₂. This means that 1 mole of any ideal gas occupies 22.4 L at Standard Temperature and Pressure (STP: 0 °C, 1 atm). Avogadro's Law explains Gay-Lussac's Law of Combining Volumes — for example, \ce{2H_2 + O_2 -> 2H_2O} means 2 volumes of hydrogen react with 1 volume of oxygen to yield 2 volumes of water vapor.

Combining Boyle's, Charles's, and Gay-Lussac's laws yields the Combined Gas Law: (P₁V₁)/T₁ = (P₂V₂)/T₂, useful when comparing two states of the same amount of gas. Incorporating Avogadro's Law gives the Ideal Gas Law: PV = nRT, where R = 8.314 J mol⁻¹ K⁻¹ (or 0.08206 L·atm mol⁻¹ K⁻¹) is the universal gas constant. An ideal gas is a theoretical model assuming perfectly elastic collisions between point-mass molecules with no intermolecular forces — an approximation that works best at low pressure and high temperature.

• P — Pressure (Pa (or atm)): The force exerted per unit area by gas molecules colliding with the container walls.
• V — Volume (m³ (or L)): The space occupied by the gas; must match units used for R.
• n — Amount of substance (mol): The number of moles of gas molecules present.
• R — Universal gas constant (8.314 J mol⁻¹ K⁻¹): A proportionality constant that links the energy scale to temperature and moles.
• T — Absolute temperature (K): Temperature measured in Kelvin; always convert from Celsius by adding 273.15.

Problem. A sample of nitrogen gas occupies 4.50 L at 25 °C and 1.20 atm. What volume will it occupy at 75 °C and 0.800 atm? Assume ideal behavior.

Answer. V₂ ≈ 7.88 L

• Kinetic Molecular Theory of Gases — The gas laws are the macroscopic result of the microscopic behavior described by Kinetic Molecular Theory — understanding molecular motion, speed distributions, and collision frequency explains why each gas law holds mathematically.
• Ideal vs. Real Gases: van der Waals Equation — At high pressures and low temperatures, real gases deviate from PV = nRT because intermolecular forces and molecular volume matter; the van der Waals equation corrects for these deviations.
• Intermolecular Forces — The ideal gas law assumes no intermolecular forces; understanding London dispersion, dipole–dipole, and hydrogen bonding forces is critical to understanding when and why gases deviate from ideal behavior.
• Introduction to Thermodynamics — Gas laws are deeply connected to thermodynamic concepts such as internal energy, work done by expansion (w = −PΔV), and the First Law of Thermodynamics.
• Dalton's Law of Partial Pressures — In mixtures of gases, each component exerts its own partial pressure independently; Dalton's Law extends the ideal gas model to gas mixtures and is essential in topics such as atmospheric chemistry and gas collection over water.