Gay-Lussac's Law states that pressure and temperature are directly proportional at constant volume. Heat a gas in a fixed container and its pressure increases proportionally.
Pâ‚ / Tâ‚ = Pâ‚‚ / Tâ‚‚
Initial pressure / initial temperature = Final pressure / final temperature
ALWAYS convert °C or °F to Kelvin before using Gay-Lussac's Law. Using Celsius will give completely wrong answers!
K = °C + 273.15
Example: 25°C = 298.15 K (often rounded to 298 K)
P ∠T (at constant V and n)
Common Units: atm, mmHg, torr, kPa, Pa, bar, psi
Pressure before the temperature change
Units: K (Kelvin) - MUST USE KELVIN!
Temperature before the change
⌠Do NOT use °C or °F directly!
Units: Same as Pâ‚
Pressure after the temperature change
Units: K (Kelvin) - MUST USE KELVIN!
Temperature after the change
Volume (V) must remain constant
Amount of gas (n) must remain constant
Container must be rigid (cannot expand)
Pâ‚‚ = Pâ‚Tâ‚‚ / Tâ‚
Most common use!
Tâ‚‚ = Pâ‚‚Tâ‚ / Pâ‚
Pâ‚ = Pâ‚‚Tâ‚ / Tâ‚‚
Tâ‚ = Pâ‚Tâ‚‚ / Pâ‚‚
Tâ‚ = 25 + 273 = 298 K
Tâ‚‚ = 100 + 273 = 373 K
Pâ‚/Tâ‚ = Pâ‚‚/Tâ‚‚
Pâ‚‚ = Pâ‚Tâ‚‚ / Tâ‚
Pâ‚‚ = (2.50 atm)(373 K) / (298 K)
P₂ = 932.5 atm·K / 298 K = 3.13 atm
Answer: Pâ‚‚ = 3.13 atm
✅ Makes sense: Temperature increased by 25%, pressure increased by 25%
Drive on hot pavement → tire heats up → pressure increases → check tire pressure when cool!
Heat sealed pot → temperature rises → pressure builds up → cooks food faster at higher pressure
Warning: "Do not heat" - hot can = high pressure = explosion risk!
Autoclave sterilization: high temperature creates high pressure to kill microorganisms
THE #1 MISTAKE! Temperature MUST be in Kelvin. Using °C gives completely wrong answers. Always convert: K = °C + 273.
Gay-Lussac's Law ONLY works when volume is constant (rigid container). If V changes, use the Combined Gas Law instead.
Pâ‚ and Pâ‚‚ must be in the same units. Tâ‚ and Tâ‚‚ must BOTH be in Kelvin. Convert before calculating!
If temperature increases, pressure MUST increase. If temperature decreases, pressure MUST decrease. Verify your answer makes physical sense!
Pâ‚/Tâ‚ = Pâ‚‚/Tâ‚‚ at constant volume. Pressure and temperature are directly proportional - when one goes up, the other goes up.
Gay-Lussac's Law requires an absolute temperature scale. 0 K is absolute zero - no molecular motion. Using °C would incorrectly suggest zero pressure at 0°C!
Higher temperature = faster molecular motion = molecules hit walls harder and more often. In a rigid container, this increased kinetic energy shows up as higher pressure.
Charles's Law: V and T (P constant) - container can expand. Gay-Lussac's: P and T (V constant) - rigid container. Different conditions!
If volume can change, use Charles's Law (constant P) or Combined Gas Law (P, V, and T all change). Gay-Lussac's only works for rigid containers.