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CHM 151 · Ch 10 · Gases

Gas Laws

Gas pressure is particles hitting walls. Every gas law is just a way to make them hit harder, more often, or less.

the idea

Pressure is collisions. Change how many, how fast, or how much room they have.

Gas particles fly around and bounce off the walls, and each bounce is a tiny push. Pressure is all those pushes added up. Every gas law follows from three questions: how many particles (n), how fast they're moving (T), and how much room they have (V).

Plant version: a domed yogurt lid is a pressure gauge for yeast. Fermentation produces CO₂, which raises n inside a container whose V can't change, so P climbs until the foil bulges. The same cup cooled after a hot fill does the opposite: T drops, P drops, and the lid pulls in.

Ideal gas law

PV = nRT
R = 0.08206 L·atm/(mol·K)

Always Kelvin

K = °C + 273.15
At 0 K particles stop moving, so the gas laws only work on the absolute scale.
simulate

Gas in a box

Boyle's lawP₁V₁ = P₂V₂Less room means more wall hits, so P goes up. (n, T constant)
Charles's lawV₁/T₁ = V₂/T₂Heat it with a free piston and it expands. (n, P constant)
Gay-Lussac's lawP₁/T₁ = P₂/T₂Heat a rigid container and P climbs. (n, V constant)
Avogadro's lawV₁/n₁ = V₂/n₂More particles need more room at the same P. (T, P constant)
calculate

Combined gas law

P₁V₁/T₁ = P₂V₂/T₂. Leave one box blank. Any pressure and volume units work as long as both sides match. Enter temperatures in °C and they get converted to K.

practice

Gas law problems

engineering version

Three ways gas laws show up on a shipping report

  1. Hot fill, then cool. Headspace sealed at 85 °C and cooled to 4 °C: P₂ = 1.00 atm × 277 K ÷ 358 K = 0.774 atm, a partial vacuum (the default numbers in the calculator above). Steam condensing in the headspace makes the vacuum even stronger. That's why hot-filled bottles panel.
  2. Gas production. Yeast or heterofermentative bacteria add moles of CO₂ to a fixed volume. P rises with n until the seal or container gives. A swollen container is a microbial red flag before anything else.
  3. Altitude. A truck over a mountain pass sees lower outside pressure. The headspace gas expands (Boyle), so lids can dome in transit with nothing wrong with the product.
exam traps

Common mistakes