What is the Ideal Gas Law?
The ideal gas law is the fundamental equation linking pressure, volume, moles and temperature of a gas — it works well for most gases at normal conditions. The equation PV = nRT tells us how gases respond to changes in their surroundings.
The ideal gas law is PV = nRT, where pressure times volume equals moles times the gas constant times absolute temperature. It predicts how gases behave when pressure, volume or temperature changes.
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Step-by-step worked examples
A 5 L flask contains 2 mol of N₂ gas at 300 K. What is the pressure? (R = 8.314 J/(mol·K); 1 Pa·m³ = 1 J)
PV = nRT P × 5 = 2 × 8.314 × 300 P = 4988.4 / 5 = 997.68 Pa ≈ 0.0098 atm (or ~1 kPa)
At STP (273 K, 1 atm), how many moles are in 22.4 L of gas?
PV = nRT 1 × 22.4 = n × 0.08206 × 273 n ≈ 1 mol
If a sealed 10 L container of gas at 300 K is heated to 600 K, and pressure doubles, how many moles were inside?
At 300K: P₁V = n × R × 300 At 600K: 2P₁V = n × R × 600 Dividing: 2 = 600/300 ✓ (confirms the relationship) Using first: n = P₁ × 10 / (8.314 × 300)
Flashcards
Quick quiz
Q1.Using PV = nRT, if you double the temperature of a gas at constant volume and moles, pressure will…
Q2.The units of R are typically…
Q3.At STP (1 atm, 273 K), one mole of ideal gas occupies roughly…
Q4.An ideal gas assumes molecules…
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Common mistakes
Using temperature in °C instead of K. — Correct: Always convert to Kelvin: K = °C + 273.
Confusing R values (8.314 vs 0.08206). — Correct: Use 8.314 J/(mol·K) or 0.08206 L·atm/(mol·K) consistently with your pressure units.
Thinking n is 'number of molecules.' — Correct: n is moles — 1 mole = 6.022 × 10²³ molecules.
The law works perfectly for all gases. — Correct: It breaks down at very high pressure or low temperature.
FAQ
What is the ideal gas law formula?
PV = nRT — it relates pressure, volume, moles and temperature of a gas.
Why is the gas constant R important?
It links pressure, volume and temperature units to moles and absolute temperature.
What are ideal gas law examples?
Any calculation of pressure, volume or temperature of air, nitrogen or other gases at normal conditions.
Can the ideal gas law predict real gas behavior?
Yes, reasonably well at low pressure and high temperature — but it fails at extreme conditions.