What Is the Ideal Gas Law?
The ideal gas law, PV = nRT, links pressure, volume, temperature, and moles of an ideal gas. It's one of chemistry's most powerful tools, accurate for most gases at moderate conditions.
The ideal gas law is PV = nRT, where P is pressure (Pa), V is volume (m³), n is moles (mol), R is the gas constant (8.314 J/mol·K), and T is absolute temperature (K).
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Step-by-step worked examples
1 mole of ideal gas at 298 K occupies 0.0244 m³. Find its pressure.
PV = nRT → P = nRT/V P = (1 × 8.314 × 298) / 0.0244 P = 2481.572 / 0.0244 P ≈ 101,690 Pa ≈ 1 atm
A 2 L tank contains 0.5 mol of gas at 25 °C. Find pressure in Pa.
2 L = 0.002 m³; T = 25 + 273 = 298 K P = nRT/V = (0.5 × 8.314 × 298) / 0.002 P = 1238.786 / 0.002 = 619,393 Pa
If 3 moles expand from 0.5 m³ to 1.5 m³ at 300 K, find final pressure.
P₁V₁ = P₂V₂ (same T, n) P₁ = nRT/V₁ = (3 × 8.314 × 300) / 0.5 = 14,965.2 Pa P₂ = nRT/V₂ = (3 × 8.314 × 300) / 1.5 = 4,988.4 Pa
Flashcards
Quick quiz
Q1.The ideal gas law is…
Q2.If volume doubles at constant T and n, pressure…
Q3.Unit of R is…
Q4.Temperature must be in…
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Common mistakes
Using °C in PV = nRT without converting to K. — Correct: Always convert to Kelvins: K = °C + 273.15.
Forgetting to convert liters to m³. — Correct: 1 L = 0.001 m³; use consistent SI units.
Assuming pressure cancels with volume in the law. — Correct: PV is constant for ideal gas; they're inversely proportional.
Using R = 0.0821 L·atm/(mol·K) without unit conversion. — Correct: Pick either R = 8.314 (SI) or 0.0821 (liters, atm); match your units.
FAQ
What is the ideal gas law formula?
PV = nRT, where n is moles, R = 8.314 J/(mol·K), T is absolute temperature.
When do real gases deviate from the ideal gas law?
At very high pressures or low temperatures, when molecules interact strongly.
How do you find pressure from the ideal gas law?
P = nRT/V — rearrange by dividing both sides by V.
Why is temperature in Kelvins?
The ideal gas law is derived from kinetic theory, which uses absolute temperature.