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.

Short answer

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).

Pressure vs Temperature (constant n, V)

x: Temperature (K) · y: Pressure (Pa)

Try it: interactive calculator

Pressure (P)

103,232Pa

= (1*8.314*298)/0.024

Amount of gas (n)1 molGas constant8.314 J/(mol·K)Temperature (T)298 KVolume (V)0.024 m³

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…

Correct answer: B. PV = nRT is the correct form.

Q2.If volume doubles at constant T and n, pressure…

Correct answer: B. PV = nRT; if V doubles, P must halve to keep product constant.

Q3.Unit of R is…

Correct answer: B. 8.314 J/(mol·K); J = Pa·m³.

Q4.Temperature must be in…

Correct answer: C. Kelvins (absolute scale) for PV = nRT.

📄Download this topic as a printable worksheet (PDF)Summary + 10 questions + answer key — print it, share it in class.↓

Common mistakes

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Using °C in PV = nRT without converting to K. — Correct: Always convert to Kelvins: K = °C + 273.15.

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Forgetting to convert liters to m³. — Correct: 1 L = 0.001 m³; use consistent SI units.

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Assuming pressure cancels with volume in the law. — Correct: PV is constant for ideal gas; they're inversely proportional.

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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.