What is the Ideal Gas Law?
The ideal gas law connects pressure, volume, temperature, and the amount of gas into a single equation. It's one of the most useful relationships in physics and chemistry for predicting how gases behave under changing conditions.
The ideal gas law states that PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is absolute temperature — meaning pressure and volume together scale directly with the amount of gas and its temperature.
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Step-by-step worked examples
2 mol of gas at 300 K occupies 0.05 m³. Find the pressure.
P = nRT/V = 2 × 8.314 × 300 / 0.05 = 4988.4 / 0.05 P ≈ 99768 Pa ≈ 99.77 kPa
A gas at pressure 101325 Pa and volume 0.025 m³ is at 273 K. How many moles does it contain?
n = PV/RT = (101325 × 0.025) / (8.314 × 273) = 2533.125 / 2269.7 n ≈ 1.12 mol
1 mol of gas at constant volume 0.02 m³ is heated from 250 K to 500 K. Find the pressure change.
P1 = nRT1/V = 1 × 8.314 × 250 / 0.02 = 103925 Pa P2 = nRT2/V = 1 × 8.314 × 500 / 0.02 = 207850 Pa Pressure doubles when temperature doubles at constant n and V.
Flashcards
Quick quiz
Q1.In PV = nRT, what does 'n' represent?
Q2.If temperature doubles at constant volume and moles, what happens to pressure?
Q3.What are the correct SI units of R?
Q4.A gas has n = 0.5 mol, T = 400 K, V = 0.01 m³. What is P?
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Common mistakes
Using Celsius temperature in the equation. — Correct: Always convert to Kelvin (K = °C + 273.15) since the law requires absolute temperature.
Forgetting to convert volume to m³ when using R = 8.314. — Correct: Match units — use R = 8.314 J/(mol·K) with V in m³, or R = 0.0821 L·atm/(mol·K) with V in liters and P in atm.
Treating the ideal gas law as exact for all gases. — Correct: It's an approximation that works best at low pressure and high temperature; real gases deviate, especially near condensation.
Assuming n stays constant when gas escapes a container. — Correct: n changes if gas is added or removed — it isn't always fixed.
FAQ
What is the ideal gas law?
PV = nRT relates the pressure, volume, amount of gas, and temperature of an ideal gas.
What is the ideal gas law formula?
PV = nRT, where R = 8.314 J/(mol·K).
What are examples of the ideal gas law?
Predicting pressure in a scuba tank, calculating gas volume changes when heated, and weather balloon expansion at altitude.
How do you calculate pressure using the ideal gas law?
Rearrange to P = nRT/V and plug in moles, temperature in Kelvin, and volume in m³.