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Ideal gas law practice problems

The ideal gas law connects pressure, volume, amount and absolute temperature. Choose a compatible gas constant and convert temperature to kelvin before calculating.

By ExamCat · Original study lesson · Published September 24, 2026

Understand the method

PV = nRT describes an idealized gas. With R ≈ 0.08206 L·atm/(mol·K), pressure must be in atmospheres and volume in liters. Real gases depart from this model, especially where particle volume and attractions become important.

Worked example, step by step

Find the volume of 0.50 mol of an ideal gas at 300 K and 1.0 atm.

  1. Rearrange to V = nRT/P before substituting.
  2. Insert compatible values: V = 0.50 × 0.08206 × 300/1.0.
  3. The unrounded result is 12.309 L, approximately 12 L to two significant figures.
  4. Check the direction: at the same pressure and temperature, twice the amount would occupy twice the volume.

A mistake to watch for

Using 27 instead of approximately 300 for a temperature near 27°C does not merely change rounding; it changes the physical temperature scale in the proportionality.

Try it yourself: three questions

Write an answer before opening the explanation. For calculations, keep your units and intermediate steps; for concepts, state the reason for your choice.

1. At fixed amount and temperature, pressure doubles. What happens to ideal-gas volume?

Show answer and explanation

It halves because PV remains constant under these specific conditions.

2. At fixed volume and amount, temperature rises from 250 K to 500 K. What happens to pressure?

Show answer and explanation

Pressure doubles. This uses absolute temperature; doubling a Celsius reading is not the same operation.

3. A gas has P = 2 atm, V = 4.1 L and T = 250 K. Estimate n.

Show answer and explanation

n = PV/RT = 8.2/(0.08206 × 250) ≈ 0.40 mol. The chosen units cancel to moles.

Build your next practice session

Mark the first step where your reasoning differed from the explanation. Turn that step into a question, answer it without looking, then change one condition in the example and explain what would change. A correct guess is a reason to revisit the method.

Use the free flashcard maker for your own question-and-answer pairs, or bring your course material into PDF-to-flashcards practice.

Further reading

OpenStax Chemistry 2e provides textbook background. The worked scenario and practice questions on this page were written independently for ExamCat.

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