IntoChemistry

I-11: Gas law mathematics

IntoChemistry | General Chemistry I Math Readiness

Free of subscriptions • Self-paced • Text-based and keyboard accessible

Course home

Module I-11 · Recommended before: Before ideal-gas and gas-mixture problems

Gas law mathematics

Temperature in gas equations is absolute: convert °C to K. Pressure and gas-constant units must match.

Learn the method

P V = n R T

  1. Write the relevant law.
  2. Convert temperature to kelvin.
  3. Choose a gas constant with matching units.
  4. Rearrange the equation.
  5. Check whether the answer has the requested units.

Common mistake: Never place a Celsius temperature directly into PV = nRT.

Worked example

Problem: A sample has n = 1.00 mol, T = 300 K, and P = 1.00 atm. Find V using R = 0.08206 L·atm/(mol·K).

Step-by-step solution: V = nRT/P = (1.00)(0.08206)(300)/(1.00) = 24.6 L.

Check the units and whether the answer is reasonable before continuing.

More applications of this mathematics

Try each extension before expanding its solution.

Combined gas law

At constant moles, gas changes from 2.00 L at 300 K to 350 K at constant pressure: V₂ = V₁T₂/T₁ = 2.33 L.

Partial pressure

For gas mole fraction 0.30 at total pressure 2.00 atm, partial pressure = (0.30)(2.00) = 0.60 atm.

Graham’s law and gas density

For gases at the same temperature, r₁/r₂=√(M₂/M₁). Approximate H₂ relative to O₂: √(32/2)=4 times the effusion rate. Gas density can also be found from d=PM/(RT).

Independent practice — five questions

Suggested mastery threshold: four out of five. Incorrect answers display a worked explanation after submission.

Choose one response for each question, then select “Check my answers.” No timer. Hints are optional. You can retry freely. Questions are formative, not proctored.

Question 1. Find V for n=2.5 mol, T=320 K and P=1.25 atm. Use R=0.08206 L·atm/(mol·K).
Hint for question 1

Use absolute temperature and match pressure units.

Question 2. Find V for n=0.75 mol, T=280 K and P=0.75 atm. Use R=0.08206 L·atm/(mol·K).
Hint for question 2

Use absolute temperature and match pressure units.

Question 3. Find V for n=1.25 mol, T=360 K and P=1.2 atm. Use R=0.08206 L·atm/(mol·K).
Hint for question 3

Use absolute temperature and match pressure units.

Question 4. Find V for n=3 mol, T=310 K and P=3 atm. Use R=0.08206 L·atm/(mol·K).
Hint for question 4

Use absolute temperature and match pressure units.

Question 5. Find V for n=4 mol, T=290 K and P=2 atm. Use R=0.08206 L·atm/(mol·K).
Hint for question 5

Use absolute temperature and match pressure units.

Supporting reference

OpenStax Chemistry 2e / NIST — reference for this subject. This lesson’s wording, examples and questions are original.

W3C WCAG 2.2 accessibility guidance.

IntoChemistry original instructional content, 2026. Formative feedback is not an official course grade. Sources are linked for independent reading. Accessibility testing with your institution and assistive technology is still recommended.