What stays fixed when a gas variable changes?
You will be able to: Predict and graph direct or inverse gas-law relationships under stated constraints.
What stays fixed when a gas variable changes?
Compressing a sealed gas slowly at constant temperature raises its pressure. Warming it in a rigid sealed container also raises pressure, but a different variable was held fixed.
A useful starting point: How can pressure tell us how much gas is present? →
Words and symbols before equations
- Direct proportion
- Multiplying one quantity by a factor multiplies the other by the same factor.
- Inverse proportion
- Multiplying one quantity by a factor divides the other by that factor.
- Rigid container
- A container whose volume stays fixed.
- Isothermal
- At constant temperature.
What this picture assumes
Ideal gas at equilibrium: negligible particle volume and attractions. R = 0.08206 L·atm·mol⁻¹·K⁻¹. The P–V graph changes V while keeping the displayed n and T fixed; its dot marks the selected V.
Read the picture in three steps
- Read the species and labels first. Identify what each symbol and line represents. Read the units and fixed conditions before comparing quantities.
- P = 1.231 atm; PV = 4.924 L·atm for n = 0.2 mol and T = 300 K.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the chemistry
At fixed n and T, PV = nRT is constant. P therefore varies as 1/V: a P–V graph is a curve, while a P versus 1/V graph is a straight line through the ideal origin.
At fixed n and V, P/T is constant when T is in kelvin. At fixed n and P, V/T is constant. Name the fixed quantities before applying any simplified law.
For a sealed sample that remains ideal, P₁V₁/T₁ = P₂V₂/T₂. If gas enters, escapes or reacts to change the gas amount, this fixed-n relation is insufficient.
A worked example, step by step
A sealed ideal sample occupies 6.0 L at 1.0 atm. It is compressed isothermally to 2.0 L. Find the new pressure.
- Sealed means n is constant; isothermal means T is constant.
- Use P₁V₁ = P₂V₂.
- P₂ = (1.0 atm)(6.0 L)/(2.0 L) = 3.0 atm.
- Volume became one-third, so pressure tripled. The product PV remained 6.0 L·atm.
“Pressure increases with temperature” assumes other relevant variables stay fixed. A flexible container can expand instead.
At fixed amount and volume, does heating from 20 °C to 40 °C double pressure?
Compare with an explanation
No. The relevant ratio is 313.15/293.15, about 1.068, not 40/20.
Predict. Change one thing. Explain.
Hold amount and temperature fixed. Compare V = 2, 4 and 8 L on the P–V graph. Check that PV remains constant even though the graph is not a straight line.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
P = 1.231 atm; PV = 4.924 L·atm for n = 0.2 mol and T = 300 K.
Ideal gas at equilibrium: negligible particle volume and attractions. R = 0.08206 L·atm·mol⁻¹·K⁻¹. The P–V graph changes V while keeping the displayed n and T fixed; its dot marks the selected V.
Explain what you noticed: Answer the investigation prompt above. State one observation and explain it using particle interactions, concentration, gas behavior or energy transfer. Identify what the representation cannot tell you.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionAn ideal sample changes from 2.0 L, 300 K to 4.0 L, 450 K at fixed n. Its initial pressure is 3.0 atm. Predict P₂ and explain why heating did not necessarily increase pressure.
This response is not submitted or saved. Copy it before leaving.
Compare with the answer and four-point rubric
- 1 point: Use P₂ = P₁(V₁/V₂)(T₂/T₁).
- 1 point: Substitute 3.0 × (2.0/4.0) × (450/300).
- 1 point: Obtain 2.25 atm, about 2.3 atm to two significant figures.
- 1 point: Heating raises the pressure factor by 1.5, but doubling volume supplies a factor of 0.5; the net factor is 0.75.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1What must every gas-law comparison state?
Which variables are fixed.
RECALL 2Why is P versus V curved at fixed n,T?
Pressure is proportional to 1/V.
RECALL 3Can a pressure prediction use Celsius ratios?
No; convert to kelvin first.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
What stays fixed when a gas variable changes?
- Fixed n,T: P₁V₁ = P₂V₂.
- Fixed n,V: P₁/T₁ = P₂/T₂.
- Fixed n: P₁V₁/T₁ = P₂V₂/T₂.
Remember: “Pressure increases with temperature” assumes other relevant variables stay fixed. A flexible container can expand instead.
Conditions: Ideal gas at equilibrium: negligible particle volume and attractions. R = 0.08206 L·atm·mol⁻¹·K⁻¹. The P–V graph changes V while keeping the displayed n and T fixed; its dot marks the selected V.
Refresh Kid · AP Chemistry Unit 3 · Objectives 3.4.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 3.4, objective 3.4.A. CED effective Fall 2024 and June 2026 clarifications checked September 16, 2026. Unit 3: Properties of Substances and Mixtures, Topics 3.1–3.13. Focused lesson names, examples, models and assessments are original Refresh Kid teaching materials, not additional official topics or official AP questions. Official corrections.
The model states its assumptions beside the diagram. Colligative-property calculations and solution molality/mass-percent/volume-percent calculations are not required here. The optional speed-density model illustrates distributions; it does not require memorizing its mathematical derivation.
Teaching resources: The Organic Chemistry Tutor video titles/descriptions and topic coverage were checked for optional links; no claim is made to have watched every video. No creator scripts, examples, worksheets or artwork were copied. GitHub’s 3D website collection and its Three.js camera-control example informed the idea of controllable spatial inspection. Scientific diagrams, geometry and interactions here are original. The self-hosted Three.js runtime retains its MIT license. Camera rotation changes the view, not the chemistry.
Independent teacher review and observation of students remain pending. Implementation checks do not certify scientific accuracy, accessibility or learning effectiveness. This is a review edition.
Optional official resource: Released AP Chemistry questions and scoring guides. This archive contains questions across units; it is not an assignment of every question to this lesson.
The teaching sequence is informed by the IES learning guide; this exact implementation has not been evaluated with learners.
Want to work through this with a tutor?
Bring your question about What stays fixed when a gas variable changes? Your explanation and answers remain free to access.