How can pressure tell us how much gas is present?
You will be able to: Choose consistent units and solve PV = nRT for an unknown gas quantity.
How can pressure tell us how much gas is present?
A sealed 4.00 L container holds 0.200 mol of a gas at 300 K. Pressure depends on how many particles strike the walls, how vigorously they move, and how much space they occupy.
A useful starting point: What changes when a substance changes state? →
Words and symbols before equations
- P
- Gas pressure; use atmospheres with the R value here.
- V
- Container volume in liters (L).
- n
- Amount of gas in moles (mol).
- T
- Absolute temperature in kelvin (K), T = °C + 273.15.
- R
- Gas constant, 0.08206 L·atm·mol⁻¹·K⁻¹ for this unit choice.
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
The ideal gas model treats particle volume and attractions as negligible. Under appropriate conditions it relates observable pressure, volume, amount and temperature through PV = nRT.
Before calculating, list quantities with their units. Rearrange for the unknown, then substitute. Converting 4000 mL to 4.000 L or Celsius to kelvin is part of the reasoning, not an optional final step.
The units in R determine which pressure and volume units to use. The result should also make qualitative sense: more gas or higher temperature raises pressure at fixed volume.
A worked example, step by step
Find P for n = 0.200 mol, V = 4.00 L and T = 300 K, assuming ideal behavior.
- Choose R = 0.08206 L·atm·mol⁻¹·K⁻¹ to match L, mol and K.
- Divide PV = nRT by V: P = nRT/V.
- Substitute: P = (0.200)(0.08206)(300)/(4.00) = 1.2309 atm.
- Report about 1.23 atm. This is an absolute pressure for the ideal model, not a gauge-pressure difference.
Use kelvin, not Celsius, in gas-law ratios and products. Match the units of R.
Does doubling n double P at fixed V and T in this model?
Compare with an explanation
Yes. P = (RT/V)n, so the fixed factor multiplies twice as many moles.
Predict. Change one thing. Explain.
Start at 0.200 mol, 4.00 L and 300 K. Double the amount while holding temperature and volume fixed. Predict and explain the pressure change.
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 gas has P = 2.00 atm, V = 3.00 L and T = 300 K. Find n using R = 0.08206 L·atm·mol⁻¹·K⁻¹, and state a condition that can make the model inaccurate.
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Compare with the answer and four-point rubric
- 1 point: Rearrange to n = PV/(RT).
- 1 point: Substitute n = (2.00)(3.00)/[(0.08206)(300)].
- 1 point: Obtain approximately 0.244 mol with consistent units.
- 1 point: High density or appreciable attractions, often at high pressure or low temperature, can cause nonideal behavior.
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 1Why convert °C to K?
The gas law uses absolute temperature, proportional to average translational kinetic energy.
RECALL 2What does n measure?
Amount of gas in moles.
RECALL 3Which two idealizations matter?
Negligible particle volume and negligible interparticle attractions.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
How can pressure tell us how much gas is present?
- PV = nRT; P = nRT/V.
- R = 0.08206 L·atm·mol⁻¹·K⁻¹; T(K) = T(°C) + 273.15.
Remember: Use kelvin, not Celsius, in gas-law ratios and products. Match the units of R.
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.
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