Preview

Gases: Introduction

Q: If you halve the volume at constant temperature, what happens to pressure?

Boyle's Law: PV = const → P doubles.

Q: At 300K the gas occupies 10L. What volume at 600K (constant pressure)?

Charles's Law: V₁/T₁ = V₂/T₂ → V₂ = 20L.

Q: Why does a sealed balloon shrink in a cold room?

Constant n and P → V ∝ T; lower T means smaller V.

Explore pressure, volume, temperature, and the Ideal Gas Law

Pump fifty invisible particles into a glass box and nothing seems to happen. Nothing you can see, anyway — inside, every particle is sprinting in a straight line until it slams into a wall, bounces, and does it again, billions of times a second in a real gas. That drumbeat on the walls has a name you already know: pressure. This lab lets you watch the drumbeat get negotiated. The particles never touch each other — they can't, there's no code for it — yet the box still reads a pressure, because pressure was never about particles jostling each other. It is only ever the wall hits: how hard, and how many per second. Now you get three levers. Temperature makes every sprinter faster — but obeying a square root, so doubling the kelvins buys only √2 the speed while the pressure, which cashes both the speed and the hit-rate, doubles in full. Particle count adds drummers — twice the particles, exactly twice the pressure, and the temperature row doesn't even blink, because temperature is the average energy per particle and never sees the headcount. And the box itself shrinks, crowding the same drummers onto less wall, so the hits-per-second climb. Keep one eye on the PV/nRT row: it reads 1.000 everywhere, the signature of an ideal gas — a gas that plays by PV = nRT exactly. You've met that law from the outside, on PV diagrams. This is the same law from the inside — one wall hit at a time.

What you'll be able to do

Run the ideal-gas-law accounts with the panel's own numbers: at the factory state (50 particles = 0.5 mol, Volume Scale 3 → 0.885 L, 400 K) the P row reads 1879.4; double the count 50→100 and it doubles exactly to 3758.9 — 'equal volumes of all gases, measured under the same conditions of temperature and pressure, contain the same number of molecules' read backward as P ∝ n (§9.2, Avogadro); sweep T 200→800 K at fixed box and count and P climbs linearly 939.7 → 3758.9 ('directly proportional to its temperature on the kelvin scale', §9.2); squeeze Volume Scale 5→1 and P rises 962.3 → 4454.9, inversely with the TRUE volume (6+1.2s)³ — never with the slider's ×-label (registered affine quirk b)
Explain pressure microscopically: it 'results from collisions between the gas molecules and the container walls' (§9.5, postulate 3) — this engine renders the postulate literally, with ZERO particle-particle collisions anywhere in the code, and still reads 7883.9 on High Density; pressure 'depends directly on the number of molecules hitting a unit area of the wall per unit of time' (§9.5), which is why doubling the count doubles P; heating works because 'the average kinetic energy of the gas molecules is proportional to the kelvin temperature' (postulate 5), so the reseeding machine's speed scale obeys v ∝ √T — 2.86 → 4.04 → 5.72 scene units across 200 → 400 → 800 K, doubling the kelvins buys only √2 the speed
Read the PV/nRT row as the ideality ledger: it sits at 1.000 at every state because this gas is ideal by construction — and, honestly, because the panel COMPUTES P from the law itself (registered quirk d: the row is self-carried, an identity, not a measurement); the row's real teaching payload is scope — the ideal approximation holds 'under conditions of relatively low pressure and high temperature' (§9.2) — and unit discipline: R = 8.314 with litres gives kPa (§9.2's own '8.314 kPa L mol⁻¹ K⁻¹'), so the panel's 'Pa' label is 1000× off as physics (registered quirk a) and the displayed number is anchored as-is

Formulas

PV = nRT

Ideal Gas Law

P \propto \frac{1}{V}

Boyle's Law (constant T)

V \propto T

Charles's Law (constant P)

Make a prediction

Default state: 50 particles in the ×3 box at 400 K — the panel reads P = 1879.4. You drag Particle Count from 50 to 100 (Temperature and Volume Scale locked). What happens?

No grading here — commit to a guess, then scroll down and test it yourself.

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Run the doubling gate live: from the default state (P = 1879.4), drag Particle Count 50 → 100 and watch the formation — P doubles exactly to 3758.9, the Temperature row holds 400 K without blinking, and PV/nRT stays pinned at 1.000. Twice the drummers, twice the drumbeat, same average energy per drummer.
Sweep Temperature 200 → 800 K at the default box and count: the P row climbs linearly 939.7 → 3758.9 while the swarm migrates from blue to red. The square root hides underneath: the engine's speed scale runs 2.86 → 4.04 → 5.72 scene units — doubling the kelvins buys only √2 the speed, but pressure cashes speed AND hit-rate, so it doubles in full.
Squeeze the box at fixed 400 K and 50 particles: drag Volume Scale 5 → 1 and watch P climb 962.3 → 4454.9 — rising as the box shrinks, Boyle's inverse law. Then catch the slider in its fib: '×3' is not a scale factor (the edge is 6 + 1.2×s), so dragging 3 → 1.5 shrinks the true volume only ×0.536 and P rises ×1.86, not ×2. Trust the Volume row, not the ×-label.
Audit all three presets: High Density (500 K, ×1.5, 90 particles) reads 7883.9 — the board's ceiling, booked by wall hits alone with zero particle-particle collisions in the code. Then compare Boyle's Demo against the default state: volume ×1/1.4927, pressure ×1.4927, exact inverses. Finish on the PV/nRT row: 1.000 at every state you can build — the ideal-gas signature.

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Check

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Your prediction

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Answer: P doubles to 3758.9 and the Temperature row holds 400 K — twice the particles means twice the wall-collision drumbeat, but temperature is the AVERAGE kinetic energy per particle, and the average never saw the headcount

Avogadro's law read backward: at fixed temperature and volume, pressure is proportional to the amount of gas — 'equal volumes of all gases, measured under the same conditions of temperature and pressure, contain the same number of molecules' (OpenStax Chemistry 2e §9.2). The mechanism is one section over: pressure 'depends directly on the number of molecules hitting a unit area of the wall per unit of time' (§9.5), so doubling the headcount doubles the drumbeat — the engine's own ledger moves 0.5 → 1.0 mol and P = nRT/V answers 1879.4307 → 3758.8614, displayed 3758.9. Option B fails on that same sentence: the state DID change — you added gas — and the wall hits per second doubled with it. Option C is the misconception this gate targets, and the sim's own Key Facts card carries the antidote verbatim: 'Temperature measures average kinetic energy per molecule — not total energy. More molecules = more total energy even at same T.' The textbook states it as a postulate: 'The average kinetic energy of the gas molecules is proportional to the kelvin temperature' (§9.5, postulate 5). The box really does hold twice the total kinetic energy after your drag — but temperature was never the total; it is the per-particle average, and the average is untouched, so the Temperature row sits at 400 K through the whole drag. Watch the PV/nRT row as you go: it never leaves 1.000 — the gas stays ideal, just twice as crowded.

Quiz (0/3)

If you halve the volume at constant temperature, what happens to pressure?

At 300K the gas occupies 10L. What volume at 600K (constant pressure)?

Why does a sealed balloon shrink in a cold room?

You can now

Run the ideal-gas-law accounts with the panel's own numbers: at the factory state (50 particles = 0.5 mol, Volume Scale 3 → 0.885 L, 400 K) the P row reads 1879.4; double the count 50→100 and it doubles exactly to 3758.9 — 'equal volumes of all gases, measured under the same conditions of temperature and pressure, contain the same number of molecules' read backward as P ∝ n (§9.2, Avogadro); sweep T 200→800 K at fixed box and count and P climbs linearly 939.7 → 3758.9 ('directly proportional to its temperature on the kelvin scale', §9.2); squeeze Volume Scale 5→1 and P rises 962.3 → 4454.9, inversely with the TRUE volume (6+1.2s)³ — never with the slider's ×-label (registered affine quirk b)
Explain pressure microscopically: it 'results from collisions between the gas molecules and the container walls' (§9.5, postulate 3) — this engine renders the postulate literally, with ZERO particle-particle collisions anywhere in the code, and still reads 7883.9 on High Density; pressure 'depends directly on the number of molecules hitting a unit area of the wall per unit of time' (§9.5), which is why doubling the count doubles P; heating works because 'the average kinetic energy of the gas molecules is proportional to the kelvin temperature' (postulate 5), so the reseeding machine's speed scale obeys v ∝ √T — 2.86 → 4.04 → 5.72 scene units across 200 → 400 → 800 K, doubling the kelvins buys only √2 the speed
Read the PV/nRT row as the ideality ledger: it sits at 1.000 at every state because this gas is ideal by construction — and, honestly, because the panel COMPUTES P from the law itself (registered quirk d: the row is self-carried, an identity, not a measurement); the row's real teaching payload is scope — the ideal approximation holds 'under conditions of relatively low pressure and high temperature' (§9.2) — and unit discipline: R = 8.314 with litres gives kPa (§9.2's own '8.314 kPa L mol⁻¹ K⁻¹'), so the panel's 'Pa' label is 1000× off as physics (registered quirk a) and the displayed number is anchored as-is