Gases – Interactive Study Tool

Kinetic Molecular Theory

Ideal vs Real gases — particle behaviour

Toggle between ideal and real gas. In a real gas, watch particles attract each other and collisions transfer energy (flashes on impact).

Temperature 200 K

Gas type — elastic collisions, no IMFs

ideal gas simulation

Avg speed—

Avg KE—

Collisions0

ModeIdeal

Z = PV/nRT1.00

Ideal gas: point-sized particles · perfectly elastic collisions (no energy lost) · no IMFs · KE ∝ T
Real gas: particles have volume · collisions lose energy (watch the flash) · IMFs pull particles together at low T or high P.
Z factor (PV/nRT) is exactly 1 for an ideal gas. Slide the temperature down with the real gas selected — Z falls below 1 because IMFs make the real pressure lower than PV = nRT predicts. High pressure does the same.

Boyle's Law

Constant temperature · P ∝ 1/V · P₁V₁ = P₂V₂

P₁V₁ = P₂V₂

Push the piston down — same number of particles squeezed into less space → more wall collisions → higher pressure.

Piston pos. 8.0 L

Volume8.0 L

Pressure—

P × V (const.)—

Piston (primary)

P-V graph (secondary)

P × V = constant at constant temperature. The graph is a hyperbola. Double V → half P. Halve V → double P.

Real-World Applications

Medical Syringe

Boyle's Law

Pulling the plunger back increases the volume inside the barrel. Pressure drops below atmospheric, and fluid is pushed into the syringe by the higher external pressure. P₁V₁ = P₂V₂ in action.

Scuba Diving & the Bends

Boyle's Law

At depth, high pressure compresses dissolved gas in blood. If a diver ascends too fast, pressure drops quickly and dissolved N₂ expands into bubbles — causing decompression sickness (the bends).

Chip Bag on a Plane

Boyle's Law

At cruising altitude, cabin pressure is lower than at ground level. The gas inside the sealed chip bag expands (lower P → higher V), making the bag puff up noticeably.

Charles' Law

Constant pressure · V ∝ T · V₁/T₁ = V₂/T₂

V₁T₁ = V₂T₂

Heat the gas — faster particles push the piston up to maintain constant pressure. Cool it — piston drops.

Temperature 300 K

Temperature300 K

Volume—

V / T (const.)—

Piston (primary)

V-T graph (secondary)

Direct relationship — V and T move together. Graph is a straight line. At −273°C (0 K) volume → 0. Always use Kelvin!

Real-World Applications

Hot Air Balloon

Charles' Law

A burner heats the air inside the balloon. Higher T → gas expands → density decreases below surrounding cool air → buoyant force lifts the balloon. Cooling the air makes it descend.

Basketball in the Cold

Charles' Law

Leave a basketball outside on a winter day — it feels flat. The cold air (low T) reduces the volume of gas inside the ball. Bring it inside and it re-inflates as T rises.

Bread Rising in the Oven

Charles' Law

CO₂ bubbles from yeast are trapped in dough. In the hot oven, the gas expands (V ∝ T) — the bubbles grow, pushing the dough upward and giving bread its fluffy texture.

Gay-Lussac's Law

Constant volume · P ∝ T · P₁/T₁ = P₂/T₂

P₁T₁ = P₂T₂

Rigid sealed container — heat increases particle speed → more forceful wall hits → pressure rises. The piston does NOT move.

Temperature 300 K

Temperature300 K

Pressure—

P / T (const.)—

Sealed container (primary)

P-T graph (secondary)

Tire analogy: Cold morning → lower pressure. After driving → tires heat up → pressure rises. Volume stays fixed. That's Gay-Lussac's Law.

Real-World Applications

Aerosol Can Warning

Gay-Lussac's Law

"Do not expose to temperatures above 50°C." The can is a rigid container (constant V). Heating increases gas pressure inside — if P exceeds the can's structural limit, it explodes.

Pressure Cooker

Gay-Lussac's Law

A sealed pot with a fixed volume. Heating raises internal pressure, which raises the boiling point of water above 100°C. Food cooks faster at higher temperatures and pressures.

Car Tire Pressure

Gay-Lussac's Law

After highway driving, friction heats the tires. The air inside the rigid tire (constant V) increases in temperature → pressure rises. That's why TPMS readings are higher after a long drive.

Avogadro's Law

Constant T and P · V ∝ n · V₁/n₁ = V₂/n₂

V₁n₁ = V₂n₂

Blow more air into the balloon — more moles of gas → balloon visibly expands. Same T, same P throughout.

Moles (n) 1.0 mol

Moles1.0 mol

Volume—

V / n (const.)—

At STP, 1 mole of any ideal gas = 22.4 L. H₂, O₂, CO₂ — doesn't matter. Same moles, same volume. The balloon shows this directly.

Real-World Applications

Breathing & Lungs

Avogadro's Law

When you inhale, your diaphragm contracts and pulls air molecules into your lungs. More moles of gas enter → lung volume increases. Exhale and moles leave → volume decreases. V ∝ n in action.

Bicycle Pump

Avogadro's Law

Each pump stroke pushes more moles of air into the tire. As n increases at roughly constant T and P, the tire inflates — its volume grows proportionally to the moles added.

Car Airbag

Avogadro's Law

On impact, NaN₃ decomposes rapidly producing N₂ gas. A huge number of moles are generated in milliseconds — the volume of the bag inflates almost instantly to cushion the occupant.

Ideal Gas Law

PV = nRT — all four variables

PV = nRT

Pick the variable to solve for, then set the other three. R = 8.314 L·kPa/mol·K

Solve for:

P

Pressure

V

Volume

n

Moles

T

Temperature

P (kPa)250

V (L)10.0

n (mol)1.0

T (K)300

Calculated Pressure

—

kPa

Have a mass instead of moles? Use n = m ÷ mm. Fill both boxes and it overrides the n slider (unless you are solving for n).

mass m (g) molar mass mm (g/mol)

R merges Boyle's, Charles', and Avogadro's constants. Use R = 8.314 for kPa, R = 0.08206 for atm. Always work in Kelvin.

Real-World Applications

🤿

How much air is in a scuba tank

Ideal Gas Law

An 11 L tank filled to 20 000 kPa at 25 °C holds n = PV/RT = (20 000 × 11)/(8.314 × 298) ≈ 88.8 mol of air. Divers use this to work out their dive time before the tank runs low.

🎈

Sizing a weather balloon

Ideal Gas Law

Meteorologists solve V = nRT/P for the helium volume needed at launch, knowing it will expand as pressure drops with altitude. PV = nRT sets the launch size and the burst size.

⚗️

Molar mass of an unknown gas

Ideal Gas Law

Weigh a gas sample, measure P, V and T, find n = PV/RT, then mm = m ÷ n. This is how a gas of unknown identity is fingerprinted in the lab.

Combined Gas Law

P₁V₁/T₁ = P₂V₂/T₂ — solve for any variable

P₁V₁T₁ = P₂V₂T₂

Choose which variable to solve for, then set the other five.

Solve for:

P₁

Initial pressure

V₁

Initial volume

T₁

Initial temp

P₂

Final pressure

V₂

Final volume

T₂

Final temp

State 1

P₁ (atm)1.0

V₁ (L)10.0

T₁ (K)300

State 2

P₂ (atm)2.0

V₂ (L)5.0

T₂ (K)400

Solving for P₁ =

—

atm

Simplifications: constant T → Boyle's (P₁V₁=P₂V₂) · constant P → Charles' (V₁/T₁=V₂/T₂) · constant V → Gay-Lussac's (P₁/T₁=P₂/T₂).

Real-World Applications

🎈

Weather balloon rising

Combined Gas Law

As a balloon climbs, pressure falls, temperature falls, and volume grows — all three change at once. P₁V₁/T₁ = P₂V₂/T₂ predicts the balloon's size at any altitude.

🫁

A breath from cold air to body temperature

Combined Gas Law

Air inhaled on a −10 °C day is warmed to 37 °C in the lungs while pressure barely changes — its volume expands. The combined law gives the new volume from the old.

🤿

A bubble on the way up

Combined Gas Law

A diver's exhaled bubble rises through warmer, lower-pressure water and swells. Both P and T change, so you need P₁V₁/T₁ = P₂V₂/T₂, not Boyle's alone.

Dalton's Law of Partial Pressures

P_total = P_A + P_B + ... · Collecting gas over water

P_total = P_A + P_B + P_C

Partial pressure mixer

O₂ (kPa)80

N₂ (kPa)60

CO₂ (kPa)40

P_total—

Collecting gas over water

Temp (°C) 20°C

P_total—

P_H₂O—

P_dry gas—

Collecting gas over water: When gas is collected by water displacement, the collected gas is wet — it contains water vapour. Use P_{dry gas} = P_total − P_H₂O. The water vapour pressure depends only on temperature (see the vapour-pressure table below).

Mole fraction

x_A = n_An_total P_A = x_A × P_total

The mole fraction x_A is the fraction of all the gas molecules that are A. Each gas's partial pressure is that same fraction of the total pressure. All the mole fractions in a mixture add to 1.

Water vapour pressure vs temperature

T (°C)	0	5	10	15	20	22	25	30	35
P_H₂O (kPa)	0.61	0.87	1.23	1.71	2.34	2.64	3.17	4.25	5.63

P_{dry gas} = P_total (barometric) − P_H₂O at the collection temperature.

Virtual lab — collecting H₂ over water

Realistic data for a class prep of hydrogen by Zn + 2HCl, collected by water displacement. Work through it, then reveal the analysis.

Barometric pressure	101.3 kPa
Water / room temperature	22.0 °C
Volume of gas collected	45.0 mL
Water vapour pressure at 22 °C (table)	2.64 kPa

Step 1 · dry-gas pressure: P_H₂ = 101.3 − 2.64 = 98.7 kPa
Step 2 · moles of H₂: n = PV/RT = (98.7 × 0.0450) / (8.314 × 295.15) = 4.44 / 2454 = 1.81 × 10⁻³ mol
Step 3 · mass of H₂: m = n × mm = 1.81 × 10⁻³ × 2.02 = 3.66 × 10⁻³ g
Forgetting to subtract the water vapour would overstate the moles of H₂ by about 2.7 %.

Real-World Applications

Earth's Atmosphere

Dalton's Law

Atmospheric pressure (101.3 kPa) is the sum of partial pressures: ~78 kPa from N₂, ~21 kPa from O₂, and small contributions from Ar, CO₂, and other trace gases.

Scuba Tank Gas Mix

Dalton's Law

Divers use Nitrox (enriched air) to reduce N₂ partial pressure at depth. At 30 m, total pressure is ~4 atm — controlling each gas's partial pressure prevents nitrogen narcosis and oxygen toxicity.

Humidity & Weather

Dalton's Law

Water vapour adds its own partial pressure to the atmosphere. When P_H₂O reaches the saturation vapour pressure at a given temperature, condensation occurs — forming clouds, dew, and fog.

Graham's Law of Effusion

r₁/r₂ = √(mm₂/mm₁) — lighter = faster

r₁/r₂ = √(mm₂/mm₁)

Set molar masses. Lighter gas travels faster — they meet closer to the heavy gas side.

Gas 1 mm17 g/mol

H₂=2 · He=4 · CH₄=16 · NH₃=17 · Ne=20 · N₂=28 · O₂=32 · HCl=36.5 · Ar=40 · CO₂=44 · Cl₂=71 · Kr=84 · SF₆=146 · UF₆=352

Gas 2 mm36 g/mol

Gas 1 rate—

Gas 2 rate—

Rate ratio—

Meet at—

Gas 1 → ← Gas 2

All gases at the same T have the same average KE = ½mv². Lighter mass → must move faster. NH₄Cl smoke ring forms closer to HCl end because NH₃ (lighter) travels farther.

Real-World Applications

Perfume Diffusion

Graham's Law

Lighter perfume molecules diffuse faster through air. You smell perfume across the room because volatile molecules (low molar mass) travel rapidly from high to low concentration.

Smelling Dinner from Another Room

Graham's Law

Light, volatile aroma molecules (esters, ~90 g/mol) diffuse through the house faster than heavier ones. That is why the smell of baking cookies reaches the bedroom before the smell of the roast — lower molar mass means a higher average speed at the same temperature.

Helium Balloon Deflating

Graham's Law

Helium (4 g/mol) effuses through tiny pores in latex ~2.7× faster than O₂ (32 g/mol). That's why helium balloons go flat overnight while air-filled ones last weeks.

Gas Stoichiometry

Balanced equation → mole ratio → volume, mass, or moles of gas

For gases measured at the same temperature and pressure, volume ratios equal mole ratios (Avogadro). At STP use the molar volume 22.4 L/mol; at any other conditions use PV = nRT.

Practice — reveal each solution

Periodic Table

Class-standard table · based on mass of carbon-12 = 12.00

Read molar masses off this table for Graham's Law, the Ideal Gas Law and gas stoichiometry.

Ion Chart

Class-standard chart · common cations, anions & polyatomic ions with their charges

Names, formulae, and charges of common ions — positive ions (cations) and negative ions (anions)

Use these charges to write correct formulas for gases produced in reactions and for gas-stoichiometry problems.

Summary of All Gas Laws

Quick reference

Law	Formula	Constant	Relationship	Key idea
Boyle's	P₁V₁ = P₂V₂	T, n	Inverse P↑ V↓	Squeeze → more wall hits
Charles'	V₁/T₁ = V₂/T₂	P, n	Direct V↑ T↑	Heat → piston rises
Gay-Lussac's	P₁/T₁ = P₂/T₂	V, n	Direct P↑ T↑	Heat sealed tank → P rises
Avogadro's	V₁/n₁ = V₂/n₂	T, P	Direct V↑ n↑	More moles → balloon grows
Ideal Gas	PV = nRT	—	All four vars	R = 8.314 (kPa) or 0.08206 (atm)
Combined	P₁V₁/T₁ = P₂V₂/T₂	n	Solve any var	Boyle + Charles + Gay-Lussac
Dalton's	P_tot = ΣP_i	T, V	Additive	P_dry = P_total − P_H₂O
Graham's	r₁/r₂ = √(mm₂/mm₁)	T, P	Inverse √	Lighter = faster effusion

Always: T in Kelvin (K = °C + 273). For PV = nRT match R to pressure units.

Gas Laws Practice Quiz

30 questions · 20 seconds each · Speed bonus scoring

⚖️

Ready to test your knowledge?

Covers KMT, temperature conversions, Boyle's, Charles', Gay-Lussac's, Avogadro's, the Combined and Ideal Gas Laws, Dalton's Law and mole fraction, Graham's Law, and gas stoichiometry.

30

Questions

20s

Per question

1000

Max points

Tip: answer with keys 1–4 or A–D, and press Enter to move on. Answering faster scores more — but a wrong fast answer is still worth nothing. All numerical answers are rounded to 3 significant figures.

Gases — Interactive Study Tool