Gas Laws

Gas molecules fly in all directions and hit the walls; the sum of those impacts is pressure. Boyle’s law keeps PV constant at fixed T and n, and Charles’s law makes V proportional to absolute temperature at fixed P and n. Together they form the ideal gas equation PV = nRT, and mixed gases follow Dalton’s law of partial pressures. Here you change pressure and temperature to watch volume respond and build intuition for PV = nRT.

How Do Gas Molecules Behave?

💡 Analogy: A Room Full of Ping-Pong Balls

①Gas molecules = ping-pong balls flying everywhere

②Higher T → balls fly faster → hit walls harder

③Pressure = total force from balls hitting walls

④Smaller room (volume) → hit more often → pressure ↑

⑤More balls (moles) → more frequent hits → pressure ↑

Visualizing the Ideal Gas Law

Pressure P1 atm

Temperature T27 °C

Ideal Gas Equation

PV = nRT

P (atm), V (L), n (mol), R = 0.0821, T: absolute temperature (K)

🔍 Try the Two Sliders!

①P↑ → V↓ (Boyle's law: PV constant at fixed T)

②T↑ → V↑ (Charles's law: V/T constant at fixed P)

③Isotherms on PV graph are hyperbolas

④The red dot shows the current state

Combining Three Laws → Ideal Gas Equation

Boyle's Law

P₁V₁ = P₂V₂ (T, n constant)

At fixed T → P and V are inversely proportional

Charles's Law

V₁T₁ = V₂T₂ (P, n constant)

At fixed P → V proportional to absolute T

Avogadro's Law

V₁n₁ = V₂n₂ (P, T constant)

Equal volumes of gas at same conditions contain equal molecules

💡 Why Do the Three Laws Combine into One?

①Boyle: P, V inverse (push a balloon, it shrinks)

②Charles: V, T proportional (heat a balloon, it expands)

③Avogadro: V, n proportional (more air → larger balloon)

④Combine three → PV = nRT (ideal gas)

⑤T must be in K: K = °C + 273

Gas Mixtures and Partial Pressure

Dalton's Law of Partial Pressures

P_total = P₁ + P₂ + P₃ + ⋯

Sum of independent pressures from each gas

Mole Fraction and Partial Pressure

P_i = x_i × P_total = n_in_total × P_total

mole fraction × total pressure = partial pressure

💡 Why Do Real Gases Differ?

①'Ideal gas' = no intermolecular forces + negligible molecular volume

②At high P or low T, real gases deviate from ideal

③Reason: intermolecular attraction and finite molecular volume

④At STP (0°C, 1 atm), 1 mol ideal gas = 22.4 L

Worked Examples

Example 1

At constant temperature, a gas occupying 3 L at 2 atm is compressed to 6 atm. What is its volume?

Constant T and moles → Boyle’s law P₁V₁ = P₂V₂.

P₁V₁ = P₂V₂

Substitute into V₂ = P₁V₁/P₂.

V₂ = 2 × 36 = 1 L

▸ 1 L

Boyle’s law: at constant T, pressure and volume are inversely proportional. 3× pressure → 1/3 volume.

Example 2

What volume does 1 mol of ideal gas occupy at 27°C and 1 atm? (R = 0.0821)

From PV = nRT, V = nRT/P. Use absolute temperature in K.

V = nRTP, T = 27 + 273 = 300 K

Substitute n = 1, R = 0.0821, T = 300, P = 1.

V = 1 × 0.0821 × 3001 ≈ 24.6 L

▸ about 24.6 L

When using PV = nRT, T must be in kelvin. 27°C = 300 K.

Summary

Ideal Gas Equation

PV = nRT

R = 0.0821 L·atm/(mol·K) = 8.314 J/(mol·K)

CSAT-style

A steel vessel holds 2 mol N₂ and 3 mol O₂ with total pressure 5 atm. What is the partial pressure of O₂?

①1 atm

②2 atm

③3 atm

④4 atm

⑤5 atm

▸ ③ 3 atm

Dalton’s law of partial pressures: partial pressure = mole fraction × total pressure.

P_{O_2} = n_{O_2}n_total × P_total

O₂ mole fraction = 3/(2+3) = 3/5, total pressure 5 atm.

P_{O_2} = 35 × 5 = 3 atm

🎯 Exam Points

①PV = nRT — the most important formula (memorize both R values)

②Boyle: PV constant; Charles: V/T constant

③T must be in K: K = °C + 273

④Dalton partial: P_total = P₁ + P₂ + ...

⑤At STP (0°C, 1 atm), 1 mol gas = 22.4 L

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