Graham's Law of Effusion

Graham's Law states that the rate of gas effusion (or diffusion) is inversely proportional to the square root of molar mass. Lighter gases move faster than heavier gases.

Graham's Law

Rate₁ / Rate₂ = √(M₂/M₁)

Or equivalently:

Rate₁ / Rate₂ = √(MM₂/MM₁)

Variable Definitions

Rate = Effusion/Diffusion Rate

Units: mol/s, mL/s, or any volume/time

How fast gas passes through opening or spreads

💡 Can also be velocity (m/s) or average speed

M or MM = Molar Mass

Units: g/mol

Molecular weight of the gas

⚠️ Notice: heavier gas (M₂) goes in numerator, making ratio less than 1

Key Concepts

🎈 Effusion

Gas escaping through a tiny hole into vacuum

Example: Helium balloon deflating

🌫️ Diffusion

Gas spreading through space or another gas

Example: Perfume smell spreading across room

⚡ The Inverse Relationship

  • • Lighter gas (lower M) → faster rate
  • • Heavier gas (higher M) → slower rate
  • • Rate ∝ 1/√M (inverse square root relationship)
  • • If M increases 4×, rate decreases 2× (√4 = 2)

Step-by-Step Example

Problem: Compare effusion rates of He (4 g/mol) and O₂ (32 g/mol). How many times faster does He effuse?

Given:

  • M(He) = 4 g/mol
  • M(O₂) = 32 g/mol
  • Find: Rate(He) / Rate(O₂)

Step 1: Write Graham's Law

Rate(He) / Rate(O₂) = √[M(O₂) / M(He)]

Note: Heavier gas (O₂) goes in numerator

Step 2: Substitute values

Rate(He) / Rate(O₂) = √(32/4) = √8

Step 3: Calculate

√8 = 2.83

Answer: He effuses 2.83 times faster than O₂

Makes sense! He is 8× lighter, so it moves √8 ≈ 2.83× faster.

Rearranged Forms

Find unknown molar mass:

M₂ = M₁ × (Rate₁/Rate₂)²

Square both sides and solve

Find rate ratio:

Rate₁/Rate₂ = √(M₂/M₁)

Standard form

Using time instead:

t₁/t₂ = √(M₁/M₂)

Time ratio is inverted (slower = more time)

For velocities:

v₁/v₂ = √(M₂/M₁)

Same relationship as rates

Common Mistakes

❌ Putting lighter gas in numerator

It's √(M₂/M₁) with HEAVIER molar mass in numerator. Getting this backwards gives upside-down answer!

❌ Forgetting the square root

It's √(M₂/M₁), NOT just M₂/M₁. The square root is critical!

❌ Using atomic mass for molecules

For O₂, use 32 g/mol (molecular), not 16 g/mol (atomic). For H₂, use 2 g/mol, not 1 g/mol.

❌ Confusing with Dalton's Law

Graham's Law is about SPEED (how fast), Dalton's is about PRESSURE (how much). Different concepts!

Related Calculators

Graham's Law Calculator

Calculate effusion rates instantly

Gas Diffusion Calculator

Calculate diffusion rates

Molar Mass Calculator

Find MM from formula

KMT Calculator

Molecular velocities

Frequently Asked Questions

What is Graham's Law?

Rate₁/Rate₂ = √(M₂/M₁). The rate of gas effusion or diffusion is inversely proportional to the square root of molar mass. Lighter gases move faster.

What's the difference between effusion and diffusion?

Effusion is gas escaping through a tiny hole into vacuum. Diffusion is gas spreading through space or another gas. Graham's Law applies to both.

Why does molar mass affect rate?

From kinetic molecular theory: lighter molecules move faster at the same temperature because KE = ½mv². Same energy with less mass means higher velocity.

Why is there a square root?

Comes from kinetic energy equation: v ∝ √(T/M). Velocity is proportional to square root of temperature divided by mass.

Can I use this for liquids?

No, Graham's Law is for ideal gases only. Liquids have strong intermolecular forces that dominate diffusion behavior.

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