Graham's Law Calculator

Calculate gas diffusion and effusion rates based on molar mass using Graham's Law

Graham's Law Calculator

Graham's Law: rate₁/rate₂ = √(M₂/M₁)
The rate of diffusion or effusion is inversely proportional to the square root of molar mass

Solve For

Rate of Gas 1 (rate₁) ← Solving for this

Rate of Gas 2 (rate₂)

Same units as rate₁

Molar Mass of Gas 1 (M₁)

g/mol

Molar Mass of Gas 2 (M₂)

g/mol

Common Gas Molar Masses:

• H₂: 2.02 g/mol

• He: 4.00 g/mol

• N₂: 28.01 g/mol

• O₂: 32.00 g/mol

• CO₂: 44.01 g/mol

• Ar: 39.95 g/mol

Understanding Graham's Law

Graham's Law states that the rate of diffusion or effusion of a gas is inversely proportional to the square root of its molar mass.

rate₁/rate₂ = √(M₂/M₁)

rate = diffusion or effusion rate
M = molar mass (g/mol)
Lighter gases move faster

Diffusion vs Effusion

Diffusion

Movement of gas molecules through another gas or medium

Effusion

Escape of gas molecules through a tiny hole into a vacuum

Where It's Used

•Isotope Separation: Enriching uranium-235 from uranium-238
•Gas Leaks: Detecting helium leaks in vacuum systems
•Atmospheric Science: Understanding gas mixing in air
•Medical: Anesthetic gas delivery and ventilation

Example Calculation

Problem:

If helium (He, M = 4.00 g/mol) effuses at a rate of 10.0 mL/min, how fast will oxygen (O₂, M = 32.00 g/mol) effuse?

Step 1: Identify values

rate_He = 10.0 mL/min
M_He = 4.00 g/mol
M_O₂ = 32.00 g/mol

Step 2: Apply Graham's Law

rate_He/rate_O₂ = √(M_O₂/M_He)

Step 3: Calculate

10.0/rate_O₂ = √(32.00/4.00)
10.0/rate_O₂ = √8 = 2.828
rate_O₂ = 10.0/2.828 = 3.54 mL/min

Result:

Helium effuses 2.83 times faster than oxygen because it's much lighter.

Relative Rates of Common Gases

Relative to oxygen (O₂ = 1.00):

Gas	M (g/mol)	Relative Rate
H₂	2.02	3.98×
He	4.00	2.83×
CH₄	16.04	1.41×
N₂	28.01	1.07×
O₂	32.00	1.00×
CO₂	44.01	0.85×
Cl₂	70.90	0.67×

Uranium Enrichment Application

The Process:

Graham's Law is used to separate uranium-235 from uranium-238 for nuclear fuel:

UF₆ (²³⁵U): M = 349.03 g/mol

UF₆ (²³⁸U): M = 352.04 g/mol

Rate Ratio:

rate₂₃₅/rate₂₃₈ = √(352.04/349.03) = 1.0043

²³⁵UF₆ effuses only 0.43% faster! Requires thousands of stages.

Practical Considerations:

⚠Requires gaseous uranium hexafluoride (UF₆)
⚠Thousands of effusion stages needed for enrichment
⚠Very small mass difference (3 amu out of ~352)
⚠Energy-intensive industrial process
✓Centrifuges now more common than gaseous diffusion

Kinetic Molecular Theory Connection

Root-Mean-Square Velocity:

v_rms = √(3RT/M)

R = 8.314 J/(mol·K), T = temperature (K), M = molar mass (kg/mol)

Graham's Law comes from the fact that rate ∝ velocity ∝ 1/√M

Average Velocities (25°C):

Gas	v_rms (m/s)
H₂	1927
He	1363
N₂	515
O₂	482

Graham's Law Calculator