Rate of Effusion Calculator

Kinetic Molecular Theory of Gases & Graham's Law

Formulated in 1848 by Scottish physical chemist Thomas Graham, Graham's Law describes the physical transport process of effusion (gas molecules escaping from a pressurized container through a microscopic pinhole into a vacuum without intermolecular collisions) and diffusion (gas spreading gradually through another medium or ambient air).

Core Physical Chemistry Equations

• Graham's Law of Effusion: Rate_1Rate_2 = √((M_2) / (M_1)) = √((ρ_2) / (ρ_1))

• Effusion Time Relation (Inverse to Rate): (t_1) / (t_2) = Rate_2Rate_1 = √((M_1) / (M_2)) t_1 = t_2 √((M_1) / (M_2))

• Root-Mean-Square Thermal Velocity (v_rms): v_rms = √((3 R T) / (M))

• Unknown Gas Molar Mass: M_x = M_known × ((t_x) / (t_known))^2 = M_known × (Rate_knownRate_x)^2

Key Principles of Gaseous Transport

• Lighter gas molecules possess higher average velocities at the same thermodynamic temperature (T) because their kinetic energies are identical in thermal equilibrium.

• Consequently, lighter gases collide with the container wall and escape through pinhole apertures at a significantly higher frequency than heavier molecules, accelerating volumetric flow rates.

How to Use This Calculator

Enter your Variable to Calculate — choose from Relative Effusion Rate Ratio (Rate₁ ÷ Rate₂), Effusion Time for Gas 1 (t₁ from t₂), Effusion Rate for Gas 1 (R₁ from R₂), Gas 1 Selection (Lighter / Faster Gas) — choose from Helium (He - 4.003 g/mol), Hydrogen (H₂ - 2.016 g/mol), Methane (CH₄ - 16.04 g/mol), Molar Mass Gas 1 [M₁] (e.g. 4.003 in g/mol), Gas 2 Selection (Heavier / Reference Gas) — choose from Oxygen (O₂ - 32.00 g/mol), Nitrogen (N₂ - 28.01 g/mol), Carbon Dioxide (CO₂ - 44.01 g/mol), Molar Mass Gas 2 [M₂] (e.g. 32.00 in g/mol), Effusion Time for Gas 2 [t₂] (e.g. 60.0 in seconds), and Effusion Rate for Gas 2 [Rate₂] (e.g. 10.0 in mL/s). Results update instantly as you type — adjust any value to compare scenarios.

The Formula

Conversion factors (to SI base unit or reference unit):

h2_2_016: 2.016

he_4_003: 4.003

ch4_16_04: 16.04

nh3_17_03: 17.03

n2_28_01: 28.01

o2_32_00: 32.00

co2_44_01: 44.01

sf6_146_06: 146.06

Worked Example

Comparing Helium and Oxygen: sqrt = 2.

• Helium particles travel and effuse 2.83 times faster, taking 21.2s to effuse compared to 60.0s for O

2.

Understanding Your Result

Evaluate your result in the context of your specific use case and relevant industry standards or reference values. A single calculated result is a starting point — test two to three scenarios to understand how sensitive the outcome is to your key input assumptions. For high-stakes decisions, verify your result against a secondary source or subject-matter expert before acting.