Graham's Law of Diffusion
Calculate gas diffusion rates using Graham's Law v₁/v₂ = √(M₂/M₁). Free online chemistry calculator for students and lab professionals with rate ratios and charts.
About This Calculator
Graham's Law of Diffusion, formulated by Scottish chemist Thomas Graham in 1848, describes how gases diffuse or effuse at rates inversely proportional to the square root of their molar masses. This free online calculator helps chemistry students, researchers, and lab professionals quickly compare diffusion rates between any two gases using the formula v₁/v₂ = √(M₂/M₁).
The calculator works by taking the molar masses of two gases and computing the rate ratio. If you provide a rate for Gas 1, the calculator will also determine the corresponding rate for Gas 2. For example, hydrogen (H₂, 2 g/mol) diffuses 4 times faster than oxygen (O₂, 32 g/mol) because √(32/2) = 4. Heavier gases always diffuse more slowly than lighter ones under identical conditions of temperature and pressure.
This principle has important real-world applications including uranium isotope enrichment for nuclear energy (separating ²³⁵UF₆ from ²³⁸UF₆), designing gas detection and separation systems, and determining the approximate molar mass of unknown gases by measuring their diffusion rate relative to a known gas.
The calculation assumes ideal gas behavior at the same temperature and pressure. Graham's Law is most accurate for effusion (gas escaping through a small hole) and provides a good approximation for diffusion of one gas into another.
Frequently Asked Questions
What is Graham's Law of Diffusion?
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. Lighter gases diffuse faster than heavier ones under the same conditions of temperature and pressure.
What is the formula for Graham's Law?
The formula is v₁/v₂ = √(M₂/M₁), where v₁ and v₂ are the rates of diffusion of gas 1 and gas 2, and M₁ and M₂ are their respective molar masses.
How much faster does hydrogen diffuse than oxygen?
Hydrogen (H₂, 2 g/mol) diffuses 4 times faster than oxygen (O₂, 32 g/mol). This is calculated as √(32/2) = √16 = 4.
What is the difference between diffusion and effusion?
Effusion is the escape of gas molecules through a tiny hole into a vacuum, while diffusion is the spread of gas molecules through another gas. Graham's Law applies to both processes, though it is most accurate for effusion.
What are common applications of Graham's Law?
Graham's Law is used in isotopic separation (such as enriching uranium-235 for nuclear energy), gas detection systems, determining molar masses of unknown gases, and understanding respiratory gas exchange in biology.
Does temperature affect Graham's Law?
Graham's Law itself compares rates at the same temperature and pressure. While the ratio of diffusion rates remains constant at a given temperature, absolute diffusion rates increase with temperature as molecular kinetic energy increases.