Rate of Effusion Calculator

Formulated by Scottish chemist Thomas Graham in 1848, Graham's law states that the rate of effusion or diffusion of a gas is inversely proportional to the square root of its molar mass. Mathematically, the relationship between two gases is expressed as Rate1 / Rate2 = sqrt(Molar Mass2 / Molar Mass1). This means lighter gas molecules possess higher average speeds at a given temperature, causing them to move and escape faster than heavier molecules. Rearranging this core formula lets you isolate and calculate any missing variable—whether you need to find an unknown diffusion rate or determine the molar mass of an unidentified gas sample.

Imagine you want to compare the effusion rate of Helium (He) against an unknown gas with a molar mass of 64 g/mol. Helium has a known molar mass of approximately 4.00 g/mol, and let us assume its measured effusion rate is 4.0 units. Using Graham's law rearranged to find the unknown rate (Rate2 = Rate1 * sqrt(Molar Mass1 / Molar Mass2)), we plug in our values: Rate2 = 4.0 * sqrt(4.00 / 64). First, divide the molar masses to get 4.00 / 64 = 0.0625. Next, take the square root of 0.0625, which equals 0.25. Finally, multiply 4.0 by 0.25 to yield an effusion rate of 1.0 for the heavier gas. This confirms that Helium effuses four times faster than the heavier gas due to its lower molecular weight.

Always ensure your molar mass inputs use consistent units, typically grams per mole (g/mol), to avoid scaling errors. Remember that temperature and pressure must remain constant when comparing two gases, as kinetic energy depends heavily on thermal conditions. Finally, double-check whether your specific scenario involves effusion (escaping through a barrier) or diffusion (mixing through space), as experimental setups can slightly alter observed rates.