Rate of Effusion Calculator

Effusion is the movement of gas particles through a very small opening into a vacuum or a region of much lower pressure. The rate depends on how quickly the particles move, and molecular speed depends strongly on molar mass when gases share the same temperature. Graham's law captures this relationship: the ratio of two effusion rates equals the square root of the inverse ratio of their molar masses. A lighter gas therefore passes through the opening faster than a heavier gas. This calculator finds the rate of a second gas from one measured or assigned rate and the molar masses of both gases. It evaluates Rate 2 = Rate 1 × square root of (Molar mass 1 / Molar mass 2). The known rate may use any consistent unit, such as milliliters per minute, moles per second, or a relative rate. The answer uses the same rate unit because the molar-mass ratio is dimensionless. Both molar masses must use the same unit, normally grams per mole. Graham's law follows from the kinetic molecular model. At equal temperature, gases have the same average translational kinetic energy. Since kinetic energy depends on mass and speed squared, particles with lower mass must have a higher characteristic speed. Effusion rate is proportional to that speed under ideal conditions. The square-root relationship is important: a gas with one quarter of another gas's molar mass effuses twice as fast, not four times as fast. The law works best for dilute gases, tiny openings, equal temperatures, and pressures low enough that collisions near the opening do not dominate. Real gases can deviate when intermolecular forces become important, while diffusion through another gas is more complicated because particles collide repeatedly. Effusion and diffusion are related ideas but are not interchangeable in careful laboratory work. Use molecular molar masses rather than atomic masses for gases such as hydrogen, nitrogen, and oxygen, because those elements normally occur as diatomic molecules. Keep temperatures equal when comparing experimental rates and make sure the opening and pressure conditions are unchanged. With those controls, the calculated ratio provides a quick prediction, a way to identify an unknown gas, or a useful check on experimental observations.