Rate of Effusion Calculator
Enter the molar masses of two gases and a known effusion rate to find their rate ratio under Graham's law, with a rate-vs-molar-mass chart.
💨 What is Rate of Effusion?
Rate of effusion is the speed at which a gas escapes through a tiny opening into a region of lower pressure, one molecule passing through at a time. It is governed by Graham's law, which states that a gas's effusion rate is inversely proportional to the square root of its molar mass, so lighter gases effuse faster than heavier ones under the same conditions. This calculator takes the molar masses of two gases and a known rate for one of them, then returns their rate ratio and the computed rate of the second gas.
Effusion shows up throughout chemistry and industry. Chemists use Graham's law in the lab to identify an unknown gas by comparing its effusion rate to a gas of known molar mass. Industrially, the gaseous diffusion process once used to enrich uranium relied on the tiny effusion rate difference between uranium-235 and uranium-238 hexafluoride gas. Even a leaking helium balloon deflating faster than an air-filled balloon of the same size is Graham's law in action, since helium (4.00 g/mol) is far lighter than the mix of nitrogen and oxygen in air (about 29 g/mol).
A common point of confusion is mixing up effusion with diffusion. Effusion describes gas escaping through a small opening into a vacuum or a lower-pressure space. Diffusion describes one gas gradually spreading through another gas already present, such as perfume scent spreading across a room. Both processes follow the same square root relationship with molar mass, but they describe physically different situations, and Graham's law applies to both.
This calculator is useful because it turns the square root relationship into an instant, checkable answer: enter two molar masses and a known rate, and immediately see how many times faster or slower the second gas effuses, along with a chart showing how that ratio changes as molar mass changes.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Hydrogen vs Oxygen
Gas 1 = hydrogen (M1 = 2.016 g/mol), Gas 2 = oxygen (M2 = 32.00 g/mol), known rate of Gas 1 = 1 mol/min.
Example 2 — Helium vs Argon
Gas 1 = helium (M1 = 4.003 g/mol), Gas 2 = argon (M2 = 39.95 g/mol), known rate of Gas 1 = 5 mL/s.
Example 3 — Uranium-235 vs Uranium-238 Hexafluoride
Gas 1 = uranium-235 hexafluoride (M1 = 349.03 g/mol), Gas 2 = uranium-238 hexafluoride (M2 = 352.04 g/mol), known rate of Gas 1 = 1 (arbitrary unit).
❓ Frequently Asked Questions
🔗 Related Calculators
What is Graham's law of effusion?
Graham's law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. In formula terms, rate1 / rate2 = sqrt(M2 / M1), meaning lighter gases effuse faster than heavier gases when compared through the same small opening under the same conditions.
How do you calculate the rate of effusion ratio?
Divide the molar mass of the second gas by the molar mass of the first gas, then take the square root: rate1 / rate2 = sqrt(M2 / M1). For example, comparing hydrogen (2.016 g/mol) to oxygen (32.00 g/mol) gives sqrt(32.00 / 2.016) = 3.98, so hydrogen effuses about 3.98 times faster than oxygen.
Why does a lighter gas effuse faster than a heavier gas?
At a given temperature, all gas molecules have the same average kinetic energy, so lighter molecules must move faster to carry that same energy. Since effusion speed depends directly on molecular speed, lighter gas molecules escape through a small opening faster than heavier ones.
What is the difference between effusion and diffusion?
Effusion is the escape of gas molecules through a tiny opening into a vacuum or lower-pressure region, one molecule passing through at a time. Diffusion is the gradual mixing of one gas into another gas already present. Both follow the same Graham's law square root relationship with molar mass, but effusion describes escape through a hole while diffusion describes spreading through another gas.
How is Graham's law used in uranium enrichment?
Gaseous diffusion enrichment relies on Graham's law: uranium hexafluoride gas made from the lighter uranium-235 isotope effuses very slightly faster than the gas made from uranium-238, since the two differ in molar mass by only about 3 out of roughly 349. The ratio is close to 1.004, so enrichment plants repeat the separation across thousands of stages to build up a usable difference.
Can Graham's law be used to find an unknown molar mass?
Yes. If you measure the effusion rates of an unknown gas and a known reference gas, you can rearrange rate1 / rate2 = sqrt(M2 / M1) to solve for the unknown molar mass: M(unknown) = M(known) times (rate(known) / rate(unknown)) squared. This is a classic lab method for identifying an unknown gas.
Does Graham's law depend on temperature or pressure?
The rate ratio itself does not depend on temperature or pressure, as long as both gases being compared are at the same temperature and pressure and escape through the same opening. Absolute effusion rates do increase with temperature and pressure, but those effects cancel out when you take the ratio between two gases under identical conditions.
What units does the rate of effusion use?
Effusion rate can be expressed in any unit that counts amount of gas per unit time, such as moles per minute, milliliters per second, or molecules per second. Because Graham's law is a ratio, the unit cancels out algebraically, so the rate ratio itself is always a plain unitless number.
How much faster does hydrogen effuse than other common gases?
Hydrogen (2.016 g/mol) effuses about 3.98 times faster than oxygen (32.00 g/mol), about 4.24 times faster than carbon dioxide (44.01 g/mol), and about 4.69 times faster than chlorine (70.90 g/mol). Being the lightest naturally occurring gas, hydrogen effuses faster than any other common gas.
Is effusion rate the same as diffusion coefficient?
No, they measure different things. Effusion rate (this calculator) measures how quickly a gas escapes through a tiny opening, following Graham's law with molar mass. Diffusion coefficient measures how quickly a gas spreads out or mixes within another medium over time and depends on more variables, including temperature, pressure, and the properties of both gases involved. See the Diffusion Coefficient Calculator for that separate calculation.