Use this calculator to compare how fast two gases escape through a tiny hole or solve for an unknown rate, molar mass, or ratio.
Advanced options
How to use our Rate of Effusion Calculator
- Choose What do you want to find? so the calculator knows whether you are solving for Rate of gas 1, Rate of gas 2, Molar mass of gas 1, Molar mass of gas 2, or the Rate ratio (gas 1 divided by gas 2).
- Enter the visible known values for Molar mass of gas 1 (g/mol), Molar mass of gas 2 (g/mol), Rate of gas 1, and Rate of gas 2. If you enter both rates, use the same rate unit for each one.
- Pick Decimal places if you want a different display format, then click Calculate.
- Read Calculated value first, then check Rate ratio (gas 1 divided by gas 2), Faster gas, and How many times faster to make sure the comparison matches your chemistry setup. A ratio above 1 means gas 1 is faster; below 1 means gas 2 is faster.
Definitions
Effusion: A gas escaping through a tiny hole into empty space or a lower-pressure area.
Molar mass: The mass of 1 mole of a substance, usually written in g/mol.
Rate of gas 1 / Rate of gas 2: How fast each gas effuses. Both rates must use the same unit if you compare them directly.
Rate ratio (gas 1 divided by gas 2): The value of r1/r2. If it is greater than 1, gas 1 is faster. If it is less than 1, gas 2 is faster.
Faster gas: The gas with the larger effusion rate under the same conditions.
How many times faster: The bigger rate divided by the smaller rate, shown as an easy comparison factor.
Graham's law: A rule for comparing gas effusion rates: the rate ratio equals the square root of the inverse molar-mass ratio [2].
Common mistakes and quick fixes
Mistake: Entering different units in Rate of gas 1 and Rate of gas 2, such as mL/s for one and mol/s for the other.
Fix: Use the same rate unit in both Rate of gas 1 and Rate of gas 2 before trusting Calculated value or Rate ratio (gas 1 divided by gas 2).
Mistake: Swapping gas 1 and gas 2 by accident when typing Molar mass of gas 1 (g/mol) and Molar mass of gas 2 (g/mol).
Fix: Recheck which gas is gas 1 and which is gas 2, then compare Faster gas with your expectation. The lighter gas should come out faster under the same conditions.
Mistake: Leaving a visible required field blank after changing What do you want to find?.
Fix: Fill in every visible input for the selected solve mode. Hidden rows are ignored, but visible rows like Rate of gas 1 or Molar mass of gas 2 (g/mol) must have values.
Mistake: Typing 0 or a negative number for Molar mass of gas 1 (g/mol), Molar mass of gas 2 (g/mol), Rate of gas 1, or Rate of gas 2.
Fix: Enter values greater than 0. Graham's law comparisons in this calculator need positive molar masses and positive rates.
Mistake: Thinking Rate ratio (gas 1 divided by gas 2) is always written with the faster gas on top.
Fix: Read the label carefully. This ratio is specifically gas 1 divided by gas 2, so a value less than 1 simply means gas 2 is faster.
Mistake: Reading How many times faster as a signed comparison.
Fix: Use Faster gas to see which gas wins, and use How many times faster only for the size of the speed difference.
Limitations & Key Assumptions / Boundary Conditions
- This calculator assumes both gases are compared under the same temperature, pressure, and opening conditions.
- It uses Graham's law for idealized comparisons, so real experiments can differ if gases do not behave ideally.
- Rates and molar masses must be greater than 0. Zero or negative values are not physically valid here.
- If you solve with both rates, Rate of gas 1 and Rate of gas 2 must be in the same unit or the ratio will be meaningless.
- The tool focuses on effusion, which means escaping through a tiny hole. Classroom lessons may also mention diffusion, but this page is not modeling a full diffusion setup.
- Very large or very tiny inputs can make rounded results look less exact than the full math used behind the scenes.
Methodology
Formula used
The calculator uses Graham's law to compare two gases under the same conditions.
r1 / r2 = sqrt(M2 / M1)
Here, r1 and r2 are the effusion rates, and M1 and M2 are the molar masses in g/mol [2].
Rearranged forms
r2 = r1 / sqrt(M2 / M1)
r1 = r2 * sqrt(M2 / M1)
M2 = M1 * (r1 / r2)^2
M1 = M2 / (r1 / r2)^2
faster_factor = max(r1/r2, r2/r1)
The direction-check outputs then interpret the math: if r1/r2 is greater than 1, gas 1 is faster; if it is less than 1, gas 2 is faster.
Mini example
Suppose gas 1 is helium with Molar mass of gas 1 = 4.00 g/mol, gas 2 has Molar mass of gas 2 = 32.00 g/mol, and Rate of gas 1 = 2.00 in some shared rate unit.
r2 = 2.00 / sqrt(32.00 / 4.00)
r2 = 2.00 / sqrt(8)
r2 = 2.00 / 2.828...
r2 = 0.707...
So Calculated value for Rate of gas 2 is about 0.707 in the same rate unit, the Rate ratio (gas 1 divided by gas 2) is about 2.828, and gas 1 is 2.828 times faster.
Input checks and assumptions
The calculator only uses visible inputs for the chosen solve mode. Every required visible value must be greater than 0, and any result that is not a finite number is rejected as an error. For rate comparisons, both rates must use the same unit. Results can differ from real lab measurements because Graham's law is a simplified model for comparing gases under matching conditions.