Rate of Effusion Calculator
Our physical chemistry calculator computes rate effusion accurately. Enter measurements for results with formulas and error analysis.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
rate1/rate2 = sqrt(M2/M1)
Graham's Law of Effusion states the rate of effusion is inversely proportional to the square root of molar mass. Lighter gases effuse faster. The ratio of rates equals the square root of the inverse ratio of molar masses.
Worked Examples
Example 1: Hydrogen vs Oxygen
Problem:Compare the effusion rates of hydrogen (M=2.016 g/mol) and oxygen (M=32.00 g/mol).
Solution:rate(H2)/rate(O2) = sqrt(M(O2)/M(H2))\n= sqrt(32.00/2.016)\n= sqrt(15.873)\n= 3.984
Result:Hydrogen effuses 3.98 times faster than oxygen
Example 2: Unknown Gas Identification
Problem:A gas effuses 0.354 times as fast as helium (M=4.003). Find the molar mass of the unknown gas.
Solution:rate(X)/rate(He) = sqrt(M(He)/M(X))\n0.354 = sqrt(4.003/M(X))\n0.354^2 = 4.003/M(X)\nM(X) = 4.003/0.1253 = 31.95 g/mol (likely O2)
Result:Unknown gas molar mass = 31.95 g/mol (oxygen)
Frequently Asked Questions
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. Mathematically, rate1/rate2 = sqrt(M2/M1), where M1 and M2 are the molar masses of the two gases. This means lighter gases effuse faster than heavier ones. For example, hydrogen (M=2) effuses 4 times faster than oxygen (M=32) because sqrt(32/2) = 4. The law was discovered by Scottish chemist Thomas Graham in 1848.
What is the difference between effusion and diffusion?
Effusion is the escape of gas molecules through a tiny hole (smaller than the mean free path) into a vacuum, while diffusion is the spreading of gas molecules through another gas or medium. Both processes follow Graham's Law, but effusion is simpler because molecules pass through one at a time without collisions. Diffusion is slower due to molecular collisions and is described by Fick's laws. In practice, effusion is used in isotope separation and leak detection, while diffusion governs mixing and transport in bulk systems.
How is effusion used in isotope separation?
Gaseous diffusion was historically used to enrich uranium-235 from uranium-238 by converting uranium to UF6 gas and passing it through porous barriers. Since U-235-F6 (M=349) is slightly lighter than U-238-F6 (M=352), it effuses slightly faster with a separation factor of sqrt(352/349) = 1.0043. Because this factor is so close to 1, thousands of stages are needed for significant enrichment. This process was used in the Manhattan Project and remained in use until centrifuge technology largely replaced it.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy