Chemistry / Unit 7 Chem 1305 worked example, 60 to 90 seconds
Calculating Relative Effusion Rates
The idea
Calculating the ratio of two gases' effusion rates means taking the square root of the inverse ratio of their molar masses, or, for effusion time, inverting that same ratio since time and rate vary oppositely.
In practice
Comparing hydrogen (2.02 g/mol) to oxygen (32.00 g/mol), the effusion rate ratio is the square root of 32.00/2.02, about 4, so hydrogen effuses four times faster than oxygen under the same conditions. Equivalently, if oxygen takes 100 seconds to effuse a given amount, hydrogen takes only about 25 seconds, since effusion time is inversely proportional to effusion rate.
Where people slip
Using molar mass directly instead of its square root, or forgetting that a longer effusion time means a slower rate, produces a ratio off by more than a rounding error.
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