Graham's law describes how the speed of gas effusion or diffusion depends on molar mass. It explains why lighter gas particles pass through tiny openings or spread through space faster than heavier particles at the same temperature. This matters in chemistry because gas behavior connects microscopic particle motion to measurable rates.
It also helps explain practical processes such as gas leaks, isotope separation, and comparing unknown gases.
Key Facts
- Graham's law: rate1/rate2 = sqrt(M2/M1)
- Effusion is gas escaping through a tiny hole into a vacuum or lower-pressure region.
- Diffusion is gas particles spreading out due to random molecular motion.
- At the same temperature, gases have the same average kinetic energy: KEavg = (3/2)RT per mole.
- Root-mean-square speed: urms = sqrt(3RT/M), where M is molar mass in kg/mol.
- A gas with one-fourth the molar mass of another effuses twice as fast because rate is proportional to 1/sqrt(M).
Vocabulary
- Effusion
- Effusion is the escape of gas particles through a very small opening from one container to another region.
- Diffusion
- Diffusion is the spreading of particles from higher concentration to lower concentration due to random motion.
- Molar mass
- Molar mass is the mass of one mole of a substance, usually measured in grams per mole.
- Root-mean-square speed
- Root-mean-square speed is a measure of the typical molecular speed in a gas at a given temperature.
- Isotope separation
- Isotope separation is the process of enriching one isotope relative to another by using small physical differences such as mass.
Common Mistakes to Avoid
- Using rate1/rate2 = M2/M1 instead of rate1/rate2 = sqrt(M2/M1). This is wrong because gas speed depends on the inverse square root of molar mass, not directly on mass.
- Putting the molar masses in the wrong order. The lighter gas should have the larger rate, so always check whether the ratio makes physical sense.
- Using grams per mole inconsistently with the velocity formula urms = sqrt(3RT/M). In that formula, M must be in kilograms per mole when R is in SI units.
- Assuming diffusion and effusion are identical. Graham's law can compare both under ideal conditions, but effusion specifically involves passage through a tiny hole while diffusion involves spreading through space.
Practice Questions
- 1 Hydrogen gas, H2, has a molar mass of 2.02 g/mol and oxygen gas, O2, has a molar mass of 32.00 g/mol. How many times faster does H2 effuse than O2?
- 2 A gas effuses 1.46 times faster than sulfur dioxide, SO2, which has a molar mass of 64.1 g/mol. What is the molar mass of the unknown gas?
- 3 Explain why uranium hexafluoride molecules containing uranium-235 effuse slightly faster than uranium hexafluoride molecules containing uranium-238, and why many repeated stages are needed for isotope separation.