The rate of effusion of a gas is inversely proportional to the square root of its molar mass.
Practise States of Matter & Solutions All States of Matter & Solutions topics
Graham's law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass at constant temperature and pressure, so rate1/rate2 = sqrt(M2/M1). Lighter molecules have higher average speeds at the same temperature, so they escape through a small hole more quickly. The law is useful for comparing the escape rates of gases and for estimating unknown molar masses. Historically it was used to separate uranium isotopes by effusion of gaseous UF6, because the lighter isotope escapes slightly faster. The law applies only when the hole is small enough that molecules do not collide with one another as they pass through it.
Key ideas: The rate ratio uses molar masses inverted: rate_A / rate_B = sqrt(M_B / M_A). The same ratio holds for effusion times, but inverted: time_A / time_B = sqrt(M_A / M_B). If the same amount of gas escapes, time is inversely proportional to rate. Rates may be expressed as moles per second, volume per second or distance travelled.
Common mistakes and connections: Students invert the ratio and conclude that heavier gases escape faster. Another mistake is applying it for large holes, where bulk flow takes over, or for gases at different temperatures without correcting. For UF6 isotopes 235 and 238 the ratio is only about 1.0043, so thousands of stages are needed. Links to rms speed, diffusion and isotope enrichment.
Effusion rate varies as 1/sqrt(M): lighter gases escape faster; relative rate of H2 over He ratio is sqrt(4/2) and vs O2 is 4. The interactive lesson shows this as a live animation or chart.
Hydrogen (M = 2 g/mol) effuses about four times faster than oxygen (M = 32 g/mol), since sqrt(32/2) = 4.
The rate of effusion of a gas is inversely proportional to the square root of its molar mass.
Graham's Law of Effusion is a intermediate topic in States of Matter & Solutions. It builds on the vocabulary of beginner topics in this area.
Study these earlier topics in States of Matter & Solutions first: Dalton's Law of Partial Pressures, Mole Fraction, Gas Collection Over Water.
The next topics in States of Matter & Solutions are Diffusion and Effusion.
Yes. The interactive lesson includes a self-check question on Graham's Law of Effusion, and the States of Matter & Solutions quiz draws on every topic in this area.
Graham's Law of Effusion is topic 19 of 109 in States of Matter & Solutions.