Graham's Law of Effusion/Diffusion Calculator Chemistry

Rate Ratio: ---
Rate1 / Rate2 = -- Time1 / Time2 = --

What is Graham's Law of Effusion/Diffusion Calculator?

Quick Answer: An interactive tool that computes the ratio of effusion or diffusion rates of two gases using Graham's law: rate1/rate2 = sqrt(M2/M1). Enter molar masses or choose from common gases to instantly see the relative speeds and times.

Theory of Graham's Law

Graham's law of effusion (also applies to diffusion) 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:
Rate1 / Rate2 = √(M2 / M1)
Equivalently, the time taken for the same amount of gas to effuse is directly proportional to the square root of molar mass:
t1 / t2 = √(M1 / M2)
The calculator instantly computes both ratios. The visual shows two containers with particles escaping through a small hole; the speed of particles is proportional to the rate of effusion, demonstrating the concept dynamically.

Step-by-Step Examples

Example 1: Hydrogen vs Oxygen

  1. Select H2 (M=2) for Gas 1 and O2 (M=32) for Gas 2. Click Calculate.
  2. RateH2 / RateO2 = √(32/2) = 4. So hydrogen effuses 4 times faster than oxygen.
  3. TimeH2 / TimeO2 = √(2/32) = 0.25; hydrogen takes one‑quarter the time.

Example 2: Helium vs Nitrogen

  1. He (4) vs N2 (28). Ratio = √(28/4) = 2.65. Helium effuses 2.65 times faster.

Frequently Asked Questions

What is the difference between effusion and diffusion?

Effusion is the escape of gas through a tiny hole into a vacuum; diffusion is the mixing of gases due to random motion. Graham's law applies to both under similar conditions.

Why does rate depend on molar mass?

At the same temperature, lighter molecules have higher average speeds (from kinetic theory: v_rms = √(3RT/M)). So they collide with the hole more frequently, leading to faster effusion.

Can I use this for diffusion times?

Yes, the time ratio is the inverse of the rate ratio. The tool displays both for convenience.

Are the gases assumed ideal?

Yes, Graham's law is most accurate for ideal gases at low pressure. Real gases may show slight deviations.

What units are molar masses in?

Grams per mole (g/mol). The ratio is dimensionless, so any consistent mass unit works.