Particle Mass and the Rate of Diffusion

Introduction

Helium balloons go flat within a day, while air-filled balloons stay firm for weeks. A leak of hydrogen spreads through a room faster than a leak of a heavy gas such as carbon dioxide. Both observations point to the same rule: at the same temperature, light particles move faster than heavy ones and so diffuse more quickly. This page explains why, and shows how to use relative formula mass to predict which gas spreads fastest.

Core explanation

Same temperature, same average kinetic energy. Temperature measures the average kinetic energy of particles. If two gases are at the same temperature, their particles have, on average, the same kinetic energy.

Kinetic energy depends on mass and speed. A moving particle's kinetic energy depends on both its mass and its speed. A heavy particle has a lot of kinetic energy even at a modest speed. A light particle needs a much higher speed to have the same kinetic energy. So, at the same temperature:

lighter particles → higher average speed → faster diffusion

heavier particles → lower average speed → slower diffusion

Comparing masses with Mr. We compare how heavy particles are using their relative formula mass , Mr. Some common gases:

Gas Formula Mr --- --- --- Hydrogen H₂ 2 Helium He 4 Methane CH₄ 16 Ammonia NH₃ 17 Nitrogen N₂ 28 Oxygen O₂ 32 Hydrogen chloride HCl 36.5 Carbon dioxide CO₂ 44

The lower the Mr, the faster the gas diffuses. Hydrogen, with the smallest Mr of any gas, diffuses fastest of all. Carbon dioxide, with Mr 44, is slower than the nitrogen and oxygen in air.

Only compare at the same temperature. The rule "lighter is faster" is a fair comparison only when temperature is the same, because temperature also changes particle speed. A heavy gas that is very hot could diffuse faster than a light gas that is very cold.

Mass, not size, is the key idea at this level. Heavier molecules are often larger too, but the explanation you should give is in terms of mass and speed.

Step-by-step reasoning

To predict which of two gases diffuses faster:

1. Write the formula of each gas. 2. Calculate each Mr by adding the relative atomic masses. 3. Check that the gases are at the same temperature. 4. The gas with the lower Mr has faster particles, so it diffuses faster.

Visual explanation

Picture two gases released at one end of a long tube: small, light particles drawn as tiny dots and large, heavy particles drawn as big circles. Both move randomly, but the tiny dots dart along with long quick strokes while the big circles lumber more slowly. After a few seconds, the dots have spread much further down the tube.

Real-world analogy

Imagine a table-tennis ball and a bowling ball each given exactly the same push energy. The table-tennis ball shoots away quickly; the bowling ball rolls slowly. Equal energy gives a light object a much higher speed, just as equal kinetic energy gives light gas particles a higher speed.

Real-world example

Party balloons filled with helium shrink much faster than balloons filled with air. Helium atoms, with Mr 4, move quickly and escape through tiny gaps in the rubber more easily than the heavier nitrogen and oxygen molecules in air. Foil balloons are used for helium because the metal layer blocks the escaping atoms far better.

Why?

Why must lighter particles move faster at the same temperature? Kinetic energy depends on both mass and speed. If two particles have the same kinetic energy but one has less mass, it must make up for this with more speed. That extra speed carries it further in each second, so it diffuses faster.

Common misconception

"Heavy gases do not diffuse; they just sink." All gases diffuse because all gas particles move randomly. Heavy gases such as carbon dioxide diffuse more slowly and may collect in low places before mixing, but they do still spread and mix with the air over time.

Worked example

Question: Which diffuses faster at room temperature: methane (CH₄) or oxygen (O₂)? Relative atomic masses: C = 12, H = 1, O = 16.

Reasoning: Mr of CH₄ = 12 + (4 × 1) = 16. Mr of O₂ = 2 × 16 = 32. Methane has the lower Mr, so its molecules move faster at the same temperature.

Answer: Methane diffuses faster, because its molecules are lighter (Mr 16 compared with 32).

Quick check

1. Which gas diffuses faster at the same temperature: helium (Mr 4) or nitrogen (Mr 28)? Answer: Helium, because its particles are lighter and move faster.

Exam focus

Examiners expect you to calculate Mr values and use them to rank gases. Always state "at the same temperature" and explain using speed: lighter particles move faster. Simply writing "it is lighter" without linking to speed may not earn the full marks.

Advanced insight

Graham's law states that the rate of diffusion of a gas is inversely proportional to the square root of its relative formula mass. Hydrogen (Mr 2) and oxygen (Mr 32) differ in Mr by a factor of 16, so hydrogen diffuses about √16 = 4 times faster. This law was used to separate uranium isotopes, whose compounds differ in mass by less than one per cent.

Summary

At the same temperature, all gas particles have the same average kinetic energy. Lighter particles must therefore move faster than heavier ones, so they diffuse more quickly. Relative formula mass, Mr, lets us rank gases: the lower the Mr, the faster the diffusion. Hydrogen diffuses fastest of all gases.

Practice questions

1. Calculate Mr for ammonia, NH₃ (N = 14, H = 1), and for carbon dioxide, CO₂ (C = 12, O = 16). Which diffuses faster? Answer: NH₃ = 14 + 3 = 17; CO₂ = 12 + 32 = 44. Ammonia diffuses faster because its molecules are lighter. 2. Explain, in terms of particles, why helium balloons go down faster than air-filled balloons. Answer: Helium atoms are lighter than the molecules in air, so at the same temperature they move faster and escape through the rubber more quickly. 3. Why must two gases be at the same temperature to compare their rates of diffusion fairly? Answer: Temperature also affects particle speed, so a difference in temperature could hide or reverse the effect of mass. 4. Place these gases in order of rate of diffusion, fastest first: O₂ (Mr 32), H₂ (Mr 2), CO₂ (Mr 44), N₂ (Mr 28). Answer: H₂, N₂, O₂, CO₂.