Relative Molecular Mass

Summary: The relative molecular mass (Mr) of a substance is the sum of the relative atomic masses of the atoms in its formula, and it determines how quickly a gas diffuses — lighter molecules diffuse faster. Tags: igcse chemistry Created: 2026-07-17

Relative molecular mass, given the symbol Mr, is the mass of one molecule of a substance measured on the relative atomic mass scale, and it is calculated by adding together the relative atomic masses (Ar) of all the atoms shown in the molecular formula. Like relative atomic mass, Mr is a pure ratio compared against one-twelfth of the mass of a carbon-12 atom, so it has no units; for ionic compounds, which do not contain discrete molecules, the equivalent quantity is called the relative formula mass but is calculated in exactly the same way. Beyond its central role in mole calculations (see Relative Masses and Moles), relative molecular mass has a direct physical consequence for gases: at the same temperature all gas particles have the same average kinetic energy, so lighter molecules must travel faster than heavier ones, and therefore gases with a lower Mr diffuse more quickly. This relationship — the rate of diffusion is inversely proportional to the square root of Mr — is known as Graham’s law, and at IGCSE it is required only qualitatively: lower Mr means faster Diffusion. The classic demonstration is the ammonia and hydrogen chloride experiment, in which a white ring of ammonium chloride forms nearer the hydrogen chloride end of a glass tube because the lighter ammonia molecules cover more distance in the same time. The whole effect is a direct prediction of the Kinetic Particle Theory.

Calculating Relative Molecular Mass

To find Mr, add up the relative atomic masses of every atom in the formula:

Mr has no units because it is a ratio relative to 1/12 of the mass of a carbon-12 atom.

Relative Molecular Mass and Diffusion Rate

At any given temperature, all gas molecules have the same average kinetic energy (KE = ½mv²). It follows that molecules with a smaller mass must be moving faster on average, and molecules with a larger mass must be moving more slowly. Since diffusion happens because of this random molecular motion, the speed of the molecules controls how quickly a gas spreads out:

• Lower Mr → faster-moving molecules → faster diffusion
• Higher Mr → slower-moving molecules → slower diffusion

Quantitatively, this is expressed by Graham’s law of diffusion:

Rate of diffusion ∝ 1 / √Mr

At IGCSE level you only need the qualitative conclusion: the lighter the gas (the lower its Mr), the faster it diffuses at a given temperature. For example, hydrogen (Mr = 2) diffuses faster than carbon dioxide (Mr = 44), which is why a balloon filled with hydrogen or helium deflates faster than one filled with air.

The Ammonia and Hydrogen Chloride Experiment

The classic demonstration of the link between Mr and diffusion rate uses a long, horizontal glass tube:

1. A cotton wool plug soaked in concentrated ammonia solution (releasing NH₃ gas, Mr = 17) is placed in one end of the tube, and a plug soaked in concentrated hydrochloric acid (releasing HCl gas, Mr = 36.5) is placed in the other end, at the same time. The tube is then sealed.
2. The two colourless gases diffuse toward each other through the air in the tube.
3. Where they meet, they react to form a white ring of solid ammonium chloride:

NH₃(g) + HCl(g) → NH₄Cl(s)

4. The white ring forms closer to the HCl end of the tube — roughly two-thirds of the way along from the ammonia end.

Explanation: ammonia has a much lower relative molecular mass (17) than hydrogen chloride (36.5), so at the same temperature its molecules travel faster and cover a greater distance in the same time. The faster gas travels further before the two meet, so the ring forms nearer the source of the slower, heavier gas (HCl).

The experiment takes several minutes even though gas molecules move at hundreds of metres per second, because the diffusing molecules constantly collide with air molecules in the tube and follow zig-zag paths rather than straight lines — further evidence for the Kinetic Particle Theory.

Sources

• Cambridge IGCSE Chemistry 0620 Syllabus (2023-2025), Cambridge Assessment International Education

Common Misconceptions