Using Relative Masses to Compare Substances

Introduction

Methane, the main gas in natural gas, has Mr = 16 and boils at about −162 °C. Octane, a main part of petrol, has Mr = 114 and is a liquid that boils at about 126 °C. Both are made only of carbon and hydrogen. The big difference comes largely from the size and mass of their molecules. Relative masses let us compare substances quickly and predict trends in their properties.

Core explanation

Ranking by Mr. Once Mr is known, molecules can be ranked from lightest to heaviest: hydrogen H₂ (2), helium He (4), methane CH₄ (16), water H₂O (18), nitrogen N₂ (28), oxygen O₂ (32), carbon dioxide CO₂ (44), chlorine Cl₂ (71). This is a comparison of the masses of single particles.

Boiling point trends in similar molecules. Separate molecules attract each other through weak intermolecular forces . To boil a liquid, these attractions must be overcome. In a family of similar molecules, larger and heavier molecules have more electrons and more surface in contact, so the forces between them are stronger and the boiling point is higher.

Molecule Mr Boiling point (°C) State at 20 °C --- --- --- --- Methane, CH₄ 16 −162 gas Ethane, C₂H₆ 30 −89 gas Propane, C₃H₈ 44 −42 gas Butane, C₄H₁₀ 58 about −1 gas Pentane, C₅H₁₂ 72 36 liquid Octane, C₈H₁₈ 114 126 liquid

The halogens show the same pattern: fluorine (F₂, 38) and chlorine (Cl₂, 71) are gases, bromine (Br₂, 160) is a liquid and iodine (I₂, 254) is a solid at room temperature.

Gas density. At the same temperature and pressure, equal volumes of gases contain equal numbers of molecules. So a gas made of heavier molecules is denser. Air behaves as if its average Mr were about 29. Helium (4) is much less dense than air and rises; carbon dioxide (44) is denser and tends to collect in low places.

Diffusion. At the same temperature, lighter molecules move faster on average, so they diffuse more quickly. Ammonia (17) spreads faster than hydrogen chloride (36.5).

The limits of the rule. Mr comparisons work best for molecules of the same type. Water (Mr 18) boils at 100 °C, far higher than methane (16), because water molecules attract each other especially strongly through hydrogen bonds. Giant structures such as sodium chloride and diamond do not consist of small molecules at all, so their high melting points are not explained by Mr.

Step-by-step reasoning

To predict which of two similar substances has the higher boiling point:

1. Check that they belong to the same family (for example, both hydrocarbons or both halogens). 2. Calculate Mr for each. 3. The one with the larger Mr has stronger intermolecular forces. 4. Predict that it has the higher boiling point. 5. If the substances are of different types, treat the prediction with caution.

Visual explanation

Picture short and long strands of spaghetti. Short strands (small molecules) slide apart easily. Long strands (large molecules) tangle and touch along more of their length, so more energy is needed to separate them. A particle diagram of octane molecules shows long chains lying alongside each other with many points of contact.

Real-world analogy

Pulling apart two strips of sticky tape is easy when they overlap by a centimetre, but hard when they overlap along their whole length. Larger molecules are like longer strips: more contact means more attraction to overcome.

Real-world example

Camping gas cylinders contain butane and propane, whose small molecules boil well below room temperature, so they come out as gases. Petrol contains molecules with around five to ten carbon atoms, liquid at room temperature, while candle wax contains molecules with twenty or more carbon atoms and is a solid.

Why?

Why do heavier gas molecules make a denser gas? Equal volumes of gases at the same temperature and pressure hold equal numbers of molecules, so the volume with heavier molecules contains more mass. More mass in the same volume means greater density.

Common misconception

"Heavier molecules have higher boiling points because gravity holds them down." Gravity plays no meaningful part. The trend arises because larger molecules attract one another more strongly, and those attractions must be overcome for boiling.

Worked example

Question: Hydrogen sulfide, H₂S, and carbon dioxide, CO₂, can both leak into low-lying places. Use Mr values to decide whether each is denser or less dense than air (average Mr about 29). (H = 1, S = 32, C = 12, O = 16)

Reasoning: H₂S: 2 + 32 = 34. CO₂: 12 + 32 = 44. Both are greater than 29, so both are denser than air and tend to sink and collect in low areas such as cellars and pits.

Answer: Both are denser than air; CO₂ is the denser of the two.

Quick check

1. Which would you expect to have the higher boiling point, propane (Mr 44) or pentane (Mr 72)? Why? Answer: Pentane, because its larger molecules have stronger intermolecular forces.

Exam focus

When explaining a boiling point trend, mention intermolecular forces between molecules, not bonds within molecules. Covalent bonds inside a molecule are not broken when a substance boils. Always name the forces and link their strength to molecule size.

Advanced insight

The rate of diffusion of a gas is roughly inversely proportional to the square root of its molar mass (Graham's law). Hydrogen (2) diffuses about four times faster than oxygen (32), because the square root of 32 ÷ 2 = 16 is 4. This effect was used to separate isotopes of uranium by repeated diffusion of a gaseous compound.

Summary

Relative molecular masses let us rank molecules and predict trends. In families of similar molecules, higher Mr means stronger intermolecular forces and higher boiling points. Gases with higher Mr are denser and diffuse more slowly. Comparisons fail between very different substances, such as water with its hydrogen bonds or giant structures.

Practice questions

1. Rank these gases from lightest to heaviest molecules: O₂, He, CO₂, N₂. Answer: He (4), N₂ (28), O₂ (32), CO₂ (44). 2. Explain why bromine is a liquid but chlorine is a gas at room temperature. Answer: Br₂ (Mr 160) molecules are larger than Cl₂ (Mr 71), so the intermolecular forces are stronger and the boiling point is above room temperature. 3. Will a balloon filled with neon (Mr 20) rise or sink in air? Explain. Answer: It will tend to rise, because neon is less dense than air (average Mr about 29), though the balloon's own mass may reduce the lift. 4. Why does water not fit the Mr trend for boiling points? Answer: Water molecules attract each other through strong hydrogen bonds, so water boils much higher than its small Mr suggests.