Avogadro’s Law and Gas Volumes in Reactions

Specification Reference S1.4.6

Quick Notes

Avogadro’s Law: Equal volumes of all gases, at the same temperature and pressure, contain the same number of molecules.
This means 1 mole of any gas occupies the same volume under the same conditions.
At standard conditions (STP), 1 mol of gas = 22.7 dm³.
Use balanced equations to determine mole ratios between gases.
Gas volume calculations follow:
Volume = mol × molar gas volume.
Reacting gas volumes can be compared directly using mole ratios, as long as all gases are under the same conditions.

Full Notes

What Is Avogadro’s Law?

Avogadro’s Law tells us:

Equal volumes of all gases, measured under the same temperature and pressure, contain the same number of molecules.

Example: 1 mole of hydrogen gas = same volume as 1 mole of oxygen gas (if Temperature and Pressure are the same).

At standard temperature and pressure (STP), 1 mol of any gas = 22.7 dm³.

This makes it easy to work with gases using volume instead of mass or moles.

Using Mole Ratios to Compare Gas Volumes

In chemical equations, coefficients (big numbers before the formulas) show the mole ratio of reactants and products. For gases, this is also the volume ratio, assuming constant conditions.

Example Hydrogen and chlorine

H₂(g) + Cl₂(g) → 2HCl(g)

1 mol H₂ reacts with 1 mol Cl₂ to produce 2 mol HCl.
So: 1 dm³ H₂ + 1 dm³ Cl₂ → 2 dm³ HCl.

You can use these ratios directly to solve volume problems without needing to calculate moles if all gases are measured under the same conditions.

Gas Volume Formula at STP

To calculate gas volumes at standard temperature and pressure (STP) we can use:

Volume = n × 22.7 (when at STP)

Volume = in dm³
n = amount in mol
22.7 dm³ mol⁻¹ is the molar volume at STP (0°C and 1 atm)

Worked Example

How many dm³ of CO₂ are produced from 0.50 mol at STP?

Use the formula: Volume = n × 22.7
Volume = 0.50 × 22.7 = 11.35 dm³

Worked Example

Given: N₂(g) + 3H₂(g) → 2NH₃(g). If you have 60.0 dm³ of hydrogen at STP, how much ammonia will form?

Use ratio H₂ : NH₃ = 3 : 2
60.0 dm³ H₂ × (2 NH₃ / 3 H₂) = 40.0 dm³ NH₃

Summary

Avogadro’s Law states equal volumes of gases contain the same number of molecules at the same temperature and pressure.
At STP, molar volume = 22.7 dm³ mol⁻¹.
Gas volume ratios can be read directly from balanced equations.
We can use Volume = n × 22.7 to convert between moles and volume.

Linked Question

Structure 1.5 – Linked Course Question

Avogadro’s law applies to ideal gases. Under what conditions might the behaviour of a real gas deviate most from an ideal gas?

Real gases deviate most from ideal behaviour at high pressures and low temperatures. Under these conditions, the assumptions of the ideal gas model – that gas particles have negligible volume and no intermolecular forces – are no longer valid. At high pressures, particles are forced closer together, so their finite size becomes significant. At low temperatures, the kinetic energy of particles decreases, making intermolecular attractions more noticeable. These factors cause real gases to have lower volumes and pressures than predicted by the ideal gas law.