When gases react at the same temperature and pressure, the volumes of the gases used up and the gases produced are in a simple whole-number ratio such as 1 : 1 : 2 or 2 : 1 : 2. This is the law of combining volumes.
Two volumes of hydrogen and one volume of oxygen give two volumes of steam, so three volumes before the reaction become two after it, which also shows that volume, unlike mass, is not conserved.
Avogadro proposed that equal volumes of any gases contain equal numbers of molecules; if so, the ratio of volumes is the ratio of molecules, and it matches the coefficients of the balanced equation.
In the picture below each box holds the same number of model molecules per volume, so you can count how the atoms regroup during the reaction.
Volume ratios in gas reactions
🎈 The volumes come out in simple whole numbers
①In 1808 Gay-Lussac found that when gases react at the same temperature and pressure, their volumes always form a simple whole-number ratio
②Two volumes of hydrogen and one volume of oxygen give two volumes of steam (2 : 1 : 2)
③The total volume before and after need not be equal. Mass is conserved, but volume is not
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The volumes of the gases used up and produced in a gas reaction shown as box sizes, with each molecule drawn as a model of its atoms
④Count the atoms in the model molecules in each box and you find the same kinds and numbers of atoms before and after
Avogadro's law
🔬 Equal volumes, equal numbers of molecules
①At the same temperature and pressure
②whatever the gas
③equal volumes contain the same number of molecules
④Molecules differ in size, but in a gas the spaces between them are far larger, so the volume depends on how many molecules there are, not on how big they are
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Hydrogen, oxygen and carbon dioxide at the same temperature and pressure, with the same number of molecules in the same volume
22.4 L
Why the volume ratio is the molecule ratio
💡 Linking combining volumes and Avogadro's law
①If hydrogen and chlorine were single atoms, as Dalton thought, one volume of each should give just one volume of hydrogen chloride
②In fact two volumes of hydrogen chloride form
③Avogadro explained this by treating hydrogen and chlorine as molecules of two atoms each (H₂ and Cl₂)
④Since equal volumes hold equal numbers of molecules, the volume ratio 1 : 1 : 2 is a molecule ratio of 1 : 1 : 2, the same as the coefficients in H₂ + Cl₂ → 2HCl
Summary
Law of combining volumes
Volumes of gases used up and produced = simple whole-number ratio
Compare volumes measured at the same temperature and pressure
Avogadro's law
Same temperature and pressure, same volume → same number of molecules
At 0 °C and 1 atm, one mole of gas takes up about 22.4 L (covered further in upper secondary)
Key relationship
Volume ratio = molecule ratio = coefficient ratio
Holds when all the substances involved are gases at the same temperature and pressure
🎯 Points that often come up
①At the same temperature and pressure, reacting gas volumes are in a simple whole-number ratio
②Equal volumes of gases contain equal numbers of molecules, whatever the gas
③In gas reactions the volume ratio equals the molecule ratio and the coefficient ratio
④The total volume can change during a reaction, but the mass and the kinds and numbers of atoms do not
⑤The volume ratio can be used directly only when the product, such as steam, is also a gas
Worked examples and unit test
Example 1
At the same temperature and pressure, hydrogen and oxygen react to form steam (2H₂ + O₂ → 2H₂O). How many mL of oxygen are needed to react with all of 20 mL of hydrogen, and how many mL of steam form?
1
All are gases, so the volume ratio equals the coefficient ratio: H₂ : O₂ : H₂O = 2 : 1 : 2.
2
With 20 mL of hydrogen, oxygen is half of that, 10 mL, and steam is the same as the hydrogen, 20 mL.
▸ 10 mL of oxygen is needed, and 20 mL of steam forms
The gas takes up 30 mL before the reaction and 20 mL after. The volume shrank, but the number of atoms and the mass did not change.
Example 2
At the same temperature and pressure, how do the numbers of molecules in equal volumes of hydrogen and oxygen compare? How does this connect to the volume ratio in gas reactions?
1
By Avogadro's law, equal volumes of gases at the same temperature and pressure contain the same number of molecules, whatever the gas.
2
So when gases react, the volume ratio equals the molecule ratio and also the coefficient ratio of the equation.
▸ They contain the same number of molecules, so volume ratio = molecule ratio = coefficient ratio
Thanks to Avogadro's law, measuring volumes is a way of comparing numbers of molecules too small to see.
Unit Test
Which statement about the law of combining volumes and Avogadro's law is correct?
①In a gas reaction the volume ratio is always a complicated decimal ratio
②Equal volumes of gas contain different numbers of molecules depending on the gas
③In a gas reaction the volume ratio equals the coefficient ratio of the chemical equation
④Avogadro's law holds only for solids
⑤At 0°C and 1 atm the volume of 1 mole of gas is 11.2 L
▸ ③ In a gas reaction the volume ratio equals the coefficient ratio of the chemical equation
1
The volume ratio of a gas reaction is a simple whole-number ratio (① wrong), and equal volumes of gas contain the same number of molecules regardless of the gas (② wrong, Avogadro).
2
Avogadro's law holds for gases (④ wrong), and at 0°C and 1 atm 1 mole of gas = 22.4 L (⑤ wrong); in a gas reaction the volume ratio = the coefficient ratio (③ correct).