The laws of chemical combination

Weighing changes everything

Before the 1770s, chemists described reactions mainly by colour, smell and taste. Then a few of them began to weigh everything, before and after a reaction, with good balances. Patterns appeared at once. These patterns are the laws of chemical combination. They were found before anyone could see an atom, and they led John Dalton to the idea of atoms.

The law of conservation of mass

Antoine Lavoisier heated metals inside sealed glass vessels. The metal changed into a powder, but the sealed vessel weighed the same before and after. When he opened it, air rushed in, and only then did the mass go up.

Matter can neither be created nor destroyed in a chemical reaction. The total mass of the products equals the total mass of the reactants.

Here is the law at work in a test tube. A solution of silver nitrate is mixed with a solution of sodium chloride, and a white solid, silver chloride, appears.

Before: $3.40 + 1.17 = 4.57\ \text{g}$. After: $2.87 + 1.70 = 4.57\ \text{g}$. Nothing is lost. A burning candle seems to lose mass only because its products, carbon dioxide and water vapour, escape into the air.

The law of definite proportions

Joseph Proust analysed copper carbonate from nature and copper carbonate made in the laboratory. Both had the same make-up by mass.

A given compound always contains exactly the same elements in the same proportion by mass, whatever its source.

Copper(II) oxide shows it well. It can be made in three ways, and each sample is analysed:

The masses differ, but the share of copper is the same. If a sample gave $70\%$ copper, it would not be copper(II) oxide.

The law of multiple proportions

Some pairs of elements form more than one compound. Dalton noticed a pattern in them.

If two elements form more than one compound, the masses of one element that combine with a fixed mass of the other are in a ratio of small whole numbers.

Nitrogen and oxygen form five oxides. Fix the mass of nitrogen at $1$ g and look at the oxygen:

The ratio is $1 : 2 : 3 : 4 : 5$. Oxygen joins nitrogen only in whole steps. This is a strong hint that oxygen comes in pieces of fixed mass: atoms.

Gay Lussac's law of gaseous volumes

Joseph Gay Lussac measured gases, not by mass but by volume, at the same temperature and pressure.

When gases combine or are produced in a reaction, their volumes are in a simple whole-number ratio, if all are measured at the same temperature and pressure.

• $1$ volume of hydrogen and $1$ volume of chlorine give $2$ volumes of hydrogen chloride.
• $1$ volume of nitrogen and $3$ volumes of hydrogen give $2$ volumes of ammonia.

Notice that volume, unlike mass, is not conserved: $1 + 3$ volumes become only $2$.

Set the nitrogen to $40$ mL and change the hydrogen. Below $120$ mL of hydrogen, some nitrogen is left over. Above it, some hydrogen is left.

Avogadro's law

In 1811, Amedeo Avogadro explained Gay Lussac's numbers.

Equal volumes of all gases, at the same temperature and pressure, contain equal numbers of molecules.

Take $1$ volume of hydrogen and $1$ volume of chlorine, giving $2$ volumes of hydrogen chloride. Suppose each volume holds $n$ particles. Then $n$ particles of hydrogen and $n$ of chlorine give $2n$ particles of hydrogen chloride. Each of them needs some hydrogen, so each particle of hydrogen must split into two. So hydrogen gas is made of molecules of two atoms, $\text{H}_2$, and so is chlorine. Avogadro was the first to separate atoms from molecules. Few chemists accepted it for fifty years.

Practise with new numbers

Try it in Python

The program finds the oxygen for each gram of nitrogen in the five oxides, and divides by the first.

Common mistakes

• Thinking mass is lost when a gas escapes. The mass is still there, in the air. Weigh in a closed vessel and nothing is lost.
• Expecting volumes to add up. Masses add up in every reaction. Volumes of gases do not: $1$ volume of nitrogen and $3$ of hydrogen give $2$ of ammonia.
• Mixing up the two proportion laws. Definite proportions is about one compound. Multiple proportions compares two or more compounds of the same two elements.
• Comparing volumes at different conditions. Gay Lussac's and Avogadro's laws hold only at the same temperature and pressure.

Remember these

• Conservation of mass: total mass of products = total mass of reactants.
• Definite proportions: one compound, always the same make-up by mass.
• Multiple proportions: for a fixed mass of one element, the masses of the other are in a small whole-number ratio.
• Gay Lussac: reacting gases have volumes in a small whole-number ratio.
• Avogadro: equal volumes of gases at the same temperature and pressure hold equal numbers of molecules.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. A strip of iron rusts in a sealed jar of air. Does the mass of the jar and its contents go up, go down or stay the same?

2. Two samples of pure table salt are $39.3\%$ sodium by mass. A third white powder is $27.4\%$ sodium. Can the third be table salt?

3. Carbon forms two oxides. For $12$ g of carbon, one holds $16$ g of oxygen and the other $32$ g. Which law do they show?

4. At the same temperature and pressure, $2$ volumes of carbon monoxide react with $1$ volume of oxygen. What volume of carbon dioxide forms?

5. How did Avogadro's law show that hydrogen gas is made of molecules of two atoms?