Laws of chemical combination

Law of conservation of mass (Lavoisier). In any chemical reaction, matter is neither created nor destroyed, so the total mass of the reactants exactly equals the total mass of the products.

where: $m_{\text{reactants}}$ and $m_{\text{products}}$ are the masses of every substance going into and coming out of the reaction, all measured in the same units (typically grams).

Law of definite (constant) proportions (Proust). A given compound always contains its constituent elements combined in the same fixed proportion by mass, no matter how the sample was prepared or where it came from. Water made in a lab and water condensed from a cloud both contain hydrogen and oxygen in the same $1 : 8$ mass ratio.

Law of multiple proportions (Dalton). When two elements combine to form more than one compound, the different masses of one element that combine with a fixed mass of the other stand to each other in a ratio of small whole numbers. Carbon and oxygen, for instance, form both CO and $\text{CO}_2$; for a fixed mass of carbon, the oxygen masses in the two compounds are in the ratio $1 : 2$.

Gay-Lussac's law of gaseous volumes. When gases react, the volumes of the reacting gases and of the gaseous products, measured at the same temperature and pressure, are in a ratio of small whole numbers. In $\text{H}_2 + \text{Cl}_2 \rightarrow 2\text{HCl}$, the volumes of $\text{H}_2$, $\text{Cl}_2$ and $\text{HCl}$ stand in the ratio $1 : 1 : 2$.

Avogadro's law. Equal volumes of any gas, at the same temperature and pressure, contain equal numbers of molecules. This was the missing piece that reconciled Gay-Lussac's whole-number volume ratios with Dalton's atomic theory: it forced chemists to accept that elemental gases such as $\text{H}_2$, $\text{O}_2$ and $\text{N}_2$ exist as diatomic molecules rather than lone atoms, since a single-atom picture could not produce Gay-Lussac's ratios without splitting atoms.

When $2.4\ \text{g}$ of magnesium is burnt completely in oxygen, $4.0\ \text{g}$ of magnesium oxide is obtained. In a separate experiment, $6.0\ \text{g}$ of magnesium gives $10.0\ \text{g}$ of magnesium oxide. Show that these results obey the law of definite proportions, and verify conservation of mass for the second experiment.

Step 1. Find the mass of oxygen that combined in each experiment. By conservation of mass, the mass of $\text{O}_2$ that reacted equals the mass of $\text{MgO}$ formed minus the mass of $\text{Mg}$ used, so for Experiment 1, $m_{\text{O}} = 4.0 - 2.4 = 1.6\ \text{g}$, and for Experiment 2, $m_{\text{O}} = 10.0 - 6.0 = 4.0\ \text{g}$.

Step 2. Compute the $\text{Mg} : \text{O}$ mass ratio in each experiment.

Step 3. Compare the two ratios. Both experiments give exactly the same $\text{Mg} : \text{O}$ mass ratio of $1.5 : 1$, even though the total masses used are quite different. This is the law of definite proportions in action: magnesium oxide always contains magnesium and oxygen combined in the same fixed mass ratio, regardless of how much of it you make.

Step 4. Verify conservation of mass for Experiment 2 by checking that reactant mass equals product mass. $m_{\text{Mg}} + m_{\text{O}} = 6.0 + 4.0 = 10.0\ \text{g} = m_{\text{MgO}}$, which confirms the law of conservation of mass: nothing was gained or lost, the oxygen mass simply joined the magnesium mass to give the oxide's mass. Both results obey the law of definite proportions (ratio $1.5:1$ in both experiments) and Experiment 2 obeys conservation of mass ($10.0\ \text{g} = 10.0\ \text{g}$).

Competitive stretch

Hydrogen and nitrogen react to form ammonia gas, $\text{N}_2 + 3\text{H}_2 \rightarrow 2\text{NH}_3$. If $20\ \text{mL}$ of nitrogen is used, what volumes of hydrogen and ammonia are involved, at the same temperature and pressure? By Gay-Lussac's law (explained by Avogadro's law — equal volumes contain equal numbers of molecules at fixed $T$, $P$), the reacting gas volumes follow the equation's coefficients directly: $\text{N}_2 : \text{H}_2 : \text{NH}_3 = 1 : 3 : 2$. Since $20\ \text{mL}$ of $\text{N}_2$ is the "1" part, $V_{\text{H}_2} = 3 \times 20 = 60\ \text{mL}$ and $V_{\text{NH}_3} = 2 \times 20 = 40\ \text{mL}$.

• Mixing up definite proportions (one compound, always the same mass ratio, any source) with multiple proportions (two different compounds of the same two elements, whole-number ratio between the combining masses).
• Applying Gay-Lussac's law to solids or liquids — it strictly concerns gas volumes only, and only when compared at the same temperature and pressure.
• Reading Avogadro's law as "equal numbers of atoms" — it says equal numbers of molecules, which is exactly why it forced elemental gases like $\text{H}_2$ and $\text{O}_2$ to be recognised as diatomic.
• Checking conservation of mass on a single element or compound instead of the total mass of the whole reacting system.

Ask the tutor: want to practise telling definite proportions apart from multiple proportions, or work through another Gay-Lussac gas-volume problem step by step?