Laws of Chemical Combinations

Stoichiometry describes the quantitative relationships that exist between substances undergoing chemical changes. The word comes from Greek: stoicheion (element) + metron (measure).

It is built on five foundational laws of chemical combination:

1. Law of Conservation of Mass
2. Law of Definite Proportions
3. Law of Multiple Proportions
4. Law of Reciprocal Proportions
5. Gay Lussac's Law of Gaseous Volumes

Avogadro's Law is closely related and ties gaseous volumes to molecules.

Lavoisier (1744) stated: "Matter can neither be created nor destroyed during any chemical or physical change; however, its physical or chemical nature may change."

In simple terms: the total mass of reactants = total mass of products.

Examples:

• Ice $\rightarrow$ Water: 20 g of ice gives exactly 20 g of water
• $\ce{H2(g) + \frac{1}{2}O2(g) -> H2O(l)}$: 2 g + 16 g $\rightarrow$ 18 g
• $\ce{H2 + Cl2 -> 2HCl}$: 2 g + 71 g $\rightarrow$ 73 g

Exception: In nuclear reactions, some mass is converted into energy as per $E = mc^2$.

Proust (1799) stated: "A chemical compound, irrespective of the source from which it is obtained, always contains the same elements combining in definite ratios by mass."

Examples:

• $\ce{H2O}$ from a river, pond, or rain — H and O are always in a 1:8 ratio by mass
• $\ce{CO2}$ formed by burning carbon or decomposing limestone — C and O always in a 3:8 ratio by mass (i.e., 12 g C + 32 g O = 44 g $\ce{CO2}$)

Exceptions: Isotopes and non-stoichiometric compounds.

• $\ce{H2^{16}O}$ has H:O = 1:8, but $\ce{H2^{18}O}$ has H:O = 1:9 (due to heavier oxygen isotope)
• $\ce{Fe_{0.95}O}$ is a non-stoichiometric compound containing a mixture of $\ce{Fe^{2+}}$ and $\ce{Fe^{3+}}$ ions

Dalton stated: "When two elements combine with each other to form two or more compounds, then the different amounts of one element which react with a definite amount of the second element are in a simple whole number ratio."

Classic example — nitrogen and oxygen form five different oxides:

The masses of oxygen combining with a fixed 28 g of nitrogen are: 16 : 32 : 48 : 64 : 80 = 1 : 2 : 3 : 4 : 5 — a simple whole number ratio. ✓

Another example: CO and $\ce{CO2}$ both contain C and O. In CO, C:O = 12:16. In $\ce{CO2}$, C:O = 12:32. For a fixed 12 g of carbon, oxygen masses are 16 g and 32 g → ratio 1:2.

Richter stated: when two different elements each combine separately with a fixed mass of a third element, the ratio of their two masses is the same as — or a simple multiple of — the ratio in which those two elements combine directly with each other.

Take hydrogen, oxygen and sulphur:

• In $\ce{H2O}$, 1 g of hydrogen combines with 8 g of oxygen.
• In $\ce{H2S}$, 1 g of hydrogen combines with 16 g of sulphur.
• So, measured against the same 1 g of hydrogen, oxygen and sulphur stand in the ratio 8 : 16 = 1 : 2.

Now let sulphur and oxygen combine directly: in $\ce{SO2}$ they react as 32 g : 32 g = 1 : 1. The law predicts that direct ratio should be 1 : 2 or a simple multiple of it, and 1 : 1 is exactly that (a 2× multiple). The prediction holds — without anyone ever weighing a single atom.

Gay Lussac's Law of Gaseous Volumes: In a gaseous reaction, the reactants combine in simple ratios by volume, and the products are also formed in simple ratios by volume — at the same temperature and pressure.

Examples:

• $\ce{H2(g) + Cl2(g) -> 2HCl(g)}$: 1 L + 1 L $\rightarrow$ 2 L (ratio 1:1:2)
• $\ce{N2 + 3H2 -> 2NH3}$: 1 L + 3 L $\rightarrow$ 2 L (ratio 1:3:2)

This law applies only to gaseous reactions. It relates volume to moles or molecules — NOT directly to mass.

Avogadro's Law: Equal volumes of all gases contain equal number of molecules at the same temperature and pressure.

$PV = nRT \quad \Rightarrow \quad n = \frac{PV}{RT}$

If V, P, and T are the same for two gas containers, then $n$ (number of moles / molecules) must also be the same — regardless of which gas is inside.