# Avogadro's Law

Discovering that the volume of a gas was directly proportional to the number of particles it contained was crucial in establishing the formulas for simple molecules at a time (around 1811) when the distinction between atoms and molecules was not clearly understood. In particular, the existence of diatomic molecules of elements such as \(H_2\), \(O_2\), and \(Cl_2\) was not recognized until the results of experiments involving gas volumes was interpreted.

Early chemists mistakenly assumed that the formula for water was \(HO\), leading them to miscalculate the molecular weight of oxygen as 8 instead of 16. However, when chemists found that an assumed reaction of

\[H+Cl→HCl\]

yielded twice the volume of \(HCl\), they realized hydrogen and chlorine were diatomic molecules. The chemists revised their reaction equation to be

\[H_2+Cl_2→2HCl.\]

When chemists revisited their water experiment and their hypothesis that

\[HO \rightarrow H + O\]

they discovered that the volume of hydrogen gas consumed was twice that of oxygen. By Avogadro's Law, this meant that hydrogen and oxygen were combining in a 2:1 ratio. This discovery led to the correct molecular formula for water (\(H_2O\)) and the correct reaction

\[2H_2O→2H_2+O_2.\]

### Summary

- The number of molecules or atoms in a specific volume of ideal gas is independent of size or the gas' molar mass.
- Avogadro's Law is stated mathematically as follows: \(\frac{V}{n} = k\), where \(V\) is the volume of the gas, n is the number of moles of the gas, and k is a proportionality constant.
- Volume ratios must be related to the relative numbers of molecules that react; this relationship was crucial in establishing the formulas of simple molecules at a time when the distinction between atoms and molecules was not clearly understood.

### Contributors

Boundless (www.boundless.com)