#### Learning Objective

- State Avogadro’s Law and its underlying assumptions

#### Key Points

- 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: [latex]\frac{V}{n} = k[/latex] , 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.

#### Term

- Avogadro’s Lawunder the same temperature and pressure conditions, equal volumes of all gases contain the same number of particles; also referred to as Avogadro’s hypothesis or Avogadro’s principle

## Definition of Avogadro’s Law

Avogadro’s Law (sometimes referred to as Avogadro’s hypothesis or Avogadro’s principle) is a gas law; it states that under the same pressure and temperature conditions, equal volumes of all gases contain the same number of molecules. The law is named after Amedeo Avogadro who, in 1811, hypothesized that two given samples of an ideal gas—of the same volume and at the same temperature and pressure—contain the same number of molecules; thus, the number of molecules or atoms in a specific volume of ideal gas is independent of their size or the molar mass of the gas. For example, 1.00 L of N_{2} gas and 1.00 L of Cl_{2} gas contain the same number of molecules at Standard Temperature and Pressure (STP).

Avogadro’s Law is stated mathematically as:

[latex]\frac{V}{n} = k[/latex]

V is the volume of the gas, n is the number of moles of the gas, and k is a proportionality constant.

As an example, equal volumes of molecular hydrogen and nitrogen contain the same number of molecules and observe ideal gas behavior when they are at the same temperature and pressure. In practice, real gases show small deviations from the ideal behavior and do not adhere to the law perfectly; the law is still a useful approximation for scientists, however.

## Significance of 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 calculated the molecular weight of oxygen using the incorrect formula HO for water. This lead to the molecular weight of oxygen being miscalculated as 8, rather than 16. However, when chemists found that an assumed reaction of H + Cl [latex]\rightarrow[/latex] 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}[latex]\rightarrow[/latex] 2HCl.

When chemists revisited their water experiment and their hypothesis that [latex]HO \rightarrow H + O[/latex], 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_{2}O) and the correct reaction [latex]2H_2O \rightarrow 2H_2 + O_2[/latex].