Avogadro's law establishes a fundamental relationship between the volume of a gas and the number of moles it contains, asserting that these two quantities are directly proportional when pressure and temperature remain constant. This principle, named after the Italian scientist Amedeo Avogadro, highlights how the volume of a gas is linked to the number of molecules present.

In practical terms, if the number of moles of gas increases, the volume must also increase to accommodate the additional molecules, ensuring that they maintain an optimal distance from one another. Conversely, if gas molecules are removed, the number of moles decreases, leading to a reduction in volume. This direct proportionality can be visually represented in a graph where the volume (V) increases as the number of moles (n) increases, starting from zero and rising steadily.

The mathematical expression of Avogadro's law can be articulated as:

$$\frac{V_1}{n_1} = \frac{V_2}{n_2}$$

In this equation, \(V_1\) and \(n_1\) represent the initial volume and number of moles, while \(V_2\) and \(n_2\) denote the final volume and number of moles. This relationship reinforces the concept that volume and moles change in tandem under constant pressure and temperature conditions, emphasizing their interconnected nature in the behavior of gases.