Moles and Volume
Proposed by Amedeo Avogadro in 1811, Avogadro's Law states that equal volumes of all ideal gases, measured at the exact same temperature and pressure, contain the exact same number of molecules.
This means that the volume of a gas is directly proportional to the amount of substance (the number of moles) of the gas present. The true brilliance of this law is its independence from the type of gas. Whether you have lightweight Hydrogen or heavy Xenon gas, if they occupy the same space under the same conditions, you have the exact same number of atoms.
Chemical Stoichiometry
Avogadro's law is the bedrock of modern chemistry:
- Molar Volume: It established the famous constant that at Standard Temperature and Pressure ($273.15 , \text{K}$ and $1 , \text{atm}$), exactly $1 , \text{mole}$ of any ideal gas will occupy precisely $22.4 , \text{Liters}$ of physical space.
- Blowing up a Balloon: At the most basic level, this law explains why a balloon gets larger as you blow into it. You are forcing more molecules (moles) of air into the balloon. Since the pressure and temperature are relatively constant, the volume must increase proportionally to make room for the new molecules.
- Gas Reactions: If $2 , \text{Liters}$ of Hydrogen gas react with $1 , \text{Liter}$ of Oxygen gas to form water, chemists know immediately that there are twice as many molecules of Hydrogen reacting than Oxygen.
The Formula
Example Calculation
A piston contains $1 , \text{mole}$ of gas occupying exactly $22.4 , \text{Liters}$. You inject an additional $1 , \text{mole}$ of gas into the piston while maintaining constant pressure and temperature.
- Divide Initial Volume by Initial Moles ($V_1 / n_1$): $22.4 / 1 = 22.4$.
- Multiply by New Total Moles ($n_2 = 1 + 1 = 2$): $22.4 \cdot 2 = 44.8 , \text{Liters}$.
Because you doubled the amount of physical gas molecules inside the container, the volume of the container perfectly doubled to $44.8 , \text{Liters}$ to maintain equilibrium.