Avogadro's Law
The Relationship between Volume and Amount of Gas.
In 1811, Italian scientist Amedeo Avogadro made a bold hypothesis connecting the macroscopic volume of a gas to the microscopic number of molecules it contains. This law completes the puzzle needed to formulate the Ideal Gas Equation.
1. Statement & Mathematical Formula
Avogadro's Law states: Equal volumes of all gases, under the exact same conditions of temperature and pressure, contain an equal number of molecules (or moles).
Stated differently: If temperature and pressure are kept constant, the volume of a gas is directly proportional to the number of moles ($n$) of the gas. If you pump more gas into a balloon, it expands!
$$\frac{V}{n} = k \quad (\text{where } k \text{ is a constant})$$
The Problem-Solving Equation:
If you add or remove gas from a flexible container at constant T and P:
2. Moles vs. Mass (The Exam Trick)
Examiners love to test if you understand that Avogadro's law deals with the number of molecules (moles), NOT the mass.
- Do they have the same volume? Yes (1 L).
- Do they have the same number of molecules? Yes (Avogadro's Law).
- Do they have the same mass? NO!
Because $O_2$ ($32 \text{ g/mol}$) is much heavier than $H_2$ ($2 \text{ g/mol}$), the flask with Oxygen will weigh significantly more, even though it contains the exact same number of molecules.
3. Graphical Representation
A graph plotted between Volume ($V$) and the number of moles ($n$) at constant temperature and pressure is a straight line passing through the origin.
Volume vs Moles (n)
Straight line through origin.
4. Connection to Molar Volume
Avogadro's Law is the reason we have standard Molar Volumes!
- Since $V \propto n$, if we set $n = 1 \text{ mole}$, the volume becomes a fixed constant for any specific temperature and pressure.
- At Old STP ($0^\circ C$, $1 \text{ atm}$), $1 \text{ mole}$ of ANY ideal gas occupies $22.4 \text{ L}$.
- At New STP ($0^\circ C$, $1 \text{ bar}$), $1 \text{ mole}$ of ANY ideal gas occupies $22.7 \text{ L}$.
Knowledge Check
Test your understanding of Avogadro's Law
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