Avogadro's Law

The Fundamental Principle

"Equal volumes of all gases at the same temperature and pressure contain the same number of molecules."

This revolutionary idea, proposed by Amedeo Avogadro in 1811, resolved many inconsistencies in chemistry and led to our modern understanding of molecules.

Mathematical Expressions

Volume-Mole Relationship

V1n1=V2n2\frac{V_1}{n_1} = \frac{V_2}{n_2}

Direct Proportionality

V∝n(at constant T and P)V \propto n \quad (\text{at constant }T\text{ and }P)

Molar Volume

Vm=Vn=22.4 L/mol at STPV_m = \frac{V}{n} = 22.4\text{ L/mol at STP}

where:

  • V = volume of gas
  • n = number of moles
  • Vm = molar volume
  • STP = Standard Temperature and Pressure (0°C, 1 atm)

Visualization

Below is a visualization showing equal volumes of two different gases containing the same number of molecules:

The visualization shows two containers of equal volume with the same number of molecules (represented by spheres) in random motion, demonstrating Avogadro's principle.

Applications and Implications

  • Determination of molecular masses
  • Gas stoichiometry calculations
  • Understanding gas density relationships
  • Development of the ideal gas law
  • Modern chemical analysis techniques

Historical Impact

Avogadro's hypothesis was initially controversial but gained acceptance after Cannizzaro's 1858 presentation at the Karlsruhe Congress. It became a cornerstone of modern atomic-molecular theory and helped establish the field of stoichiometry.