In 1861, 40-year-old Austrian physicist and chemist Johann Josef Loschmidt (1821–1895) published his historic paper, “Chemische Studien” (“Chemical Studies”), followed by his 1865 memoir in Sitzungsberichte der Wiener Akademie.

Loschmidt achieved the world’s first realistic measurement of the absolute size of molecules and determined the number of molecules per unit volume of ideal gas (Loschmidt Constant).

Mathematical Calculation of Molecular Diameter ($\sigma$)

Loschmidt combined Rudolf Clausius’s mean free path formula ($\lambda$) with the condensation volume fraction ($V_{\text{liquid}} / V_{\text{gas}}$):

1. Mean Free Path Relation

$$\lambda = \frac{1}{\sqrt{2} \pi n \sigma^2}$$

2. Condensation Fraction Relation

The total volume occupied by $N$ spherical molecules of diameter $\sigma$ in liquid condensation state is:

$$V_{\text{liquid}} \approx N \frac{\pi}{6} \sigma^3$$

3. Loschmidt’s Result

By eliminating molecular number density $n = N/V$, Loschmidt calculated:

$$\sigma \approx 1.0 \times 10^{-9}\,\text{meters} = 1.0\,\text{nanometer}$$

And calculated the number of gas molecules per cubic centimeter at STP (Loschmidt Constant $n_0 \approx 2.68 \times 10^{19}\,\text{cm}^{-3}$), yielding Avogadro’s number $N_{\text{A}} \approx 6 \times 10^{23}\,\text{mol}^{-1}$.

Scientific Significance & Atomic Reality

Loschmidt’s calculation proved that atoms and molecules are real physical objects of finite nanometer size, disproving 19th-century energeticist theories that denied atomic reality.

Key Takeaways

  • Year: 1861
  • Key Figure: Johann Josef Loschmidt (Austrian Physicist)
  • Core Discovery: Calculated the absolute size of molecules ($\sigma \approx 1\,\text{nm}$) and Avogadro’s constant.
  • Named Constant: The Loschmidt Constant ($n_0 = 2.6868 \times 10^{25}\,\text{m}^{-3}$) bears his name.
  • Quantum Relevance: Established physical atomic scale ($1\,\text{nm}$) governing quantum nanostructures and atomic orbitals.