Ludwig Wilhelmy and the birth of chemical kinetics

Wilhelmy’s birthplace – Stargard, Pomerania – in less happy times

The mid-point of the 19th century – 1850 – was a milestone year for the neophyte science of thermodynamics. In that year, Rudolf Clausius in Germany gave the first clear joint statement of the first and second laws, upon which Josiah Willard Gibbs in America would develop chemical thermodynamics. 1850 was also the year that the allied discipline of chemical kinetics was born, thanks to the pioneering work of Ludwig Wilhelmy.

Phase Equilibria and the usefulness of μ

It was the American mathematical physicist Josiah Willard Gibbs who introduced the concepts of phase and chemical potential in his milestone monograph On the Equilibrium of Heterogeneous Substances (1876-1878) with which he almost single-handedly laid the theoretical foundations of chemical thermodynamics.

In a paragraph under the heading “On Coexistent Phases of Matter” Gibbs mentions – in passing – that for a system of coexistent phases in equilibrium at constant temperature and pressure, the chemical potential μ of any component must have the same value in every phase.

This simple statement turns out to have considerable practical value as we shall see. But first, let’s go through the formal proof of Gibbs’ assertion.

How Gibbs derived the Phase Rule

The Phase Rule formula was first stated by the American mathematical physicist Josiah Willard Gibbs in his monumental masterwork On the Equilibrium of Heterogeneous Substances (1875-1878), in which he almost single-handedly laid the theoretical foundations of chemical thermodynamics.

In a paragraph under the heading “On Coexistent Phases of Matter”, Gibbs gives the derivation of his famous formula in just 77 words. Of all the many Phase Rule proofs in the thermodynamic literature, it is one of the simplest and shortest. And yet textbooks of physical science have consistently overlooked it in favor of more complicated, less lucid derivations.

Conditions of equilibrium and stability

In terms of simplicity, purely mechanical systems have an advantage over thermodynamic systems in that stability and instability can be defined solely in terms of potential energy. For example the center of mass of the tower at Pisa, in its present state, must be higher than in some infinitely near positions, so we can conclude that the structure is not in stable equilibrium. This will only be the case if the tower attains the condition of metastability by returning to a vertical position or absolute stability by exceeding the tipping point and falling over.

Thermodynamic systems lack this simplicity, but in common with purely mechanical systems, thermodynamic equilibria are always metastable or stable, and never unstable. This is equivalent to saying that every spontaneous (observable) process proceeds towards an equilibrium state, never away from it.

Reversible and irreversible change

Reversible change is a key concept in classical thermodynamics. It is important to understand what is meant by the term as it is closely allied to other important concepts such as equilibrium and entropy. But reversible change is not an easy idea to grasp – it helps to be able to visualize it.