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Bill Brum's revolutionary discovery: How did he determine the stability constant?
In coordination chemistry, the stability constant (also called the formation constant or binding constant) is the equilibrium constant for the formation of a complex in solution. It measures the strength of the interaction between reactants to form a complex. These complexes mainly include compounds formed by metal ions and ligands, as well as supramolecular complexes such as host-guest complexes and anion complexes. Stability constants provide the information needed to calculate the concentration of a complex in solution and have a wide range of applications in several fields including chemistry, biology, and medicine.
Historical BackgroundIn 1941, Jannik Bjerrum developed the first general method for determining the stability constants of metal-amide complexes. This progress came relatively late, since the correct structure of the coordination compound had been proposed by Alfred Werner nearly fifty years earlier. The key to Bilrum's method was the use of the then-newly developed glass electrode and pH meter, which could be used to determine the concentration of hydrogen ions in solution. He realized that the process of metal ions and ligands forming metal complexes is actually an acid-base equilibrium: there is a competition between metal ions (Mn+) and hydrogen ions (H+), resulting in the existence of two equilibria at the same time.
"Bill Rummel determined the stability constant of ML by tracking the hydrogen ion concentration by adding alkaline acid to the mixture and using the acid dissociation constant of HL."
Bilrum then set out to determine the stability constants for the many possible complexes that could be formed. Over the next two decades, the number of stability constants grew almost exponentially, with relationships discovered including the Irving-Williams series. Computing at that time was mainly done by hand, relying on so-called graphical methods. The mathematical methods used during this period are briefly described in detail in the works of Rossotti and Rossotti. The next key development was the use of the computer program LETAGROP for calculations, which made it possible to examine overly complex systems.
Theory
The reaction between the metal ion M and the ligand L to form a complex is usually a substitution reaction. For example, in aqueous solutions, metal ions usually exist in the form of hydrated ions. Therefore, the reaction to form the first complex can be expressed as:
[M(H2O)n] + L ⇋ [M(H2O)n-1L] + H2O. The equilibrium constant of this reaction can be expressed as: β' = [M(H2O)n-1L][H2O] / [M(H2O)n][L]. In dilute solutions, the water concentration can be considered a constant, resulting in a more simplified form:
β = [ML] / [M][L].
"With the deepening of research, the determination of stability constants has become almost a "routine" operation today, and the data of various complexes have accumulated to thousands."
Step constants and cumulative constants
The accumulation constant (β) is the constant in the process of forming the complex from the raw material. For example, for the accumulation constant that forms ML2, it can be expressed as β1,2 = [ML2] / [M][L]2. The step constants K1 and K2 refer to the step-by-step formation of the complex. This occupancy representation facilitates the understanding of the dynamic process of metal-ligand complex formation.
Hydrolysis products
Hydrolysis reactions generally involve a chemical reaction with water as a substrate and produce hydroxide and hydrogen ions. Typical hydrolysis complex formation can be represented as M + OH ⇋ M(OH). The reaction constant can be expressed as K = [M(OH)] / [M][OH]. Studying these hydrolysis reaction constants can provide a deeper understanding of the chemical properties of metals.
Thermodynamics and Stability Constants
Studying the thermodynamics of complex formation between metal ions and ligands provides important information, especially in distinguishing between enthalpic and entropic effects. These thermodynamic concepts are particularly useful in explaining phenomena such as the chelation effect. There is a close relationship between the standard Gibbs free energy change (ΔGθ) and the equilibrium constant of the reaction:
ΔGθ = -2.303RT log β. These relationships not only provide insights into responses, but also help predict impacts from the micro to the macro scale.
With the development of research, the determination and analysis of stability constants has become one of the important areas of contemporary chemistry. Can we expect more such groundbreaking discoveries in the future?
