Coordination Complex Stability - Overall vs. Stepwise Formation Constants

Thermodynamic Equations:

$$\begin{aligned} \text{Stepwise Stability:} &\quad K_n = \frac{[\text{ML}_n]}{[\text{ML}_{n-1}][\text{L}]} \\ \text{Overall Stability (\beta\_n):} &\quad \beta_n = K_1 \cdot K_2 \cdot K_3 \dots K_n \implies \log \beta_n = \sum_{i=1}^{n} \log K_i \end{aligned}$$

Concept: The synthesis of a complex occurs in sequential equilibrium steps. The cumulative overall stability constant ($$\beta_n$$) represents the complete thermodynamic stability of a complex in aqueous solution. Larger values of $\beta$ indicate higher thermodynamic stability.

Notation:

• $$K_1, K_2, \dots, K_n$$ = Stepwise equilibrium formation constants;
• $$\beta_n$$ = Overall cumulative formation constant;
• Instability constant (dissociation constant) $$= \frac{1}{\beta_n}$$.