Editing Equilibrium constant (section)

=== Cumulative and stepwise formation constants ===
A cumulative or overall constant, given the symbol ''β'', is the constant for the formation of a complex from reagents. For example, the cumulative constant for the formation of ML<sub>2</sub> is given by
:M + 2&nbsp;L {{eqm}} ML<sub>2</sub>; {{spaces|5}} [ML<sub>2</sub>] = ''β''<sub>12</sub>[M][L]<sup>2</sup>
The stepwise constant, ''K'', for the formation of the same complex from ML and L is given by
:ML + L {{eqm}} ML<sub>2</sub>; {{spaces|5}} [ML<sub>2</sub>] = ''K''[ML][L] = ''Kβ''<sub>11</sub>[M][L]<sup>2</sup>
It follows that
:''β''<sub>12</sub> = ''Kβ''<sub>11</sub>
A cumulative constant can always be expressed as the product of stepwise constants. There is no agreed notation for stepwise constants, though a symbol such as ''K''{{su|b=ML|p=L}} is sometimes found in the literature. It is best always to define each stability constant by reference to an equilibrium expression.

==== Competition method ====
A particular use of a stepwise constant is in the determination of stability constant values outside the normal range for a given method. For example, [[EDTA]] complexes of many metals are outside the range for the potentiometric method. The stability constants for those complexes were determined by competition with a weaker ligand.
:ML + L′ {{eqm}} ML′ + L {{spaces|5}} <math>[\mathrm{ML}']=K\frac{[\mathrm{ML}][\mathrm{L}']}{[\mathrm{L}]} = K \frac{\beta_\mathrm{ML}[\mathrm{M}][\mathrm{L}][\mathrm{L}']}{[\mathrm{L}]}= K \beta_\mathrm{ML}[\mathrm{M}][\mathrm{L}']; \quad \beta_{\mathrm{ML}'}=K\beta_\mathrm{ML}</math>
The formation constant of [[Palladium(II) cyanide|[Pd(CN)<sub>4</sub>]<sup>2−</sup>]] was determined by the competition method.