Surface Reactions and Speciation

For common adsorbates the equilibrium constants of reactions involving only solution species are available from literature for less common adsorbates they can be determined in separate experiments that do not involve the adsorbent. The equilibrium constants of (hypothetical) surface reactions are the adjustable parameters of the model, and they are determined from the adsorption data by means of appropriate fitting procedure. With simple models (e.g. the model leading to Langmuir equation which has two adjustable parameters) the analytical equations exist for least-square best-fit model parameters as the function of directly measured quantities, but more complicated models require numerical methods to calculate their parameters. 

The equilibrium constants of (m + n)x(m + -l)/2 reversible reactions involving the adsorbate of interest are interrelated and only m + n-l of them are independent. On the other hand the availability of surface sites and solution species involved in these m + n-l independent reactions is affected by other surface and solution reactions (not involving the adsorbate of interest, e.g. adsorption of the competitors), thus the number of independent reactions whose equilibrium constants have to be pre-determined or fitted is usually much greater than m + n-l. 

The following general formulation is used to describe a chemical equilibrium problem (not necessarily related to adsorption). The system contains a number of chemical species. For each species i the stability constant Ki and the concentration c, are defined. In order to define K a set of components must be selected in such manner that  

There is no unique set of components for given problem. For example when the equilibrium between H3PO4, H2PO4, HP04 , P04 , and H is considered (cf. Fig. 4.4), any two (exactly two) of these five species can be selected as components. 

Mass Law equation is written for each species logc,- = log i + Evylog Jf  

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