Special Case Explicit Calculation for Polyprotic Acids

Special Case Explicit Calculation for Polyprotic Acids 

The Newton-Raphson algorithm we have developed can deal with any equilibrium situation. There is no limit to the number of components or species. The disadvantage is that the computations are iterative and this is clearly unsuitable for Excel applications. While it is possible to resolve complicated equilibria, it is inconvenient for complete titrations, as only one cell at a time can be evaluated. However, there are important special cases that can be solved explicitly. We deal with one here. 

Polyprotic acids are fairly important and their potentiometric pH titrations are common. For 2-component systems of this kind, it is possible to turn around the computations and come up with explicit, non-iterative solutions. So far we have computed the species concentrations knowing the total component concentrations, which is an iterative process. This is the normal arrangement in titrations where volumes and total concentrations are known and the rest is computed, e.g. the [H+] and thus the pH. Turning around things in this context means that one calculates the titration volume required to reach a given (measured) pH. One knows the i/-value and computes the corresponding x-value. In this way there are explicit equations that can directly be implemented in Excel. 

We develop the equations for the special case of a weak two-protic acid titrated with a strong base, and then generalise. 

The following equilibria occur and the law of mass action applies. 

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The concentrations of the differently protonated species, as a function of pH, are calculated with the explicit function we developed in Special Case Explicit Calculation for Polyprotic Acids, (p.64). A data matrix Y is constructed as before. Data eqAH2a. m generates the data, it is called by Main eqAH2a. m. 

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