Graphical Solutions to Polyprotic pH Problems

If we could know the equilibrium fractions a of the species present, it would be a simple matter to find the pH of solutions. However, we usually know only the initial materials, the analytical concentrations. Algebraic methods of approximation will be given in the next chapter. The graphical methods here help in understanding these equilibria and in evaluating the approximate equations to be found later. 

We follow a similar course to that in Chapter 4, where the intersection of equilibrium and material balance fraction functions solves the problem. Here, the fraction of combined protons is needed. Take the sum of all available H acidity (using a triprotic example) 

For example, a 0.1 M H3A solution should have Ch = 0.3 M but distributed in an unknown proportion among the terms on the right-hand side of equation (5-6). We can rearrange this to get two expressions for the bound proton concentration  

Ch — D is just the material balance statement that the bound acidity is the total acidity minus the unbound acid D. The other term is the sum of the equilibrium species binding protons. Next we obtain our ratio of bound acidity to the total A species C. This is the average number of protons per A, called h, a very useful experimental function. Divide by C  

We call the first n, and the second having the same significance as in Chapter 4, for equilibrium condition and for material balance condition, respectively. From the definitions of the a fractions in set of equations (5-4), we can write these as 

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