Equilibria in Multiple Acid-Base Systems

When more than one conjugate add-base pair is in equilibrium with water, the exact mathematical relations for calculation of [H ] become complex, especially if a single equation is to represent all possible initial conditions. The derivation of such equations can clarify the nature of approximations made in practical applications. In many cases, however, simplification may be achieved at the outset by using approximate calculations to estimate the concentrations of the major species concerned and then testing the validity of the approximations. If the concentration levels or equilibrium constants for a system are so unusual that the simple equations are not valid, exact equations can be used.  

Solution of polybasic add A solution containing only a polybasic add and water can almost always be treated by considering only tKe first step of ionization. To illustrate, if the dibasic acid HjA is added to water, we have the equilibria 

As a first approximation, ignore the second ionization step. Thus 

If necessary, second and further approximations may be made by adding (3-35) and (3-36) to give 

From the new values of [H ] and [HA-] a better value of [A ], namely [A ] , is calculated, which can be substituted for [A ] in (3-39) and (3-40). These additional steps, however, are rarely necessary, as is demonstrated by the following examples. 

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