Systematic Solution to Buffer Problems

Equation 6.44 is written in terms of the concentrations of CH3COOH and CH3COO- at equilibrium. A more useful relationship relates the buffer s pH to the initial concentrations of weak acid and weak base. A general buffer equation can be derived by considering the following reactions for a weak acid, HA, and the salt of its conjugate weak base, NaA. 

Since the concentrations of Na+, A-, HA, H3O+, and OH- are unknown, five equations are needed to uniquely define the solution s composition. Two of these equations are given by the equilibrium constant expressions 

The remaining three equations are given by mass balance equations on HA and Na+ 

Substituting equation 6.46 into the charge balance equation and solving for [A ] gives 

Finally, substituting equations 6.47 and 6.48 into the equation for HA and solving for pH gives the general buffer equation 

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