Calculation of Titration Curves for Acid and Base Determination

4 Calculation of Titration Curves for Acid and Base Determination 

In following hand calculations of titration results we will ignore activity coefficients to avoid excessively complicating the calculations. Titration curves are typically plotted in two ways. The plot is usually either (1) of the volume of a titrant acid or base added (Vg) versus the pH of the solution or (2) of the concentration of acid or base added (Q or C ) versus the solution pH. The plots have a similar appearance. We will derive algebraic expressions for each type of plot. The advantage of or Cfi versus pH plots and mathematical expressions is that they can be used to derive the buffer 

As a modeling exercise, consider the titration of a strong acid (HCl) with a strong base (NaOH). Derivation of the titration curve without volume correction must be in terms of Q or Cg versus pH. For titration of an HCl solution with NaOH titrant, the amount of base added will equal the Na+ in solution. In other words, Cg = Na. The charge-balance equation for the solution being titrated is 

This last equation is now in the proton condition. This means that we have eliminated all terms other than Cg, H as pH, and known concentrations and stability constants, allowing us to plot the equation as Cg versus pH. Assuming Cl = 0.01 eq/L, we now introduce values of H and solve for Cg. The results are plotted in Fig. 5.5. The figure shows the inflection point and endpoint at pH 7.0. 

We will next derive an expression for the titration curve showing the change in pH with volume of added base (cf. Butler 1964 Pankow 1991). First, define and as the original volume of solution to be titrated and the volume of added titrant. Thus, is known and fixed, and the final volume, V, is P = Vo -I- Vg. The original concentration of strong acid, HCl, will equal Clo, the original 

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