Weak bases simplifying assumptions

In the following discussions of expressions relating hydrogen ion concentration to various points in the titration of a weak base with an acid, several simplifying assumptions are made ... 

We will hot constract a diprotic titration curve here, but if you want a good mental exercise, try it You just can t make the simplifying assumptions that we can usually use with monoprotic acids that are sufficiently weak or not too dilute. See your CD, Chapter 8, for auxiliary data for the spreadsheet calculation of the titration curve for 50.00 mL 0.1000 M H2C1O4 versus 0.1000 M NaOH. You can download that and enter the Kai and Kai values for other diprotic acids and see what their titration curves look like. Try, for example, maleic acid. For the calculations, we used the more exact equations mentioned above for the initial pH, the first buffet zone, and the first equivalence point. We did not use the quadratic equation for the second equivalence point since Cr04 is a quite weak base (Kbi = 3.12 X 10 ). See Ref. 8 for other examples of calculated titration curves. 

Weak acids and weak bases do not ionize (or protolyze) completely in aqueous solution. The approach used to solve for the concentrations of solution components for weak acid or base solutions is similar to that used for strong acids and strong bases, but we are not able to make the simplifying assumption in theKa orKt, equilibrium equations that complete dissociation takes place. Typical calculations for weak acid and weak base systems are illustrated in the following example. 

Constitutive equations can now be derived from the tube-based theories. Since the parameters in these equations are related to basic molecular parameters, these models should be truly predictive, but their ability to make quantitative predictions is limited because of the simplifying assumptions necessary to derive them. These equations and their strengths and weaknesses are presented in detail in Chapter 11. 

Examples 16-8 and 16-9 present a common problem involving weak acids and weak bases calculating the pH of a solution of known molarity. The calculation invariably involves a quadratic equation, but very often we can make a simplifying assumption that leads to a shortcut that saves both time and effort. 

In this example we will apply the same techniques as we did in Example 16-8. We will work the problem twice to see that the simplifying assumption breaks down for weak acids and weak bases at very low concentrations. 

The usual simplifying assumption is that of treating a weak acid or weak base as though it remains essentially nonionized (so that c — x c). In general, this assumption will work if the concentration (molarity) of the weak acid, c, or that of the weak base, cg, exceeds the value of or by a factor of at least 100. That is,... 

We see that in this example, the simplifying assumption works. We also note that the solution is fairly basic for a relatively dilute solution of a salt of a weak acid and a strong base. 

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