Acid-Base Titration Curves

Learning Goals

You will learn how to determine the pH at the equivalence point using acid-base titration curves and a variety of types of acid-base combinations.

Synopsis

To develop an acid-base titration curve, we need to be able to calculate the hydronium ion concentration during each point of the addition of a base to an acid. We will not be using any new concepts to do these calculations; there will just be a number of calculations to do. The best way to illustrate this technique is to work an example. We can investigate the titration of a strong acid with a strong base as done in your text. Beginning with 50 mL of a 0.100-M solution of HCl, let's calculate a number of points along the titration with 0.100 M NaOH. Because HCl is a strong acid, the initial pH is 1.000. Now let's add 10.0 mL of the 0.100 M NaOH and calculate the new pH. We then will have the following:

concentration Moles H₃O⁺ Moles OH^-

Before reaction 0.00500 M in 50.0 mL solution 0.00100 in 10 mL solution

Change on reaction -0.00100 -0.001000

After reaction 0.00400 mol in 60.0 mL solution 0

Concentration after reaction 0.0667 = 0.00400mol/0.0600L 0

The pH is then 1.176 after the addition of 10 ml of 0.100 M NaOH. We can easily develop an equation to calculate the hydronium ion concentration and hence the pH at any point in the titration:

[H₃O⁺] = (original moles of acid - total moles of base added)/(volume acid + volume base added

At the equivalence point the pH is 7.00 because we are titrating a strong acid with a strong base (at 25 ^oC). After the equivalence point we have no HCl and only an aqueous solution of NaCl to which we are adding OH^- so the pH is simply determined from the amount of hydroxyl ions added. From these calculations we can then generate an acid-base titration curve as shown by Figure 18.5 in your text and repeated below.

Refer to FIGURE 18.5 from the text

You see that when the pH approaches that of the equivalence point, there is an extremely rapid rise in the slope of the curve. The pH rises about 7 units when a very small amount of base is added.

The titration of a weak acid with a strong base is a bit more complicated because now we are dealing with an equilibrium reaction rather than a complete ionization. Your text walks you through the titration of acetic acid with sodium hydroxide which end with the titration curve

Refer to FIGURE 18.6 from the text

Again you see the rapid rise in pH as the equivalence point is raised, but the approach portion of the curve has a different shape. There is another important point in the titration and that is when half of the acid has been consumed. At this point [H3O+] is equal to Ka so we have a means of experimentally determining the value of Ka for a weak acid. The titration of a weak base with a strong acid would have the same type of titration curve but inverted as shown in Figure 18.8.

The final type of titration curve discussed is that of a diprotic acid. Now there will be two portions of a rise in the pH of the curve due to the loss of two hydrogen atoms. The first rise will not be as sharp as the second due to the presence of the weak acid (one proton lost) and its conjugate base - a buffer solution that will resist a rise in pH upon the addition of base. The second rise will be very sharp as in the monoprotic acids because there will no longer be a buffer solution.

Review Question

1. Sketch the titration curve that you would expect for the titration of phosphoric acid with sodium hydroxide.

On-Line Activity

Go to this site to practice some titration problems: titration
Here is a super neat site to practice titrations with some simulations : simulations

concentration	Moles H₃O⁺	Moles OH^-
Before reaction	0.00500 M in 50.0 mL solution	0.00100 in 10 mL solution
Change on reaction	-0.00100	-0.001000
After reaction	0.00400 mol in 60.0 mL solution	0
Concentration after reaction	0.0667 = 0.00400mol/0.0600L	0