16.4 – 16.5

	Chemistry 8th Edition / Chang
	Student Study Guide

Chapter 16: Acid-Base Equilibria and Solubility Equilibria

Index | 16.2 – 16.3 | 16.4 – 16.5 | 16.6 | 16.6 – 16.7 | 16.8 – 16.9 | 16.10 |

TITRATION CURVES AND INDICATORS (16.4 – 16.5)

STUDY OBJECTIVES

Describe the shape of titration curves for titrations involving a strong acid and a strong base, a weak acid and a strong base, and a strong acid and a weak base.
Choose the best indicator for a particular acid-base titration.

Titration Curves. Acid-base titrations were discussed in Chapter 4. With the introduction to pH in the previous chapter, it is informative to follow the pH as a function of the progress of the titration. A graph of pH versus volume of titrant added is called a titration curve. Initially, the pH is that of the unknown solution. As titrant is added, the pH becomes that of a partially neutralized solution of unknown plus titrant. The pH at the equivalence point refers to the H⁺ ion concentration when just enough titrant has been added to completely neutralize the unknown. If more titrant is added after the equivalence point has been reached, the pH assumes a value consistent with the pH of excess titrant. We will review three types of titration curves.

Strong acid-strong base titrations. Figure 16.3 of the text shows a titration curve for the addition of a strong base to a strong acid. The main features of this curve can be stated briefly. 1. The pH starts out quite low because this is the pH of the pure acid solution. 2. As base is slowly added, it is neutralized, and the pH is determined by the unreacted excess acid. Near the equivalence point, the pH begins to rise more rapidly. 3. At the equivalence point the pH changes sharply, increasing about 5.0 units upon the addition of only two drops of base. 4. Beyond the equivalence point the pH is determined by the amount of excess base that is added and is higher than 7.

The pH at the equivalence point of an acid-base titration is the pH of the salt solution that is formed by neutralization. NaCl, NaNO₃, NaBr, KCl, and KI are examples of salts that can be formed in titrations of strong acids and strong bases. These salts yield ions that do not cause hydrolysis (Chapter 15). Therefore, the pH at the equivalence point in a titration of a strong acid with a strong base is 7.

Weak acid-strong base titrations. Figure 16.4 of the text shows a titration curve for the addition of a strong base to a weak acid. Because the acid is a weak acid, the initial pH is greater than in the titration of a strong acid. At the equivalence point, the pH is above 7.0 because of salt hydrolysis. The anion of the salt is the conjugate base of the weak acid used in the titration. In the titration of acetic acid with sodium hydroxide the salt produced is CH₃COONa. The Na⁺ ion does not hydrolyze, but CH₃COO^– does:

CH₃COO^– + H₂O CH₃COOH + OH^–

Hydrolysis of acetate ions makes the solution basic at the equivalence point.

Strong acid-weak base titrations. Figure 16.5 of the text shows a titration curve for the addition of a weak base to a strong acid. The first part of the curve is the same as in the strong acid versus strong base titration. However, the pH at the equivalence point is below 7.0 because the cation of the salt is the conjugate acid of the weak base used in the titration. Hydrolysis of this salt yields an acidic solution. In the titration of hydrochloric acid with ammonia, the salt produced is NH₄Cl. The Cl^– ion does not hydrolyze, but does:

NH₄⁺ + H₂O NH₃ + H₃O⁺

EXAMPLE Net Ionic Equations

Write the net ionic equations for the neutralization reactions that occur during the following titrations. Predict whether the pH at the equivalence point will be above, below, or equal to 7.0.

a. Titration of HI with NH₃.

no reaction and pH

HI + NH₃ NH₄⁺ + I

H⁺ + NH₃ NH₄⁺

I^- + NH₃ NH₃I^-

b. Titration of HI with NaOH.

no reaction and pH

HI + NaOH H₂O + NaI

HI + OH^- H₂O + I^-

H⁺ + NaOH H₂O + Na⁺

H⁺ + OH^- H₂O

I^- + Na⁺ NaI

I^- + NaOH NaI + OH^-

c. Titration of HF with NaOH.

no reaction and pH

HF + NaOH H₂O + NaF

HF + OH^- H₂O + F^-

H⁺ + NaOH H₂O + Na⁺

H⁺ + OH^- H₂O

F^- + Na⁺ NaF

F^- + NaOH NaF + OH^-

Correct!

Click a Hint button for help.

a. This is a titration of a strong acid with a weak base. HI is 100 percent dissociated, and NH₃ is a weak base. The net ionic equation for neutralization is

H⁺ + NH₃ NH₄⁺

The result of the neutralization reaction is formation of the conjugate acid of the weak base NH₃. is an acid. Answer: The pH at the equivalence point will be below 7.0.

b. This is a titration of a strong acid and a strong base. The net ionic equation is

H⁺ + OH^– H₂O

The resulting solution is neutral at the equivalence point. Answer: pH = 7.0

c. This titration involves a weak acid and a strong base.

HF + OH^– H₂O + F^–

The reaction produces the conjugate base (F^– ion) of the weak acid. Answer: The solution will be basic at the equivalence point, pH > 7.0.

Indicators. Indicators are used in the laboratory to reveal the equivalence point of a titration. The abrupt change in color of the indicator signals the endpoint of a titration which usually coincides very nearly with the equivalence point.

Indicators are usually weak organic acids that have distinctly different colors in the nonionized (molecular) and ionized forms.

To determine the pH range in which an indicator will change color we can write the K_a expression in logarithmic form.

The color of an indicator depends on which form predominates. Typically, when [In^–]/[HIn] 10 the solution will be color 2, and when [In^–]/[HIn] 0.1, the solution will be color 1. Thus the color change will occur between

pH = pK_a + log (10/1) = pK_a + 1.0

and

pH = pK_a + log (1/10) = pK_a – 1.0

At the midpoint of the pH range over which the color changes, [HIn] = [In^–], and pH = pK_a.

Like any weak acid each HIn has a characteristic pK_a, and so each indicator changes color at a characteristic pH. Table 16.1 of the text lists a number of indicators used in acid-base titration and the pH ranges over which they change color.

The choice of indicator for a particular titration depends on the expected pH at the equivalence point. For instance, in the titration of acetic acid by sodium hydroxide, which is discussed in Example 16.5 of the text, the pH at the equivalence point is 8.72. According to Table 16.1 both cresol red and phenolphthalein change color over ranges that include pH 8.72. Therefore either of these indicators would show the equivalence point of this titration.

EXAMPLE Choosing an Indicator

Choose an indicator for the titration of 50 mL of a 0.10 M HI solution with 0.10 M NH₃. Consult a list of indicators.

HI(aq) + NH₃(aq) NH₄I(aq)

pH =

		Correct!
Click a Hint button for help.

First we need to know the pH at the equivalence point. This is the titration of a strong acid with a weak base. The net ionic equation is

The product ion is a weak acid and so we expect a slightly acidic solution at the equivalence point.

•Calculation

The concentration of ion formed at the equivalence point is 5.0 x 10^–3 mol/0.100 L = 5.0 x 10^–2 M. The [H⁺] at the equivalence point is just the pH of a 0.050 M NH₄⁺ solution. Consider the ionization of the weak acid, NH₄⁺:

NH₄⁺(aq) + H₂O NH₃(aq) + H₃O⁺(aq)
K_a = 5.6 x 10^–10

Set up and ICE box.

Concentration
NH₄⁺

+

H₂O

H⁺

+

NH₃

Initial (M)
0.050

-

0

0

Change (M)
–x

-

+x

+x

Equilibrium (M)
(0.050 – x)

-

x

x

Solving for x:

x = [NH₃] = [H₂O⁺] = 5.3 x 10^–6 M

and the pH is 5.28 at the equivalence point. According to Table 16.1 of the text, chlorophenol blue and methyl red are indicators that will change color in the vicinity of pH 5.28.

OBJECTIVE CHECK

Complete the following questions to check your understanding of the material. Select the check button to see if you answered correctly.

6. Approximately what range of pH should be expected at the equivalence points in the titration of weak acids with strong bases?

7. The pH at the equivalence point in a titration was found to be approximately 5. Give the category of titration in terms of the acid and base strengths.

8. 25.0 mL of 0.222 M HBr was titrated with 0.111 M NaOH.

a. Write the overall balanced equation for reaction.

b. After adding 30.0 mL of base solution, what is the pH?

9. Calculate the pH in the following titration after the addition of 12.0 mL of 0.100 M KOH to 20.0 mL of 0.200 M CH₃COOH.

10. Determine the pH at the equivalence point in the titration of 0.100 M NaOH with 0.100 M HNO₃.

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	no reaction	and pH
	HI + NH₃ NH₄⁺ + I
	H⁺ + NH₃ NH₄⁺
	I^- + NH₃ NH₃I^-

	no reaction	and pH
	HI + NaOH H₂O + NaI
	HI + OH^- H₂O + I^-
	H⁺ + NaOH H₂O + Na⁺
	H⁺ + OH^- H₂O
	I^- + Na⁺ NaI
	I^- + NaOH NaI + OH^-

	no reaction	and pH
	HF + NaOH H₂O + NaF
	HF + OH^- H₂O + F^-
	H⁺ + NaOH H₂O + Na⁺
	H⁺ + OH^- H₂O
	F^- + Na⁺ NaF
	F^- + NaOH NaF + OH^-


Concentration	NH₄⁺	+	H₂O	H⁺	+	NH₃

Initial (M)	0.050		-	0		0
Change (M)	–x		-	+x		+x

Equilibrium (M)	(0.050 – x)		-	x		x