Chapter 19 Ionic Equilibria in Aqueous Systems
This chapter covers titration curves, buffers, and Ksp, which are all tested on the AP
examination. Students are introduced to the Henderson-Hasselbalch (H-H) equation in
solving buffer problems. The equation is given to students in the AP equations page, so
they are expected to be able to know how and when to use it. However, all equilibrium
problems can be solved by using combinations of simultaneous equilibrium expressions
without invoking the H-H equation.
Reading student answers often indicates that they have a very poor understanding of
material in this chapter, because they really have not truly mastered the material in the
previous chapter. For example, they do not appreciate the interrelation of conjugate acids
and bases and their respective equilibrium constants.
Major Concepts to Know:
 If a base is added to a buffer system, the acid loses concentration and creates
conjugate base ions. Students should recognize that every buffer system has a
capacity and can be used up.

Students can still solve buffer problems using the ICE setup for K problems, as well
as the Henderson Hasselbalch equation, as both methods result in the same answer.

Understanding what pKa is will help the student later in finding pKa from a graph.

Students should be sure to thoroughly understand the methods used in the worked
examples in this chapter, especially examples 16.1 and 16.2 in the textbook. It is
especially important for students to learn and practice how to choose initial conditions
so that “change” is relatively small and approximations will work. So for instance, if
0.010 mol solid NaOH were to be added to 100. mL of a buffer solution, the initial
condition is with [OH−] = 0.10 and reaction proceeds to change from there.

Students need to know how to prepare a buffer system of a certain pH.

From the Henderson-Hasselbalch equation, students should know the pH is at pKa
when the conjugate base and its acid are the same molarity, so students can then
estimate the pH just by knowing Ka. A system buffers best at just ±1 pH unit from
pKa (or the corresponding pOH and pKb), because this represents a factor of 10 in
concentration on each side of the equal molarity point, allowing a “swing” of a factor
of 100 in concentration.

The concept of titrations was introduced in Chapter 4 but should be reviewed here.
Students should be able to look at any titration curve, understand the axis used, and
recognize typical acid-base reactions. Students need to recognize whether graphs are
between strong acids, weak acids, strong bases, or weak bases.
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pH Profile of a Strong-Acid Strong-Base Titration

In this graph, students should recognize that: the pH starts at 1, indicating a strong
acid; the equivalence is at 7, indicating strong acid; and strong bases have reacted and
the last point in the upper flat is 13, which also indicates a strong base.
The Relationship Between Buffer Capacity and pH Change

Two common indicators for a strong acid-strong base reaction are shown. They need
to change color at the equivalence point.
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pH Profile of a Weak-Acid Strong Base Titration

In this graph the pH starts at 3, indicating a weak acid; the equivalence is above 7,
indicating the base is strong, as is also shown by the upper flat.
pH Profile of a Strong-Acid Weak-Base Titration

This graph indicates a base is being titrated and the starting pH is at 11, indicating a
weak base. The pH at equivalence is below 7, and the ending pH is 1, indicating a
strong acid was used in the titration.
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
Keys to recognition are the starting pH, equivalence point position, and ending pH.
Students should be able to draw them as well. Strong acids with strong bases will
have an equivalence of 7 or neutral. Strong acids with weak bases will be in the acid
range at equivalence, and strong bases with weak acids will be basic.

A misperception many students have is that equivalence means neutral in all cases,
since the moles of H+ = moles of OH−, not understanding that the driving factor is the
hydrolysis of the salt that is produced by the reaction. Students need to be able to do
calculations at any point during a titration. Students also need to be able to choose
appropriate indicators given the Ka of the indicator.
Curve for the Titration of a Weak Polyprotic Acid

The chapter then switches to consideration of solubility of sparingly soluble
substances and the resulting equilibrium constant, Ksp. These are the same as all K
problems, but since the reactant is a solid, there is no denominator. Students need to
understand when they learn that a compound like AgCl is insoluble, some ions are
formed and equilibrium is established.

Confusion with vocabulary is common between molar solubility and solubility
product. Use of the calculated equilibrium quotient is best for solving prediction
problems. To determine if a precipitate will form, students need to be able to
solve for Q and then compare Q to Ksp values. Ksp values are saturation values, so if
Q > Ksp, a precipitate will form, if Q = Ksp, the solution is saturated, and if Q < Ksp,
the solution is unsaturated and no precipitate will form. More complex problems
involve figuring out which of two precipitates will form first and what happens to a
concentration when a common ion is added or when it has been added to an acidic or
basic solution.
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
Generally, AP exam problems are relatively straightforward and do not involve
multiple ions in solution.

To date, solving Kf problems with complex ions have not been on the AP exam,
though recognizing equations for complex ion formation has been tested as
descriptive chemistry on the multiple choices, or in the equations question in the
free response.
Vocabulary to Know:
 Buffer solution
 Common ion effect
 Complex ion
 End point
 Molar solubility
 Qualitative analysis
 Titration curve
 Solubility-product constant
Math Skills Students Must Know:
 pH = pKa + log[Conjugate base/acid]
 pOH = pKb + log[conjugate acid/base]
 Common ion problems and determine new pH
 Buffer problems and determine new pH
 Determine pH at any point in a titration
 Solve Ksp problems
Suggested Problems:
 Equilibria of Acid-Base Buffer Systems: 1, 7, 11, 12, 14, 15, 16, 28, 33
 Acid-Base Titration Curves: 39, 40, 42, 46, 47, 48, 50, 54, 55, 58, 125, 158
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


Equilibria of Slightly Soluble Compounds: 62, 63, 66, 67, 70, 71, 72, 73, 74, 75, 78,
82, 86, 87
Equilibria Involving Complex Ions: 93
Ionic Equilibria in Chemical Analysis: 104, 105, 135
Suggested Demonstrations or Labs:
Complexing ions demo:
o Adding NH3 to CuSO4 first forms the white/pale blue precipitate Cu(OH)2
and then with the addition of more concentrated NH3, the precipitate
dissolves and the bright blue complex ion, Cu(NH3)42+, is formed.
o Adding ammonia to a solution of silver nitrate to which NaCl has been
recently added will dissolve the AgCl precipitate, forming Ag(NH3)2+
ions.
 Cooper, Melanie M. “Project 8: Buffers,” Cooperative Chemistry Lab Manual
(McGraw-Hill, 2006).
 Paradis, Jeffrey A. “The Properties of Buffers: Resisting Change in a Turbulent
World,” Hands On Chemistry Laboratory Manual (McGraw-Hill, 2006).
Questions
*To understand this chapter, you MUST understand Chapter 18 on acids and bases and
pH calculations.
Acid-Base Equilibria:
1. What is a buffer?
a. What components must be in a buffer?
2. What is a common ion?
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3. What is the common-ion effect?
a. Why does the pH not change very much in a buffer system?
b. Using Le Châtelier’s principle, when you add a common ion you will shift
______________ to reduce the stress.
4. Write the Henderson-Hasselbalch equation.
a. Explain how to get each of the values in the equation.
b. What kind of problems can it solve?
c. When does pH = pKa?
d. Calculate the pH of a solution containing 0.20 M CH3COOH and
0.30 M NaCH3COO.
e. Calculate the pH of a solution containing 0.50 M NH3 and 0.20 NH4Cl.
5. What is a buffer capacity?
a. How do buffers work?
b. Explain what happens to a buffer system as acid or base is added.
c. What is the capacity of a buffer?
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d. When is the capacity of a buffer system the greatest?
e. Explain the concept of a buffering range.
f. Explain how you would make a buffer with a specific pH.
6. What are indicators?
a. How are they used in a titration?
b. What is the color range of indicators?
c. How do you know which indicator to pick?
7. What does a titration curve show?
a. Draw general titration curves for reactions with (1) strong acid (SA) and strong
base (SB), (2) SA and weak base (WB), and (3) weak acid (WA) and SB. When
appropriate, indicate the buffering region of the curve.
b. How do you find the equivalence point or end point on each?
c. What is the expected equivalence point pH of each type of titration?
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d. Calculate the pH of a buffering system containing 0.20 M CH3COOH
and 0.30 M NaCH3COO when 50 mL of 0.10 M HCl is added to 100 mL of
the buffer.
8. On which curves can a pKa be determined?
a. How can you find a pKa on those titration curves?
9. If you titrate a diprotic acid or triprotic acid, how will the graphs of the curves
be different from a monoprotic titration? Draw a rough sketch of each including
buffering regions.
Equilibria of Slightly Soluble Compounds:
10. What is the solubility product?
a. Write the general formula of Ksp.
b. What types of reactions use Ksp?
c. What is molar solubility?
d. When solving a problem, how can you tell if the reaction is unsaturated, saturated,
or supersaturated?
11. How does the presence of a common ion affect solubility?
a. Explain why from Le Châtelier’s principle.
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b. Using Le Châtelier’s principle, explain why adding an acid to a basic solution
increases the solubility of a base.
c. Using Le Châtelier’s principle, explain why adding a base to an acidic solution
increases the solubility of an acid.
12. Using Q and K, explain how to determine if a precipitate will form.
13. What is a complex ion?
14. What metals tend to form complex ions?
a. Why?
15. What are amphoteric hydroxides?
a. List three amphoteric hydroxides.
16. What is selective precipitation?
a. What is selective precipitation used for?
17. Define qualitative analysis.
a. Explain the general process of qualitative analysis.
b. What are the five main ion groups?
c. How would you test for Na+ and K+?
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