Applications of Aqueous
Equilibria
AP Chemistry
Seneca Valley SHS
Chapter 15
1
The Common Ion Effect
• The solubility of a partially soluble salt is decreased
when a common ion is added.
• Consider the equilibrium established when acetic
acid, HC2H3O2, is added to water.
• At equilibrium H+ and C2H3O2- are constantly moving
into and out of solution, but the concentrations of ions
is constant and equal.
• If a common ion is added, e.g. C2H3O2- from
NaC2H3O2 (which is a strong electrolyte) then
[C2H3O2-] increases and the system is no longer at
equilibrium.
• So, [H+] must decrease.
2
The Common Ion Effect
When a solution contains a salt
having an ion common with one
in equilibrium, the position of
the equilibrium is driven away
from the side containing that
ion.
Compare the pH values for sample problems 5 and 7 to see this!
3
Buffered Solutions
Composition and Action of Buffered Solutions
• A buffer resists a change in pH when a small amount
of OH- or H+ is added.
• A buffer consists of a mixture of a weak acid (HX)
and its conjugate base (X-):
H+(aq) + X-(aq)
HX(aq)
• The Ka expression is
Ka 

[H ][X ]
.
[HX]
[HX]

[H ]  K a
.
[ X- ]
4
Buffered Solutions
Composition and Action of Buffered Solutions
• When OH- is added to the buffer, the OH- reacts with
HX to produce X- and water. But, the [HX]/[X-] ratio
remains more or less constant, so the pH is not
significantly changed.
• When H+ is added to the buffer, X- is consumed to
produce HX. Once again, the [HX]/[X-] ratio is more
or less constant, so the pH does not change
significantly.
5
Buffered Solutions
Key Points on Buffered Solutions
1. They are weak acids or bases containing a
common ion.
2. After addition of strong acid or base, deal
with stoichiometry first, then equilibrium.
6
Buffered Solutions
Addition of Strong Acids or Bases to Buffers
• We break the calculation into two parts:
stoichiometric and equilibrium.
• The amount of strong acid or base added results in a
neutralization reaction:
X- + H3O+  HX + H2O
HX + OH-  X- + H2O.
• By knowing how must H3O+ or OH- was added
(stoichiometry) we know how much HX or X- is
formed.
7
Buffered Solutions
Addition of Strong Acids or Bases to Buffers
8
Buffered Solutions
Addition of Strong Acids or Bases to Buffers
• With the concentrations of HX and X- (note the
change in volume of solution) we can calculate the pH
from the Henderson-Hasselbalch equation
[ X- ]
pH  p K a  log
[HX]
conjugate base
pH  p K a  log
conjugate acid
Henderson-Hasselbalch Equation: For a particular
buffering system, all solutions that have the same
ratio [A-]/[HA] will have the same pH.
9
Buffered Solutions
Buffer Capacity and pH – HendersonHasselbach Equation
• If Ka is small (i.e., if the equilibrium concentration of
undissociated acid is close to the initial
concentration), then
[HX]

[H ]  K a
[ X- ]
[HX]

 log[H ]   log K a  log
.
[X ]
[ X- ]
 pH  p K a  log
.
[HX]
10
Buffered Solutions
Buffer Capacity and pH
• Buffer capacity is the amount of acid or base
neutralized by the buffer before there is a significant
change in pH.
• Buffer capacity depends on the composition of the
buffer.
• The greater the amounts of conjugate acid-base pair,
the greater the buffer capacity.
• The pH of the buffer depends on Ka.
11
Acid-Base Titrations
Strong Acid-Base Titrations
• Consider adding a strong base (e.g. NaOH) to a
solution of a strong acid (e.g. HCl).
– Before any base is added, the pH is controlled by the strong
acid solution. Therefore, pH < 7.
– When base is added, before the equivalence point, the pH is
controlled by the amount of strong acid left in excess.
Therefore, pH < 7.
– At equivalence point, the amount of base added is
stoichiometrically equivalent to the amount of acid
originally present. Therefore, the pH is determined by the
salt solution. Therefore, pH = 7.
12
Acid-Base Titrations
Strong Acid-Base Titrations
• Problems only involve a stoichiometry calculation.
• We know the pH at equivalent point is 7.00.
• To detect the equivalent point, we use an indicator
that changes color somewhere near 7.00.
• The equivalence point in a titration is the point at
which the acid and base are present in stoichiometric
quantities.
• The end point in a titration is the observed point.
• The difference between equivalence point and end
point is called the titration error.
13
Acid-Base Titrations
Strong Acid-Base Titrations
14
Acid-Base Titrations
Weak Acid-Strong Base Titrations
• Consider the titration of acetic acid, HC2H3O2 and
NaOH.
• Before any base is added, the solution contains only
weak acid. Therefore, pH is given by the equilibrium
calculation.
• As strong base is added, the strong base consumes a
stoichiometric quantity of weak acid:
HC2H3O2(aq) + NaOH(aq)  C2H3O2-(aq) + H2O(l)
15
Acid-Base Titrations
Weak Acid-Strong Base Titrations
16
Acid-Base Titrations
Weak Acid-Strong Base Titrations
• There is an excess of acetic acid before the
equivalence point.
• Therefore, we have a mixture of weak acid and its
conjugate base.
– The pH is given by the buffer calculation.
• First the amount of C2H3O2- generated is calculated, as well as the
amount of HC2H3O2 consumed. (Stoichiometry.)
• Then the pH is calculated using equilibrium conditions.
(Henderson-Hasselbalch.)
17
Acid-Base Titrations
Weak Acid-Strong Base Titrations
• At the equivalence point, all the acetic acid has been
consumed and all the NaOH has been consumed.
However, C2H3O2- has been generated.
– Therefore, the pH is given by the C2H3O2- solution.
– This means pH > 7.
• More importantly, pH  7 for a weak acid-strong base titration.
• After the equivalence point, the pH is given by the
strong base in excess.
18
Acid-Base Titrations
Weak Acid-Strong Base Titrations
• The inflection point is not as steep for a weak acidstrong base titration.
• The shape of the two curves after equivalence point is
the same because pH is determined by the strong base
in excess.
• Two features of titration curves are affected by the
strength of the acid:
– the amount of the initial rise in pH, and
– the length of the inflection point at equivalence.
19
Acid-Base Titrations
Weak Acid-Strong Base Titrations
• The weaker the acid,
the smaller the
equivalence point
inflection.
• For very weak acids, it
is impossible to detect
the equivalence point.
20
Acid-Base Titrations
Weak Acid-Strong Base Titrations
• Titration of weak bases with strong acids have similar
features to weak acid-strong base titrations.
Weak Acid-Strong Base Titrations: A Summary
Step 1 - A stoichiometry problem - reaction is assumed
to run to completion - then determine
remaining species.
Step 2 - An equilibrium problem - determine position of
weak acid equilibrium and calculate pH.
21
Acid-Base Titrations
Titrations of Polyprotic Acids
• In polyprotic acids, each ionizable
proton dissociates in steps.
• Therefore, in a titration there are n
equivalence points corresponding
to each ionizable proton.
• In the titration of Na2CO3 with
HCl there are two equivalence
points:
– one for the formation of HCO3– one for the formation of H2CO3.
22
Indicator Color Change
• Another way determine the equivalence point of an
•
•
•
•
acid-base titration is through the use of an acid-base
indicator.
Careful selection of the indicator will ensure that the
end point is close to the equivalence point.
Most common acid-base indicators are complex
molecules that are themselves weak acids (HIn). They
exhibit one color when the proton is attached and a
different color when the proton is absent.
Page 749 contains a list of acid-base indicators.
Henderson-Hasselbach equation is very useful in
determining the pH at which an indicator changes
color.
23
Solubility Equilibria
Solubility-Product Constant, Ksp
• Consider
BaSO4(s)
Ba2+(aq) + SO42-(aq)
• for which
2
2
K sp  [Ba ][SO 4 ]
• Ksp is the solubility product. (BaSO4 is ignored
because it is a pure solid so its concentration is
constant.)
24
Solubility Equilibria
Solubility-Product Constant, Ksp
• In general: the solubility product is the molar
concentration of ions raised to their stoichiometric
powers.
• Solubility is the amount (grams) of substance that
dissolves to form a saturated solution.
• Molar solubility is the number of moles of solute
dissolving to form a liter of saturated solution.
25
Solubility Equilibria
Solubility and Ksp
To convert solubility to Ksp
• solubility needs to be converted into molar solubility
(via molar mass);
• molar solubility is converted into the molar
concentration of ions at equilibrium (equilibrium
calculation),
• Ksp is the product of equilibrium concentration of
ions.
26
Solubility Equilibria
Solubility and Ksp
27
Solubility Equilibria
Solubility and Ksp
Exercise 15.12 Page 752
Copper (I) bromide has a measured solubility of 2.0x10-4
mol/L at 25C. Calculate its Ksp value.
28
Solubility Equilibria
Solubility and Ksp
Exercise 15.13 Page 754
Calculate the Ksp value for bismuth sulfide (Bi2S3), which has a
solubility of 1.0x10-15 mol/L at 25C.
29
Solubility Equilibria
Solubility and Ksp
Exercise 15.14 Page 755
The Ksp value for copper (II) iodate is 1.4 x 10-7 at 25º C.
Calculate its solubility.
Solubility Equilibria
Solubility and Ksp
A potassium chromate solution being
added to aqueous silver nitrate, forming silver chromate.
31
Factors That Affect Solubility
Common-Ion Effect
• Solubility is decreased when a common ion is added.
• This is an application of Le Châtelier’s principle:
CaF2(s)
2+
-
Ca (aq) + 2F (aq)
• as F- (from NaF, say) is added, the equilibrium shifts
away from the increase.
• Therefore, CaF2(s) is formed and precipitation occurs.
• As NaF is added to the system, the solubility of CaF2
decreases.
32
Factors That Affect Solubility
Common-Ion Effect
33
Factors That Affect Solubility
Common-Ion Effect
Exercise 15.15 Page 758
Calculate the solubility of solid CaF2 (Ksp = 4.0x10-11) in
a 0.025 M NaF solution.
34
Factors That Affect Solubility
Solubility and pH
• Again we apply Le Châtelier’s principle:
CaF2(s)
Ca2+(aq) + 2F-(aq)
– If the F- is removed, then the equilibrium shifts towards the
decrease and CaF2 dissolves.
– F- can be removed by adding a strong acid:
+
F (aq) + H (aq)
HF(aq)
– As pH decreases, [H+] increases and solubility increases.
• The effect of pH on solubility is dramatic.
35