TITRATION
TITRATION
A known concentration of
base (or acid) is slowly added
to a solution of acid (or base).
TITRATION
A pH meter or indicators are
used to determine when the
solution has reached the
equivalence point, at which
the stoichiometric amount of
acid equals that of base.
Colors and approximate pH range of some common acid-base
indicators.
TITRATION OF A STRONG ACID WITH A STRONG BASE
From the start of the titration
to near the equivalence
point, the pH goes up slowly.
Titration of a Strong Acid with a Strong Base
Just before and after the
equivalence point, the pH
increases rapidly.
Titration of a Strong Acid with a Strong Base
At the equivalence point,
moles acid = moles base, and
the solution contains only
water and the salt from the
cation of the base and the
anion of the acid.
Titration of a Strong Acid with a Strong Base
As more base is added, the
increase in pH again levels
off.
Titration of a Weak Acid with a Strong
Base
• Unlike in the previous case, the
conjugate base of the acid affects
the pH when it is formed.
• The pH at the equivalence point
will be >7.
• Phenolphthalein is commonly
used as an indicator in these
titrations.
Titration of a Weak Acid with a Strong
Base
At each point below the equivalence point, the pH of the
solution during titration is determined from the amounts of
the acid and its conjugate base present at that particular time.
Titration of a Weak Acid with a Strong Base
With weaker acids, the initial
pH is higher and pH changes
near the equivalence point
are more subtle.
Titration of a Weak Base with a Strong
Acid
• The pH at the equivalence
point in these titrations is <
7.
• Methyl red is the indicator
of choice.
WEAK ACID /WEAK BASE TITRATIONS
Titrations of Polyprotic Acids
In these cases there is
an equivalence point
for each dissociation.
SOLUBILITY EQUILIBRIA
DISSOLVING SILVER SULFATE, Ag2SO4, IN WATER
• When silver sulfate dissolves it dissociates into ions. When the
solution is saturated, the following equilibrium exists:
Ag2SO4 (s)  2 Ag+ (aq) + SO42- (aq)
• Since this is an equilibrium, we can write an equilibrium expression
for the reaction:
Ksp = [Ag+]2[SO42-]
Notice that the Ag2SO4 is left out of the expression! Why?
Since K is always calculated by just multiplying concentrations, it is called a “solubility
product” constant - Ksp.
WRITING SOLUBILITY PRODUCT EXPRESSIONS...
• For each salt below, write a balanced equation showing its
dissociation in water.
• Then write the Ksp expression for the salt.
Iron (III) hydroxide, Fe(OH)3
Nickel sulfide, NiS
Silver chromate, Ag2CrO4
Zinc carbonate, ZnCO3
Calcium fluoride, CaF2
SOME Ksp VALUES
Note:
These are experimentally determined, and may
be slightly different on a different Ksp table.
Calculating Ksp from solubility of a compound
• A saturated solution of silver chromate, Ag2CrO4, has [Ag+] = 1.3 x 10-4
M. What is the Ksp for Ag2CrO4?
Molar mass =
461.01
Calculating solubility, given Ksp
• The Ksp of NiCO3 is 1.4 x 10-7 at 25°C. Calculate its molar solubility.
NiCO3 (s)  Ni2+ (aq) + CO32- (aq)
---
---
Molar Mass =
147.63
Common Ion Effect in Solubility
The Common Ion Effect on Solubility
The solubility of MgF2 in pure water is 2.6 x 10-4 mol/L. What happens to
the solubility if we dissolve the MgF2 in a solution of NaF, instead of pure
water?
Calculate the solubility of MgF2 in a solution of 0.080 M
NaF.
MgF2 (s)  Mg2+ (aq) + 2 F- (aq)
Explaining the Common Ion Effect
The presence of a common ion in a solution will lower the
solubility of a salt.
• LeChatelier’s Principle:
The addition of the common ion will shift the solubility
equilibrium backwards. This means that there is more solid
salt in the solution and therefore the solubility is lower!
Ksp and Solubility
• Generally, it is fair to say that salts with very small solubility product
constants (Ksp) are only sparingly soluble in water.
• When comparing the solubilities of two salts, however, you can
sometimes simply compare the relative sizes of their Ksp values.
• This works if the salts have the same number of ions!
• For example… CuI has Ksp = 5.0 x 10-12 and CaSO4 has Ksp = 6.1 x 10-5.
Since the Ksp for calcium sulfate is larger than that for the copper (I)
iodide, we can say that calcium sulfate is more soluble.
Salt
Ksp
Solubility
(mol/L)
CuS
8.5 x 10-45
9.2 x 10-23
Ag2S
1.6 x 10-49
3.4 x 10-17
Bi2S3
1.1 x 10-73
1.0 x 10-15
Will a Precipitate Form?
• In a solution,
– If Q = Ksp, the system is at equilibrium and
the solution is saturated.
– If Q < Ksp, more solid will dissolve until Q =
Ksp.
– If Q > Ksp, the salt will precipitate until Q =
Ksp.
Pb(NO3)2 (aq) + K2CrO4 (aq)  PbCrO4 (s) + 2 KNO3 (aq)
Step 1: Is a sparingly soluble salt formed?
We can see that a double replacement reaction can occur and
produce PbCrO4. Since this salt has a very small Ksp, it may
precipitate from the mixture. The solubility equilibrium is:
PbCrO4 (s)  Pb2+ (aq) + CrO42- (aq)
Ksp = 2 x 10-16 = [Pb2+][CrO42-]
If a precipitate forms, it means the solubility equilibrium has shifted
BACKWARDS.
This will happen only if Qsp > Ksp in our mixture.
Step 2: Find the concentrations of the ions that form the sparingly
soluble salt.
Since we are mixing two solutions in this example, the concentrations
of the Pb2+ and CrO42- will be diluted. We have to do a dilution
calculation!
Dilution: C1V1 = C2V2
[Pb2+]
=
[CrO42-] =
C1V1 (0.024 M)(15 mL)

 0.0080 M Pb 2
V2
(45 mL)
C1V1 (0.030 M)(20 mL)

 0.020 M CrO4 2V2
(45 mL)
Step 3: Calculate Qsp for the mixture.
Qsp = [Pb2+][CrO42-] = (0.0080 M)(0.020 M)
Qsp = 1.6 x 10-4
Step 4: Compare Qsp to Ksp.
Since Qsp >> Ksp, a precipitate will form when
solutions are mixed!
Note: If Qsp = Ksp, the mixture is saturated
If Qsp < Ksp, the solution is unsaturated
Either way, no ppte will form!
the two
8.0 x 10-28
FRACTIONAL PRECIPITATION
Factors Affecting Solubility
• pH
– If a substance has a basic
anion, it will be more soluble
in an acidic solution.
– Substances with acidic cations
are more soluble in basic
solutions.
FACTORS AFFECTING SOLUBILITY
• Complex Ions
– Metal ions can act as Lewis acids and form complex ions with
Lewis bases in the solvent.
FACTORS AFFECTING SOLUBILITY
• Complex Ions
– The formation of
these complex ions
increases the
solubility of these
salts.
Factors Affecting Solubility
• Amphoterism
– Amphoteric metal oxides and
hydroxides are soluble in strong
acid or base, because they can
act either as acids or bases.
– Examples of such cations are
Al3+, Zn2+, and Sn2+.
Calculating the Effect of Complex-Ion Formation on Solubility
PROBLEM: In black-and-white film developing, excess AgBr is removed from
the film negative by “hypo”, an aqueous solution of sodium
thiosulfate (Na2S2O3), which forms the complex ion Ag(S2O3)23-.
Calculate the solubility of AgBr in (a) H2O; (b) 1.0 M hypo. Kf of
Ag(S2O3)23- is 4.7 x 1013 and Ksp AgBr is 5.0 x 10-13.
PLAN: Write equations for the reactions involved. Use Ksp to find S, the molar
solubility. Consider the shifts in equilibria upon the addition of the
complexing agent.
Ag+(aq) + Br -(aq)
Ksp = [Ag+][Br -]
SOLUTION: AgBr(s)
(a) S = [AgBr]dissolved = [Ag+] = [Br -]
(b)
AgBr(s)
Ksp = S2 = 5.0 x 10-13 ; S = 7.1 x 10-7 M
Ag+(aq) + Br -(aq)
Ag+(aq) + 2S2O32-(aq)
Ag(S2O3)23-(aq)
AgBr(s) + 2S2O32-(aq)
Ag(S2O3)23- (aq) + Br - (aq)
Calculating the Effect of Complex-Ion Formation on Solubility
Koverall = Ksp x Kf =
Initial
Change
Equilibrium
S2
(1.0 -
[S2O3
2-]2
AgBr(s) + 2S2O32-(aq)
Concentration (M)
Koverall =
[Ag(S2O3]23-[Br -]
= (5.0 x 10-13)(4.7 x 1013) = 24
Br -(aq) + Ag(S2O3)23-(aq)
1.0
- 2S
1.0 - 2S
= 24
2S)2
S = [Ag(S2O3)23-] = 0.45 M
S
1.0 - 2S
0
+S
S
= √24
0
+S
S
Selective Precipitation of Ions
One can use
differences in
solubilities of salts to
separate ions in a
mixture.
Calculating the Effect of Complex-Ion Formation
on Solubility
PROBLEM: In black-and-white film developing, excess AgBr is removed from
the film negative by “hypo”, an aqueous solution of sodium
thiosulfate (Na2S2O3), which forms the complex ion Ag(S2O3)23-.
Calculate the solubility of AgBr in (a) H2O; (b) 1.0 M hypo. Kf of
Ag(S2O3)23- is 4.7 x 1013 and Ksp AgBr is 5.0 x 10-13.
PLAN: Write equations for the reactions involved. Use Ksp to find S, the molar
solubility. Consider the shifts in equilibria upon the addition of the
complexing agent.
Ag+(aq) + Br -(aq)
Ksp = [Ag+][Br -]
SOLUTION: AgBr(s)
(a) S = [AgBr]dissolved = [Ag+] = [Br -]
(b)
AgBr(s)
Ksp = S2 = 5.0 x 10-13 ; S = 7.1 x 10-7 M
Ag+(aq) + Br -(aq)
Ag+(aq) + 2S2O32-(aq)
Ag(S2O3)23-(aq)
AgBr(s) + 2S2O32-(aq)
Ag(S2O3)23- (aq) + Br - (aq)
Calculating the Effect of Complex-Ion Formation on
Solubility
Koverall = Ksp x Kf =
Initial
Change
Equilibrium
S2
(1.0 -
[S2O3
2-]2
AgBr(s) + 2S2O32-(aq)
Concentration (M)
Koverall =
[Ag(S2O3]23-[Br -]
= (5.0 x 10-13)(4.7 x 1013) = 24
Br -(aq) + Ag(S2O3)23-(aq)
1.0
- 2S
1.0 - 2S
= 24
2S)2
S = [Ag(S2O3)23-] = 0.45 M
S
1.0 - 2S
0
+S
S
= √24
0
+S
S
HARD AND SOFT ACIDS AND BASES (HSAB)
The affinity that metal ions have for ligands is
controlled by size, charge and electronegativity.
This can be refined further by noting that for some
metal ions, their chemistry is dominated by size and
charge, while for others it is dominated by their
electronegativity.
These two categories of metal ions have been
termed by Pearson as hard metal ions and soft metal
ions.
HARD AND SOFT ACIDS AND BASES (HSAB)
The polarizability of an acid or base
plays a role in its reactivity. Hard acids and
bases are small, compact, and nonpolarizable.
Soft acids and bases are larger, with a
more diffuse distribution of electrons.
Hard and Soft Acids and Bases.
Figure 1. Table showing distribution of hard, soft, and intermediate Lewis
Acids in the Periodic Table, largely after Pearson.
Distribution of Hard and Soft Bases by donor
atom in the periodic Table:
C
N
O
F
P
S
Cl
As
Se
Br
I
Figure 2. Distribution of hardness and softness for potential donor atoms
for ligands in the Periodic Table.
Hard and Soft Bases.
HARD: H2O, OH-, CH3COO-, F-, NH3, oxalate (-OOCCOO-), en (NH2CH2CH2NH2).
SOFT: Br-, I-, SH-, CH3S-, (CH3)2S, S=C(NH2)2
(thiourea), P(CH3)3, PPh3, As(CH3)3, CN(thiocyanate, S-bound)
-S-C≡N
INTERMEDIATE: C6H5N (pyridine), N3- (azide), -N=C=S
(thiocyanate, N-bound), Cl(donor atoms underlined)
HARD AND SOFT ACIDS AND BASES
Hard acids react preferentially with hard
bases, and soft acids react preferentially with
soft bases.
Examples: Aqueous Solubility
Silver Halides
Compound
AgF
AgCl
AgBr
AgI
solubility product
205
1.8 x 10-10
5.2 x 10-13
8.3 x 10-17
AgX(s) + H2O(l) ↔ Ag+(aq) + X-(aq)
Example: Thiocyanate Bonding
SCN- displays linkage isomerism as the ligand
coordinates to metals via the sulfur or the
nitrogen. Mercury (II) ion bonds to the sulfur
(a soft-soft interaction) whereas zinc ion
bonds to the nitrogen atom.
Thiocyanate, an ambidentate ligand:
Thiocyanate (SCN-) is a particularly interesting ligand. It is
ambidentate, and can bind to metal ions either through the S
or the N. Obviously, it prefers to bind to soft metal ions
through the S, and to hard metal ions through the N. This can
be seen in the structures of [Au(SCN)2]- and [Fe(NCS)6]3- in
Figure 3 below:
Figure 3. Thiocyanate
Complexes showing
a) N-bonding in the
[Fe(NCS)6]3complex with the hard
Fe(III) ion, and
b) S-bonding in the
[Au(SCN)2]- complex
(CSD: AREKOX) with
Example: K for ligand exchange reactions
Compare:
[MeHg(H2O)]+ + HCl
MeHgCl + H3O+
K= 1.8 x 1012
[MeHg(H2O)]+ + HF
MeHgF + H3O+
K= 4.5 x 10-2
Hard and Soft Acids & Bases
There have been many attempts to categorize
various metal ions and anions to predict
reactivity, solubility, etc.
R.G. Pearson (1963) categorized acids and bases
as either hard or soft (using Kf values).
Hard acids bond in the order: F->Cl->Br->ISoft acids bond in the order: I- >Br- >Cl- > F-
Hard and Soft Acids & Bases
Hard acids or bases are compact, with the
electrons held fairly tightly by the nucleus.
They are not very polarizable. F- is a hard
base, and metal ions such as Li+, a hard acid.
Hard and Soft Acids & Bases
Large, highly polarizable ions are categorized
as “soft.” Iodide is a soft base, and transition
metals with low charge density, such as Ag+,
are considered to be soft acids.
Problem
• Predict the solubility (high or low) of silver
fluoride, silver iodide, lithium fluoride and
lithium iodide using the hard-soft acid/base
approach. Identify each Lewis acid and Lewis
base, and categorize each as hard or soft.
Charge Density – Hard Acids
Hard acids typically have a high charge
density. They are often metal ions with a
(higher) positive charge and small ionic size.
Their d orbitals are often unavailable to
engage in π bonding.
Charge Density – Soft Acids
Soft acids typically have lower charge density
(lower ionic charge and greater ionic size).
Their d orbitals are available for π bonding.
Soft acids are often 2nd and 3rd row transition
metals with a +1 or +2 charge, and filled or
nearly filled d orbitals.
Effect of Oxidation Number
Cu2+/Cu+ on acid hardness
SO3/SO2 on acid hardness
NO3-/NO2- on base hardness
SO42-/SO32- on base hardness
Acid or Base Strength
It is important to realize that hard/soft
considerations have nothing to do with acid or
base strength. An acid or a base may be hard
or soft and also be either weak or strong.
In a competition reaction between two bases
for the same acid, you must consider both the
relative strength of the bases, and the
hard/soft nature of each base and the acid.
Acid or Base Strength
Consider the reaction between ZnO and
LiC4H9.
ZnO + 2 LiC4H9↔ Zn(C4H9)2 + Li2O
Zinc ion is a strong Lewis acid, and oxide ion is
a strong Lewis base.
Acid or Base Strength
Consider the reaction between ZnO and LiC4H9.
ZnO + 2 LiC4H9↔ Zn(C4H9)2 + Li2O
soft -hard hard -soft
soft -soft
hard -hard
Zinc ion is a strong Lewis acid, and oxide ion is a
strong Lewis base. However, the reaction
proceeds to the right (K>1), because hard/soft
considerations override acid-base strength
considerations.
The Nature of the Adduct
Hard acid/hard base adducts tend to have
more ionic character in their bonding. These
are generally more favored energetically.
Soft acid/soft base adducts are more covalent
in nature.
APPLICATIONS OF HARD/SOFT THEORY
The Qual Scheme, a series of chemical
reactions used to separate and identify the
presence of dozens of metal ions, is based
largely on the hard and soft properties of the
metal ions.
The softer metals are precipitated out as
chlorides or sulfides, with the harder ions
formed as carbonates.
A very soft metal ion, Au(I):
The softest metal ion is the Au+(aq) ion. It is so soft that the
compounds AuF and Au2O are unknown. It forms stable
compounds with soft ligands such as PPh3 and CN-. The
affinity for CN- is so high that it is recovered in mining
operations by grinding up the ore and then suspending it in a
dilute solution of CN-, which dissolves the Au on bubbling air
through the solution:
4 Au(s) + 8 CN-(aq) + O2(g) + 2 H2O =
4 [Au(CN)2]-(aq) + 4 OH-
A very hard metal ion, Al(III):
An example of a very hard metal ion is Al(III). It has a
high log K1 with F- of 7.0, and a reasonably high log
K1(OH-) of 9.0. It has virtually no affinity in solution
for heavier halides such as Cl-. Its solution chemistry
is dominated by its affinity for F- and for ligands with
negative O-donors.