titration. a known concentration of base (or acid) is slowly added to a solution of acid (or base)

TITRATION

TITRATION

A known concentration of base (or acid) is slowly added to a solution of acid (or base).

TITRATIONA 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 maybe 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 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?

The Common Ion Effect on Solubility

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 KspSolubility(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 CrO4

2- will be diluted. We have to do a dilution calculation!

Dilution: C1V1 = C2V2

[Pb2+] =

[CrO42-] =

2

2

11 Pb M 0.0080 mL) (45

mL) M)(15 (0.024

VVC

-24

2

11 CrO M 0.020 mL) (45

mL) M)(20 (0.030

VVC

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 the two solutions are mixed!

Note: If Qsp = Ksp, the mixture is saturatedIf Qsp < Ksp, the solution is unsaturated

Either way, no ppte will form!

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

SOLUTION:

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)2

3-. Calculate the solubility of AgBr in (a) H2O; (b) 1.0 M hypo. Kf of Ag(S2O3)2

3- 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.

AgBr(s) Ag+(aq) + Br -(aq) Ksp = [Ag+][Br -]

S = [AgBr]dissolved = [Ag+] = [Br -] Ksp = S2 = 5.0 x 10-13 ; S = 7.1 x 10-7 M(a)

(b) AgBr(s) Ag+(aq) + Br -(aq)

Ag+(aq) + 2S2O32-(aq) Ag(S2O3)2

3-(aq)

AgBr(s) + 2S2O32-(aq) Ag(S2O3)2

3- (aq) + Br - (aq)

Calculating the Effect of Complex-Ion Formation on Solubility

Koverall = Ksp x Kf = [Ag(S2O3]2

3-[Br -]

[S2O32-]2

= (5.0 x 10-13)(4.7 x 1013) = 24

AgBr(s) + 2S2O32-(aq) Br -(aq) + Ag(S2O3)2

3-(aq)Concentration (M)

InitialChangeEquilibrium

---

1.0- 2S

1.0 - 2S

0 0+ S + SS S

Koverall =S2

(1.0 - 2S)2

= 24 S

1.0 - 2S= √24

S = [Ag(S2O3)23-] = 0.45 M

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

SOLUTION:

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)2

3-. Calculate the solubility of AgBr in (a) H2O; (b) 1.0 M hypo. Kf of Ag(S2O3)2

3- 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.

AgBr(s) Ag+(aq) + Br -(aq) Ksp = [Ag+][Br -]

S = [AgBr]dissolved = [Ag+] = [Br -] Ksp = S2 = 5.0 x 10-13 ; S = 7.1 x 10-7 M(a)

(b) AgBr(s) Ag+(aq) + Br -(aq)

Ag+(aq) + 2S2O32-(aq) Ag(S2O3)2

3-(aq)

AgBr(s) + 2S2O32-(aq) Ag(S2O3)2

3- (aq) + Br - (aq)

Calculating the Effect of Complex-Ion Formation on Solubility

Koverall = Ksp x Kf = [Ag(S2O3]2

3-[Br -]

[S2O32-]2

= (5.0 x 10-13)(4.7 x 1013) = 24

AgBr(s) + 2S2O32-(aq) Br -(aq) + Ag(S2O3)2

3-(aq)Concentration (M)

InitialChangeEquilibrium

---

1.0- 2S

1.0 - 2S

0 0+ S + SS S

Koverall =S2

(1.0 - 2S)2

= 24 S

1.0 - 2S= √24

S = [Ag(S2O3)23-] = 0.45 M

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 non-polarizable.

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:

Figure 2. Distribution of hardness and softness for potential donor atoms for ligands in the Periodic Table.

As Se Br

P S Cl

I

C N O F

HARD: H2O, OH-, CH3COO-, F-, NH3, oxalate (-OOC-COO-), en (NH2CH2CH2NH2).

SOFT: Br-, I-, SH-, CH3S-, (CH3)2S, S=C(NH2)2 (thiourea), P(CH3)3, PPh3, As(CH3)3, CN- -S-C≡N (thiocyanate, S-bound)

INTERMEDIATE: C6H5N (pyridine), N3- (azide), -N=C=S

(thiocyanate, N-bound), Cl-

(donor atoms underlined)

Hard and Soft Bases.

HARD AND SOFT ACIDS AND BASES

Hard acids react preferentially with hard bases, and soft acids react preferentially with soft bases.

Examples: Aqueous SolubilitySilver Halides

Compound solubility product AgF 205 AgCl 1.8 x 10-10

AgBr 5.2 x 10-13

AgI 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 (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:

Thiocyanate, an ambidentate ligand:

Figure 3. ThiocyanateComplexes showing a) N-bonding in the [Fe(NCS)6]3- complex with the hard Fe(III) ion, and b) S-bonding in the [Au(SCN)2]- complex (CSD: AREKOX) with the soft Au(I) ion

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 & BasesThere 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->I-

Soft 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-/SO3

2- on base hardness

Acid or Base StrengthIt 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 StrengthConsider 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. However, the reaction proceeds to the right (K>1), because hard/soft considerations override acid-base strength considerations.

soft -hard

hard -soft

soft -soft hard -hard

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-

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.

A very hard metal ion, Al(III):