Prof HM MarquesProf HM MarquesC301C301717-6737717-6737hmarques@chem.wits.ac.zahmarques@chem.wits.ac.za

Chemistry IIChemistry IIInorganic ChemistryInorganic ChemistryPart 2Part 2

Chapters 4 and 5

Chapter 4 – Acids and Bases

Revise from Chem I

Bronsted-Lowry definition of an acid & a base

Lewis definition of an acid & a base

Co

H3N

H3N NH3

OH-

NH3

NH3

3+

2+Complex ion

Ligands

Co

H3N

H3N NH3

OH-

NH3

NH3

3+

2+

N

H

HH

Co

Lewis base Lewis acid

HCl(g) + H2O(l) H3O+ (aq) + Cl- (aq)

NH3(g) + H2O(l) OH- (aq) + NH4+(aq)

Base

Acid

Water is amphiprotic (amphoteric) – it can act as either an acid or a base

(H3O)+(H2O)3 or H9O4+

HA(aq) + H2O (l) H3O+(aq) + A-(aq)

+ -3

a

[H O ][A ]=

[HA]K

Acid dissociation

constantMeasure of the strength of the

acid

log ( )a apK K

Perchloric acid (HClO4) Ka = 1010 pKa = -10

Sulphuric acid (H2SO4) 102 -2

Phosphoric (H3PO4) 7.5 x 10-3 1.92

Hydrocyanic acid (HCN) 4.9 x 10-10 9.31

Acid strength decreases

The higher the pKa, the weaker the acid

+ -3

a

[H O ][A ]=

[HA]K

+ a3 -

[HA][H O ] =

[A ]

K

+ a3 -

[HA]log [H O ] = log

[A ]

K

+3 a -

[HA]log [H O ] = log log

[A ]K

-+

3 a

[A ]log [H O ] = log log

[HA]K

-

a

[A ]pH = p log

[HA]K

-

a

[A ]pH = p log

[HA]K

a

[Base]pH = p log

[Acid]K

Henderson-Hasselbalch equation

•When [Base] = [Acid], pH = pKa

•At any pH, it can be shown (see Tut) that

ap pH

100%[Base] =

1 10 K

apH p

100%[Acid] =

1 10 K

B(aq) + H2O (l) OH-(aq) + HB+(aq)

- +

b

[OH ][HB ]=

[B]K

Basicity constant Measure of the

strength of the base

b blog ( )pK K

The higher the pKb, the weaker the base

H2O (l) + H2O (l) OH-(aq) + H3O+(aq)

- +w 3= [OH ][H O ]K

Autoprotolysis constant of

water= 1.00 x 10-14 at

25.0 oC

Oxalic acid is a polyprotic acid:

H2Ox + H2O HOx- + H3O+ Ka1 = 5.9 x 10-2

HOx- + H2O Ox2- + H3O+ Ka2 = 6.4 X 10-5

OH

O

HO

O

We will calculate the species distribution as a function of pH

(H2Ox)

- + 2- +

a1 a2 -2

[HOx ][H ] [Ox ][H ]= =

[H Ox] [HOx ]K K

- 2-2(H Ox) + (HOx ) + (Ox ) = 1x x x

-a1 2 a2

2 + +

[H Ox] [HOx ][H Ox] + + = 1

[H ] [H ]

K Kx x x

a1 2 a1 a2 22 + + 2

[H Ox] [H Ox][H Ox] + + = 1

[H ] [H ]

K K Kx x x

a1 a1 a22 + + 2

[H Ox] 1 + = 1[H ] [H ]

K K Kx

Fractional abundance, so 0 x

1

a1 a1 a22 + + 2

[H Ox] 1 + = 1[H ] [H ]

K K Kx

+ 2 +a1 a1 a2

2 + 2

[H ] [H ][H Ox] = 1

[H ]

K K Kx

+ 2 + 2

2 + 2 +a1 a1 a2

[H ] [H ][H Ox] =

[H ] [H ] βx

K K K

Similarly,

+- a1

2- a1 a2

[H ][HOx ] =

β

[Ox ] =β

Kx

K Kx

+ 2

2

+- a1

2- a1 a2

[H ][H Ox] =

β

[H ][HOx ] =

β

[Ox ] =β

x

Kx

K Kx

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0

pH

H2OxHOx-

Ox2-

Fra

ctio

nal a

bund

ance

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

pH

H2Ox HOx-

Ox2-

0.020.05

0.93

Species distribution at pH 3

93% HOx– ; 5% Ox2- ; 2% H2Ox

For a proton to be acidic it must be attached to an electronegative element (O, F, Cl, Br, I; to a lesser extent N, S)

R––X––H

If X is electronegative…

R––X: + H+

…and delivering H+ to a Lewis base

…then the X-H bond can split heterolytically

with X retaining the electron pair…

The acidity of a proton

Organic acids have acidic and non-acidic protons

H3C

H2C

CH2

C

O

O

HNon-acidic protons because C is not

electronegative enough

Acidic proton because H bonded to

electronegative O

AQUA ACIDS

Acidic proton on a water molecule coordinated to a metal ion

M

L

L L

O

L

L H

H

If metal is able to polarise the M-O bond towards it…

…that will cause the H-O bond to be polarised towards O…

…releasing H+ to be accepted by a Lewis base.

AQUA ACIDS

Acidic proton on a water molecule coordinated to a metal ion

M

L

L L

O

L

L H

HM

L

L L

O

L

L H

- H++

Aqua acids are in principle polyprotic acids

[Fe(OH2)6]3+ [Fe(OH2)4(OH)2]+ + H+[Fe(OH2)5(OH)]2+ + H+

etc.

HYDROXOACIDS

Acidic proton on a hydroxyl group bonded or coordinated to a central atom

OH

Si

HOOH

OH

OXOACIDS

Acidic proton on a hydroxyl group bonded or coordinated to a central atom on which there is an oxo (=O) group

Ru

L

L L

L

OH2

OH2

Ru

L

L L

L

OH

OH

- 2 H+

Ru

L

L L

L

O

OH

- H+

Aqua acids, hydroxoacids and oxoacids may be successive stages of the deprotonation of an aqua acid

Aqua acids

M

L

L L

L

OH2

OH2

Central atom in lower oxidation states

s block, d block metals in lower (+1, +2, +3) oxidation states, metals on the left of the p block

OH

H

r+ d

Strengths of aqua acids

This can be rationalised using an electrostatic (ionic) model

radius of the metal ion of charge n+

diameter of coordinated water

molecule

H H+

Work done = [Potential at r = ] – [Potential at r = (r+ + d)]

1 2

0

1

4πε

q qE

r

1 2

0

H

0

10

4πε ( )

1

4πε ( )

cation

q q

r d

z z

r d

OH

H

r+ d

H H+ H+

For this process,

G = -RT ln K = -nFE

RT ln K = nF(E)

-RT ln K = -nFE(r +d)+

RT

-2.303 nFE(r +d)+-log K =

RT

-2.303 nFE(r +d)+pKa =

RT

-2.303 nFE(r +d)+pKa =

H

0( )

0H

14πε ( )Work 1

= = charge 4πε ( )

cation

cationr d

z z

r d zE

z r d

OH

H

r+ d

H H+ H+

H

0

1

4πε ( )cationz z

Er d

RT

-2.303 nFE(r +d)+pKa =

H

0( )

0H

14πε ( )Work 1

= = charge 4πε ( )

cation

cationr d

z z

r d zE

z r d

oa

12.303

4 ( )p

cationznF

r dK

RT

a-p( )

cationzK

rpKa should become smaller, and acidity should increase with

an increase in the charge on the ion

a decrease of the size of the ion

oa

o

12.303

4 ( )p

2.303

4 ( )

cation

cation

znF

r dK

RTnFz

r d RT

a-p( )

z

Kr

The term (z/r+) is also known as the ionic potential

Alternatively we could say2

a-p( )

z

Kr d

by adding the charge on the proton and the diameter of water.

The term (z2/(r+ + d)) is called the electrostatic parameter

How good is this electrostatic model (for gas phase) in solution?

See Fig. 4.3

as electrostatic parameter increases...

pKa

gets

sm

alle

r an

d ac

idity

incr

ease

s

How good is this electrostatic model (for gas phase) in solution?

Model quite good for s block ions, some d block ions, and the lanthanides

Model quite poor for many of the d block ions; their acidity is often much higher than predicted by the model

Major reason for failure of the model: bonding between the metal and its ligands often not purely ionic, and there is some covalency in metal-ligand bonds.

Model is worst for metals like Sn2+ and Hg2+ that form very covalent complexes.

M

L

L L

O

L

L H

H

The more covalent the M-O bond…

…the more the O-H bond is polarised

towards O…

…the more readily H+ is lost, and the more acidic

the compound

Oxoacids

Formed by

electronegative elements top right of periodic table (e.g., N, P, S, Cl)

elements in high oxidation state (e.g., Te, I, As, Se)

See Table 4.2

General formula: OpE(OH)q

H3PO3, phosphorus acid, isO1(PH)(OH)2

Pauling’s rules

Empirical rules that allow one to estimate the pKa of oxoacids

General formula: OpE(OH)q

1. pKa 8 – 5p

2. For p > 1, each successive pKa increases by about 5 units

Example

Estimate the pKas of H3AsO4

O

As

HOOH

OH

Actual values: 2.3, 6.9, 11.5

*Estimates are usually good to within 1-2 units

The strengths of oxoacids can be varied by substitution:

O

S

OOH

OH

O

S

OCF3

OH

O

S

OF

OH

CF3 and F are more electron withdrawing than OH; these acids are stronger acids than H2SO4

The strengths of oxoacids can be varied by substitution:

O

S

OOH

OH

O

S

OCF3

OH

O

S

OF

OH

Electron withdrawl...

...polarises the OH bond, making the proton more acidic

The strengths of oxoacids can be varied by substitution:

O

S

OOH

OH

O

S

OCF3

OH

O

S

OF

OH

CF3 and F are more electron withdrawing than OH; these acids are stronger acids than H2SO4

NH2 and CH3 are electron donating – hence these acids are weaker acid than H2SO4

OxidesOxides of non-metals are acidic.

When dissolved in water, they bind water and release a proton

SO3(g) + H2O(l) → H2SO4(aq) → H+(aq) + HSO4–(aq)

S

O

O O

+ H2O

O

S

OOH

OH

SO3 is the anhydride of H2SO4

Acidic oxides are neutralised by bases

SO2 + NaOH → Na+HSO3–

Oxides of metals are basic.

When dissolved in water, they accept a proton from water, producing an alkaline solution

MgO(s) + H2O(l) → Mg(OH)2(s) Mg2+(aq) + 2OH–(aq)

Acidic and basic oxides neutralised each other

CaO + SO2 → CaSO3

Oxides of the elements in the boundary region between metals and non-metals often show amphoteric behaviour.

Fig. 4.4

In the d block, metals in low oxidation states tend to be basic; amphoteric in their intermediate oxidation states; and acidic in high oxidation states

Fig. 4.5

Ga2O3 + 6H3O+ + 3H2O → 2[Ga(H2O)6]3+

Ga2O3 + 2OH– + 3H2O → 2[Ga(OH)4]–

Amphoteric axides will react with acids and bases…

Polymerisation of aqua ionsAqua ions of metals that have basic or amphoteric oxides polymerise and precipitate as pH is increased.

[Fe(OH2)6]3+ - exists in strongly acidic solution

Fe

H2O

H2O OH2

OH2

OH2

OH2

3+

increase pHFe

H2O

H2O OH2

OH

OH2

OH2

2+

[Fe(H2O)6]3+(aq) + (3+n)H2O(l) → Fe(OH)3•nH2O(s) + 3H3O+(aq)

polymer of Fe(OH)3

[Al(H2O)6]3+(aq) + (3+n)H2O(l) → Al(OH)3•nH2O(s) + 3H3O+(aq)

Similarly:

As pH is increased further, the species redissolve because both Al(OH)3 and Fe(OH)3 are amphoteric.

Al(OH)3 + OH– → [Al(OH)4]–

Polyoxyanions

With early 3d elements, or oxides of elements in high oxidation states

eg V2O5

eg PO43-

As base is added, condensation reactions occur, and polyoxyanions are formed

VO42- V2O7

2- V3O93- [H2V10O28]4-

Phosphates polymerise by condensation:

H+

H2O

See pp. 123-125

etc

Lewis Acids and Bases

We have seen that compounds such as [Co(NH3)6]3+ are complexes between ligands (Lewis bases) and a metal (Lewis acid)

Electron deficient compounds can act as Lewis acids

H3C B

CH3

CH3

H

N

HH

B

H3C

H3CH3C

N

H

HH

Self-study:Write brief notes on the Lewis acid properties of compounds of the elements of the s block, of Group 13, 14, 15, 16 and the halogens

(p. 126-128)

Hard and Soft Acids and Bases (HSAB)

R.G. Pearson

Let A be a Lewis acid, and B a base

Measure log K for the reaction

A + B AB

If for B = halide, the order of log K is

I– > Br– > Cl– > F–

then A is called a soft acid

If for B = halide, the order of log K is

I– < Br– < Cl– < F–

then A is called a hard acid

Fig. 4.10

Al3+ is a hard Lewis acid

Log K increases with the ionic potential = z/r

Al3+ Anion–

r

2o

1

4πεmetal anionz z

Fr

Strength of complex 1/r2

bonding is largely ionic

ionic radius increases

Hg2+ is a soft Lewis acid

Log K increases as the radius of the anion increases

Hg2+ Anion–

Strength of complex increases as overlap between orbitals of the anion sand orbitals of the metal increases with increasing size of anion

bonding is largely covalent

ionic radius increases

Hg2+ Anion–

Similarly, if we take a hard metal ion (like Al3+), then bases which bind strongly to it are hard Lewis bases; bases which do not bind strongly are soft Lewis bases.

Pearson’s Principle:

Hard Lewis acids prefer to bind to hard Lewis bases; soft Lewis acids prefer to bind to soft Lewis bases

See Table 5.3 for a listing of hard and soft Lewis acids and bases

In summary:

Hard metal ions are small, usually highly charged. Their electron cloud is not readily polarisable.

• Alkali metals (Li+, Na+, … )

• Alkali earth metal (Mg2+, Ca2+, … )

• H+

• Lighter transition metals in their higher oxidation states: Ti(IV), Ti(III), Cr(III), Fe(III), Co(III) …

Hard Bases: contain the smaller electronegative atoms, especially O, N, F and Cl. These donor atoms also have rather unpolarisable electron clouds

Soft metal ions are larger metal ions, often in their lower oxidation states. Their electron cloud is readily polarisable.

• Heavier transition metals (Pt, Rh, Ir)

• Transition metals in their lower oxidation stateCu(I), Ag(I), Hg(I), Hg(II), Pd(II), Pt(I), Pt(II)

• As we move across the d block the +2 oxidation state is stabilised –i.e., get Sc(III), not Sc(II); but Zn(II) not Zn(III). Hence

softness tends to increase across the d block, and down each group

Common soft bases include:

• H- (hydride)

• C donors

• S, P, As donors

• I-

Soft Bases: contain the larger, more polarisable and less electronegative atoms, especially S, Se, P, C and As.

Example

Arrange the following ligands in the order of increasing log K for binding to Fe(III) and to Pb(II) (donor atoms underlined)

(a) CH3SCH3

(b) CH3OCH3

(c) CH3S-

(d) CH3O-

Example

Explain why Cu(I) and Cu(II) are found in nature as the sulphide (CuS, Cu2S) but Ti(IV) and Fe(III) are found as their oxides (TiO2, Fe2O3)