Topic 5 Acid and Bases Acid and Bases

Topic 5
5-1
Acid and Bases
Acid and Bases
5-2
There are a number definitions for aicd and bases, depending on
what is convenient to use in a particular situation:
• Arrhenius and Ostwald: Theory of electrolyte dissociation
acid + base
salt + water
• Brønsted and Lowry (1923): Protontransfer reactions
– Acid is proton donor, base is proton acceptor
• Lewis (1923): Generalization of previous theories
– Acid is electron pair acceptor, base is electron pair donor
–> Neutralization: formation of a covalent bond between acid and base

Brønsted-Lowry Acid and Bases
5-3
A Brønsted-Lowry acid is a substance that can donate a hydrogen ion
A Brønsted-Lowry base is a substance that can accept a hydrogen ion
HCl + NH 3 NH 4
+
+ Cl –
acid base conjugate acid conjugate base
Note: Water can act as base or an acid = amphoteric behavior:
–> H 2 O is the conjugate acid of OH – and the conjugate base of H 3 O +
–> H 3 O + is the conjugate acid, OH – the conjugate base of H 2 O
Brønsted-Lowry Acid and Bases
5-4
• The Brønsted-Lowry definition includes also acid-base reactions in
the gas phase, or in solvents other than water, e.g. liquid ammonia:
2 NH 3 NH 4
+
+ NH 2
–
2 H 2 O H 3 O + + OH –
Note: In any solvent, the direction of the reaction is always such, that the
products are weaker acids or bases than the reactants

Solvent Dissociation Theory
5-5
• The Brønsted-Lowry theory is limited to proton transfer reactions
(and mostly aqueous systems), therefore, aprotic nonaqueous
systems require a different definition of acid and base:
The cation resulting from autodissociation of a solvent is the acid
The anion resulting from autodissociation of a solvent is the base
2 H 2 O H 3 O + + OH –
acid base
Other solvent dissociation equilibria:
Properties of Solvents
5-6

Dissociation of Pure Water
5-7
The autodissociation of water proceeds only to a slight extent, but is
responsible for a small but measurable presence of H 3 O + and OH –
ions:
K
2 H 2 O H 3 O + + OH –
Pure water contains no other ions than H 3 O + and OH – and the
negative charges must be equal the positive:
[H 3
O + ] = [HO ! ] = 10 !7 M neutral solution
[H 3
O + ] > [HO ! ]
[H 3
O + ] < [HO ! ]
acidic solution
basic solution
The pH Function
5-8
In aqueous solution the concentration of hydronium ions can range
from 10 M to 10 –15 M. It is convenient to express this large range by a
logarithmic scale, the pH scale:
Neutral pH: [H 3 O + ] = 10 –7 M –> pH = 7
Acidic range [H 3 O + ] > 10 –7 M –> pH < 7
Basic range [H 3 O + ] < 10 –7 M –> pH > 7

The Strength of Acids and Bases
5-9
Acids are classified as strong or weak depending on whether their
reaction with water to give H 3 O + (aq) go to completion or reach an
equilibrium:
HA + H 2 O H 3 O + + A –
The acidity constant K a (also called acid dissociation constant or
acid ionization constant) is a quantitative measure of the strength of
the acid in a given solvent (in this case water)
–> the larger K a the stronger the acid
Note: Acidity constants are typically written as pK a values:
5-10
Acidity Constants in Water

Base Strength
5-11
The strength of a base is inversely related to the strength of its
conjugated acid: the weaker the acid, the stronger the conjugated
base and vice versa.
K b
B + H 2 O HB + + OH –
K b is the basicity constant. Since K w
= [H 3
O + ][HO ! ] = 10 –14 M 2
we can also write:
Multiple Equilibria
5-12
If two bases compete for hydrogen ions, the stronger base “wins” and
will hold the larger portion of hydrogen ions:
K
HF + CN – HCN + F –
K = [HCN][F ! ]
[HF][CN – ]
We can calculate K from the tabulated values for the two individual
chemical equilibria involved:
K a
HF + H 2 O H 3 O + + F – K a
= [H 3 O+ ][F ! ]
= 6.6"10 !4
[HF]
K’ a
HCN + H 2 O H 3 O + + CN – K a
= [H 3 O+ ][CN ! ]
= 6.2 "10 !10
[HCN]

5-13
Acid vs. Conjugate Base Strengths
Indicators
5-14
An indicator is a soluble compound, generally an organic dye, that
changes its color noticeably over a fairly short range of pH:
K a
HInd + H 2 O H 3 O + + Ind – K a
= [H 3O + ][Ind ! ]
[HInd]
and
[H 3
O + ]
K a
= [HInd]
[Ind ! ]
If [H 3 O + ] is much larger than K a , then [HInd] > [Ind – ]
–> most of the indicator is protonated, and the color of the acid form
is predominant (and vice versa)

5-15
Indicator Color Change as Function of pH
Color Change of Phenolphtalein
5-16
OH
O
O
O
K a
H 3 O +
O
O
OH
O
colorless
acidic solution
red
basic solution
The red color of the deprotonated indicator (pH > 8) is due to the
extended and delocalized pi-system (resonance structures)
–> the HOMO-LUMO energy difference is smaller in the conjugated
pi-system, which shifts the absorption wavelength into the visible
range

pH Indicators in Biology
5-17
SNARF is a pH sensitive fluorescent probe, which can be used to
measure the pH value inside a living cell using fluorescence microscopy:
O
OH
Me 2 N
O
Me 2 N
O
K a
COO
COO
H 3 O + 5-18
Human neutrophils loaded
with SNARF
pH Range in Various Solvents

Equilibria of Weak Acid and Bases
5-19
• Weak acid and bases react only partially with water to form H 3 O + or
OH –
–> pH calculations must be performed based on K a or K b and the
involved thermodynamic equilibrium
K a
HA + H 2 O H 3 O + + A –
K a
= [H 3O + ][A ! ]
[HA]
Solve equation for [H 3 O + ]
–> calculate pH
pH Calculations
5-20
Example: pH of 1.0 M acetic acid (K a = 1.8E-5):
K a
CH 3 COOH + H 2 O H 3 O + + CH 3 COO –
Since acetic acid is a weak acid, we can approximate above quadratic equation with
1.00–y ≈ 1.00, thus
And the fraction of ionized acetic acid is calculated to be:

pH Calculations: Diluted Solutions
5-21
If water is added to further dilute acetic acid, the concentration of H 3 O +
decreases (moving towards 10 –7 M), and the fraction of the ionized acid
CH 3 COO – increases.
Example: pH of 0.0001 M acetic acid:
K a
= [H 3O + ][CH 3
COO " ]
[CH 3
COOH]
Solving above equation with the same approximation as before gives a 42%
fraction of ionized acid –> the approximation is not valid anymore, and the
quadratic ! equation must be solved accurately:
[H 3
O + ] = [CH 3
COO " ]
ionized fraction: 5-22
!
f = [CH 3 COO– ]
[CH 3
COOH] "100
!
Weak Bases
Example: pH of 0.01 M ammonia (K b = 1.8E-5):
K a
NH 3 + H 2 O NH
+
4 + OH –
K b
= [NH + 4
][OH " ]
[NH 3
]
Above quadratic equation is solved again for y:
!
[NH 4 + ] = [OH " ]
The hydronium ion concentration (and pH) of the solution is then obtained via K w :
!
[H 3
O + ] = K w
[OH " ]
!

Hydrolysis Reactions
5-23
• Some anionic or cationic species react with water to give an acidic
or basic solution
• For example, the ammonium cation NH 4
+
is hydrolyzed to give an
acidic solution:
K a
!
NH 4
+
+ H 2 O H 3 O + + NH 3
K a
= [H 3O + ][NH 3
]
[NH 4 + ]
• Similarly, hydrolysis of F – ion increases the OH – concentration and
so raises the pH:
F – + H 2 O
K a
OH – + HF
5-24
Hydrolysis
• Most ionic species hydrolyze to a detectable extent:
–> the hydrolysis of anions typically raises the pH
–> the hydrolysis of cations typically lowers the pH
• Metal cations with a large charge/size ratio undergo extensive
hydrolysis reactions:
Al(H 2 O) 6
3+
+ H 2 O
• +1 metal cations and large +2 cations do not undergo hydrolysis
(pK a > 7) (Li + , Na + , K + , Rb + , Cs + , Mg 2+ , Ca 2+ , Sr 2+ , Ba 2+ )
• The conjugate bases of very strong acids are nonhydrolyzing
anions: ClO 4– , Cl – , Br – , I – , HSO 4– , NO 3
–

5-25
Hydrolysis Constants of Cations
Buffer Solutions
5-26
Buffer solution = any solution that maintains an approximately constant pH
despite small additions of acid or base
–> typically a buffer solution contains a weak acid and a weak base that are
conjugate to one another
Example: Calculate the pH of a mixture of 1M HCOOH and 0.5 M NaHCOO
K a (formic acid) = 1.8E–4:
K a
HCOOH + H 2 O H 3 O + + HCOO –
Since acetic acid is a weak acid, we can approximate above quadratic equation with
1.00–y ≈ 1.00 (and 0.5+y ≈ 0.5):

How Buffer Solutions Work
5-27
• In a buffer solution the concentration of [HA] and [A – ] are similar,
and therefore the addition of small amounts of acid or base will not
affect the [H 3 O + ] concentration substantially:
Designing Buffers
5-28
• Assuming that the equilibrium concentrations of [HA] and [A – ] are
very close to the initial total concentrations ([HA] 0 and [A – ] 0 ), we can
write:
K a
= [H 3 O+ ][A ! ]
[HA]
" [H 3 O+ ][A ! ] 0
[HA] 0
• Solving for [H 3 O + ] and using the definitions for pK and pH gives:
Henderson-Hasselbalch
Equation

Concentration Dependence
5-29
• Continuos dilution of buffer solutions will gradually change the
pH towards 7, since the initial assumption of [HA] 0 ≈ [HA] and
[A – ] 0 ≈ [A – ] does not apply at low buffer concentrations
pH vs. conc. plots for various buffer
systems:
1: Sodium phosphate
2: Ammonia
3: 2,4-dichlorophenol
4: Uric Acid
5: Acetic acid
6: H 2 B 4 O 7
7: Phosphoric acid
Acid-Base Titration Curves
5-30
• A graph of pH versus the volume of titrating solution is called
titration curve:
–> the exact shape of an acid-base
titration curve can be calculated based on
the ionization constants of the acid and
base and their concentrations
–> the titration curve can be used to
calculate an unknown ionization constant
of an acid or base (by titration with a
known base or acid)

Titration of a Strong Acid with a Strong Base
5-31
• Simplest type of titration, the chemical reaction corresponds to a
neutralization reaction:
The pH at each point of the titration
curve can be calculated (or
measured) assuming complete
reaction of the added base and
acid present
Concentration Dependence
5-32
• Since the measured pH reflects the total [H 3 O + ] concentration,
the shape of the titration curve depends on the concentration of
the acid (and added base):

5-33
Titration of a Weak Acid with a Strong Base
Example: Titration of acetic acid with NaOH: The titration curve has four
distinct ranges:
1) Before NaOH addition:
pH given by ionization of a weak acid
2) Less than 1 molar equivalent of NaOH added:
OH– is a much stronger base than acetate,, and therefore substracts the proton
from acetic acid to form NaOAc
–> the pH can be calculated using the Henderson-Hasselbalch equation
(buffered region of the titration curve)
Note: At the half equivalence point (V=V e /2) pH ≈ pK a = 4.74
3) Equivalence point (V NaOH = V HOAc ):
All the protons of acetic acid are neutralized –> the pH is identical with the pH
of a solution of NaOAc of identical concentration
4) After addition of more than 1 molar equivalent of NaOH:
Beyond the equivalence point, all the acetic acid has been neutralized. The
pH of the solution is approximately identical with the pH observed in the
titration of a strong acid and strong base.
Titration of HOAc with NaOH
5-34

Polyprotic Acids
5-35
• Polyprotic acids donate two or more hydrogen ions in stages
(e.g. H 2 CO 3 , oxalic acid, phosphoric acid)
Note: Even though acetic acid (CH 3 COOH) has a total of four hydrogen atoms, it
is a monoprotic acid (only one of the four hydrogen atoms is acidic!)
• The titration of a diprotic weak acid involves two simultaneous
equilibria:
K a1
!
H 2 CO 3 + H 2 O H 3 O + + HCO 3
–
K a1
=
K a2
HCO
–
3 + H 2 O H 3 O + + CO
2–
3
!
K a2
=
Titration of Polyprotic Acids
5-36
• As shown for monoprotic acids, the titration points can be
calculated according to the involved equilibria with the
corresponding ionization constants
If the pK a values reasonably apart
from each other, the inflection points
of the titration curve directly reflect the
equilibrium positions where pH ≈ pK a

Effect of pH on Solution Composition
5-37
• Changing the pH shifts the positions of all acid-base equilibria in
a solution, and therefore the overall composition with respect to
the involved species
H 2 CO 3 + H 2 O H 3 O + + HCO 3
–
HCO 3
–
+ H 2 O H 3 O + + CO 3
2–
Solution composition for the
carbonate equilibrium as a
function of pH
The pH of Blood
5-38
• Human blood has a pH near 7.4 that is maintained by a
combination of carbonate, phosphate and protein buffers (a blood
pH below 7.0 or above 7.8 leads quickly to death)
The blood pH is depended on pCO 2 , the
partial pressure of CO 2
–> in order to get the non-respiratory pH,
the pH is measured at two different CO 2
partial pressures, the intersection at 40
mmHg CO 2 gives then the (standardized)
non-respiratory blood pH
Deviations from pH 7.4 are indicative of
various disease conditions
(respiratory or metabolic acidosis or
alkalosis)
Actual pH
Non-respiratory pH

Potentiometry
5-39
• The accurate measurement of [H 3 O + ] concentration with a pH
electrode allows to solve complicated equilibrium systems with
many species, including metal complexes:
Lewis Acid and Bases
5-40
A Lewis base is any species that donates electrons through coordination
to its lone pairs, a Lewis acid is any species that accept such electron
pairs.
–> In addition to the reactions previously discussed, the Lewis definition is
much broader and includes reactions such as:
Ag + + 2 NH 3 [H 3 N-Ag-NH 3 ] +
acid base adduct
BF 3 + NH 3 H 3 N-BF 3

Donor Acceptor Bonding
5-41
empty p orbital
(LUMO)
filled orbital
(lone pair, HOMO)
energy
Types of Lewis Acids
5-42
• Metal cations can act as Lewis acids
Ag + , Ga + , Fe 3+ etc.
• Molecules with incomplete octets can act as Lewis acids
BMe 3 , BF 3 , “AlH 3 ”
• Molecules with complete octets can change their bonding to
accommodate the base, for example CO 2
CO 2 + OH - HCO 3
-
• A molecular species may become hypervalent to accommodate
the base, for example PF 5
PF 5 + F - PF 6
-
• Both low lying s and p anti-bonding orbitals can be used
I 2 + I - I 3
-

I 2 as a Lewis acid
5-43
• Lewis bases such as I - can interact with the sigma antibonding
orbital in I 2 and form an adduct
UV-vis absorption spectrum:
Bromine as a Lewis acid
5-44

Strengths of Lewis acids and bases
5-45
Not as simple to rationalize as Bronsted acids and bases
• relative acid strength depends upon which base you are
considering
• and relative base strength depends upon which acid you are
considering!
Example:
In aqueous solution Ag + has a stronger affinity for NH 3 than for F -
– this implies that NH 3 is a better base
In aqueous solution Ca 2+ has a stronger affinity for F - than for NH 3
– this implies that F - is a better base
Soft and hard acids/bases
5-46
• In any interaction between an acid and a
base to form an adduct the bonding can be
anywhere between ionic and covalent
• The hard/soft acid base principle relates to
the degree of covalency in the bonding
a hard acid is an acid that would rather bind
to F - than I -
• Hard bases have a high affinity for hard
acids and soft bases have a high affinity for
soft acids

Acidity and Basicity of Binary Hydrides
5-47
• Binary hydrogen compounds range from strong acids (HCl) to
weak bases (NH 3 ), or non-acidic molecules (CH 4 )
• Acidity is greatest with lowest electronegativity in each group
–> larger molecules have lower charge density and form less stable
bonds to hydrogen
–> larger molecules form more stable conjugate bases (better
stabilization of negative charge)
Example hard and soft acids/bases
5-48
Class
Acids
Bases
Hard
Borderline
Soft
H + , Li + , Na + , K + ,
Mg 2+ , Ca 2+
Fe 2+ , Co 2+ ,
Ni 2+ , Cu 2+ ,
Zn 2+ , Pb 2+
Cu + , Ag + ,
Hg 2
2+
, Hg 2+ ,
Cd 2+
H 2 O, NH 3 , F - ,
Cl - , OH - , NO 3- ,
ClO 4- , CO 3
2-
, O 2-
, SO 4
2-
, PO 4
3-
NO 2- , Br - , SO 3
2-
CO, CN - , I - , S 2-

Acidity and Basicity of Binary Hydrides
5-49
• Binary hydrogen compounds range from strong acids (HCl) to
weak bases (NH 3 ), or non-acidic molecules (CH 4 )
• Acidity is greatest with lowest electronegativity in each group
–> larger molecules have lower charge density and form less stable
bonds to hydrogen
–> larger molecules form more stable conjugate bases (better
stabilization of negative charge)
Inductive Effects
5-50
• Substitution of electronegative groups such as fluorine or
chlorine in place of hydrogen results in weaker bases
–> the central atom lone pair is less readily donated to an acid
(e.g. PF 3 is a much weaker base than PH 3 )
• Substitution with alkyl groups results stronger bases
–> the central atom lone pair is more electron rich
Example:
Gas phase basicity is decreasing in the order:
NMe 3 > NHMe 2 > NH 2 Me > NH 3

The Strength of Oxyacids
5-51
• In the series of oxyacids of chlorine, the acid strength in aqueous
solution is decreasing in the order
HClO 4 > HClO 3 > HClO 2 > HOCl
pK a : –10 –1 2 7.2
With increasing number of electronegative substituents on Cl, the O–H
bond is weakened due to the increasing positive charge on Cl. At the same
time the negative charge of the conjugate base is further stabilized.
–> Both effects result in an increasing acidity
• For oxyacids with more than one ionizable hydrogen, the pK a
values increase by about 5 units with each successive removal:
H 3 PO 4 > H 2 PO 4
– > HPO 4
2–
pK a : 2.15 7.20 12.37
Super Acids
5-52
• Any acid solution which is more acidic than sulfuric acid is called
a super acid
–> super acid systems are necessarily nonaqueous, since the acidity of
any aqueous system is limited by the fact that the strongest acid that
can exist in the presence of water is H 3 O +
• The acidity is measured by the Hammett acidity function (B/BH+
is an indicator and its conjugate base):
H 0
! pK BH
+ " log [BH+ ]
[B]