Acid-Base Equilibria

1
Chapter 18
2
Acid-Base Equilibria
3
Table 18.1 Some Common Acids and Bases and their
Household Uses.
4
Arrhenius Acid-Base Definition
This is the earliest acid-base definition, which
classifies these substances in terms of their
behavior in water.
An acid is a substance with H in its formula that
dissociates to yield H3O.
A base is a substance with OH in its formula that
dissociates to yield OH-.
When an acid reacts with a base, they undergo
neutralization H(aq) OH-(aq) ? H2O(l)
DHrxn -55.9 kJ
5
Strong and Weak Acids
A strong acid dissociates completely into ions in
water HA(g or l) H2O(l) ? H3O(aq) A-(aq)
A dilute solution of a strong acid contains no HA
molecules.
In a dilute solution of a weak acid, most HA
molecules are undissociated.
6
Strong acid HA(g or l) H2O(l) ? H3O(aq)
A-(aq)
There are no HA molecules in solution.
7
Most HA molecules are undissociated.
8
Figure 18.2
Reaction of zinc with a strong acid (left) and a
weak acid (right).
Zinc reacts rapidly with the strong acid, since
H3O is much higher.
1 M HCl(aq)
1 M CH3COOH(aq)
9
The Acid Dissociation Constant, Ka
The value of Ka is an indication of acid strength.
10
Table 18.2 Ka Values for some Monoprotic Acids
at 25C
11
Classifying the Relative Strengths of Acids

• Strong acids include
• the hydrohalic acids (HCl, HBr, and HI) and
• oxoacids in which the number of O atoms exceeds
  the number of ionizable protons by two or more
  (eg., HNO3, H2SO4, HClO4.)
• Weak acids include
• the hydrohalic acid HF,
• acids in which H is not bonded to O or to a
  halogen (eg., HCN),
• oxoacids in which the number of O atoms equals or
  exceeds the number of ionizable protons by one
  (eg., HClO, HNO2), and
• carboxylic acids, which have the general formula
  RCOOH (eg., CH3COOH and C6H5COOH.)

12
Classifying the Relative Strengths of Bases

• Strong bases include
• water-soluble compounds containing O2- or OH-
  ions.
• The cations are usually those of the most active
  metals
• M2O or MOH, where M Group 1A(1) metal (Li, Na,
  K, Rb, Cs)
• MO or M(OH)2 where M group 2A(2) metal (Ca, Sr,
  Ba).
• Weak bases include
• ammonia (NH3),
• amines, which have the general formula
  
  
• The common structural feature is an N atom with a
  lone electron pair.

13
Sample Problem 18.1
Classifying Acid and Base Strength from the
Chemical Formula
SOLUTION
(a) Strong base KOH is one of the group 1A(1)
hydroxides.
14
Sample Problem 18.1
(b) Weak acid (CH3)2CHCOOH is a carboxylic
acid, as indicated by the COOH group. The COOH
proton is the only ionizable proton in this
compound.
(c) Strong acid He2SO4 is an oxoacid in which
the number of atoms exceeds the number of
ionizable protons by two.
(d) Weak base (CH3)2CHNH2 has a lone pair of
electrons on the N and is an amine.
15
Autoionization of Water
Water dissociates very slightly into ions in an
equilibrium process known as autoionization or
self-ionization.
16
The Ion-Product Constant for Water (Kw)
KcH2O2 Kw H3OOH- 1.0x10-14 (at 25C)
Both ions are present in all aqueous systems.
17
A change in H3O causes an inverse change in
OH-, and vice versa.
18
Figure 18.3
The relationship between H3O and OH- and the
relative acidity of solutions.
19
Sample Problem 18.2
Calculating H3O or OH- in an Aqueous Solution
SOLUTION
Kw 1.0x10-14 H3O OH- so
3.3x10-11 M
H3O is gt OH- and the solution is acidic.
20
The pH Scale
pH -logH3O
The higher the pH, the lower the H3O and the
less acidic the solution.
21
Figure 18.4
The pH values of some familiar aqueous solutions.
pH -log H3O
22
Table 18.3 The Relationship between Ka and pKa
Acid Name (Formula) Ka at 25C pKa
Hydrogen sulfate ion (HSO4-) 1.0x10-2 1.99
Nitrous acid (HNO2) 7.1x10-4 3.15
Acetic acid (CH3COOH) 1.8x10-5 4.75
Hypobromous acid (HBrO) 2.3x10-9 8.64
Phenol (C6H5OH) 1.0x10-10 10.00
pKa -logKa
A low pKa corresponds to a high Ka.
23
pH, pOH, and pKw
Kw H3OOH- 1.0x10-14 at 25C
pH -logH3O pOH -logOH-
pKw pH pOH 14.00 at 25C
pH pOH pKw for any aqueous solution at any
temperature.

• Since Kw is a constant, the values of pH, pOH,
  H3O, and OH- are interrelated
• If H3O increases, OH- decreases (and vice
  versa).
• If pH increases, pOH decreases (and vice versa).

24
Figure 18.5
The relations among H3O, pH, OH-, and pOH.
25
Sample Problem 18.3
Calculating H3O, pH, OH-, and pOH
SOLUTION
Calculating the values for 2.0 M HNO3
H3O 2.0 M
pH -logH3O -log(2.0) -0.30
5.0x10-15 M
pOH -logOH- -log(5.0x10-15) 14.30
26
Sample Problem 18.3
Calculating the values for 0.30 M HNO3
H3O 0.30 M
pH -logH3O -log(0.30) 0.52
3.3x10-14 M
pOH -logOH- -log(3.3x10-14) 13.48
Calculating the values for 0.0063 M HNO3
H3O 0.0063 M
pH -logH3O -log(0.30) 2.20
1.6x10-12 M
pOH -logOH- -log(1.6x10-12) 11.80
27
Figure 18.6
Methods for measuring the pH of an aqueous
solution.
28
Brønsted-Lowry Acid-Base Definition

• An acid is a proton donor, any species that
  donates an H ion.
• An acid must contain H in its formula.

• A base is a proton acceptor, any species that
  accepts an H ion.
• A base must contain a lone pair of electrons to
  bond to H.

An acid-base reaction is a proton-transfer
process.
29
Figure 18.7
Dissolving of an acid or base in water as a
Brønsted-Lowry acid-base reaction.
(acid, H donor)
(base, H acceptor)
(base, H acceptor)
(acid, H donor)
30
Conjugate Acid-Base Pairs
In the forward reaction
31
Conjugate Acid-Base Pairs
H2S and HS- are a conjugate acid-base pair HS-
is the conjugate base of the acid H2S.
NH3 and NH4 are a conjugate acid-base pair NH4
is the conjugate acid of the base NH3.
A Brønsted-Lowry acid-base reaction occurs when
an acid and a base react to form their conjugate
base and conjugate acid, respectively.
32
Table 18.4 The Conjugate Pairs in some Acid-Base
Reactions
Conjugate Pair
33
Sample Problem 18.4
Identifying Conjugate Acid-Base Pairs
SOLUTION
The conjugate acid-base pairs are H2PO4-/HPO42-
and CO32-/HCO3-.
34
Sample Problem 18.4
The conjugate acid-base pairs are H2O/OH- and
SO32-/HSO3-.
35
Net Direction of Reaction
The net direction of an acid-base reaction
depends on the relative strength of the acids and
bases involved.
A reaction will favor the formation of the weaker
acid and base.
This reaction favors the formation of the
products.
36
The stronger the acid is, the weaker its
conjugate base. When an acid reacts with a base
that is farther down the list, the reaction
proceeds to the right (Kc gt 1).
37
Sample Problem 18.5
Predicting the Net Direction of an Acid-Base
Reaction
SOLUTION
The net direction for this reaction is to the
right, so Kc gt 1.
38
Sample Problem 18.5
The net direction for this reaction is to the
left, so Kc lt 1.
39
Sample Problem 18.6
Using Molecular Scenes to Predict the Net
Direction of an Acid-Base Reaction
40
Sample Problem 18.6
SOLUTION
The HX solution has a lower pH than the HY
solution, so HX is the stronger acid and Y- is
the stronger base. The reaction of HX and Y- has
a Kc gt 1, which means the equilibrium mixture
will contain more HY than HX.
Scene 1 has equal numbers of HX and HY, which
could occur if the acids were of equal strength.
Scene 2 shows fewer HY than HX, which would occur
if HY were the stronger acid.
Scene 3 is consistent with the relative acid
strengths, because it contains more HY than HX.
41
Solving Problems Involving Weak-Acid Equilibria

• Problem-solving approach
• Write a balanced equation.
• Write an expression for Ka.
• Define x as the change in concentration that
  occurs during the reaction.
• Construct a reaction table in terms of x.
• Make assumptions that simplify the calculation.
• Substitute values into the Ka expression and
  solve for x.
• Check that the assumptions are justified.

42
Solving Problems Involving Weak-Acid Equilibria

• The notation system
• Molar concentrations are indicated by .
• A bracketed formula with no subscript indicates
  an equilibrium concentration.

• The assumptions
• H3O from the autoionization of H2O is
  negligible.
• A weak acid has a small Ka and its dissociation
  is negligible. HA HAinit.

43
Sample Problem 18.7
Finding Ka of a Weak Acid from the Solution pH
44
Sample Problem 18.7
H3O 10-pH 2.4x10-3 M which is gtgt 10-7 (the
H3O from water)
x 2.4x10-3 M H3O PAc-
HPAc 0.12 - x 0.12 M
So Ka
4.8x10-5
Checking the assumptions by finding the percent
error in concentration
45
Sample Problem 18.8
Determining Concentration from Ka and Initial HA
SOLUTION
46
Sample Problem 18.8
Since Ka is small, we will assume that x ltlt 0.10
and HPr 0.10 M.
1.1x10-3 M H3O
47
Concentration and Extent of Dissociation
As the initial acid concentration decreases, the
percent dissociation of the acid increases.
The fraction of ions present increases, even
though the actual HAdissoc decreases.
48
Sample Problem 18.9
Using Molecular Scenes to Determine the Extent of
HA Dissociation
PROBLEM
A 0.15 M solution of acid HA (blue and green) is
33 dissociated. Which scene best represents a
sample of the solution after it is diluted with
water?
49
Sample Problem 18.9
SOLUTION
In each case, remember that each unit of H3O is
produced from one unit of HA, so HAinit HA
H3O.
Solution 1. dissociated 4/(5 4) x 100
44 Solution 2. dissociated 2/(7 2) x 100
22 Solution 3. dissociated 3/(6 3) x 100
33
Scene 1 represents the diluted solution.
50
Polyprotic Acids
A polyprotic acid is an acid with more than one
ionizable proton. In solution, each dissociation
step has a different value for Ka
Ka1 gt Ka2 gt Ka3
We usually neglect H3O produced after the
first dissociation.
51
Table 18.5 Successive Ka values for Some
Polyprotic Acids at 25C
52
Sample Problem 18.10
Calculating Equilibrium Concentrations for a
Polyprotic Acid
SOLUTION
53
Sample Problem 18.10
x H3O Asc-
7.1x10-4 M
pH -logH3O -log(7.1x10-4) 3.15
54
Sample Problem 18.10
Checking assumptions
2. H2Ascdissoc ltlt H2Ascinit
55
Weak Bases
A Brønsted-Lowry base is a species that accepts
an H. For a weak base that dissolves in water
The base-dissociation or base-ionization constant
is given by
Note that no base actually dissociates in
solution, but ions are produced when the base
reacts with H2O.
56
Figure 18.9 Abstraction of a proton from water by
the base methylamine.
57
Table 18.6 Kb Values for Some Molecular (Amine)
Bases at 25C
58
Sample Problem 18.11
Determining pH from Kb and Initial B
SOLUTION
59
Sample Problem 18.11
Since Kb is small, x ltlt 1.50 and 1.50 x 1.50
x OH- 3.0x10-2 M
Check assumption
60
Sample Problem 18.11
3.3x10-13 M
pH -log (3.3x10-13) 12.48
61
Anions of Weak Acids as Weak Bases
The anions of weak acids often function as weak
bases.
A solution of HA is acidic, while a solution of
A- is basic.
62
If NaF is dissolved in H2O, it dissolves
completely, and F- can act as a weak base
63
Ka and Kb for a Conjugate Acid-Base Pair
Kc for the overall equation K1 x K2, so
H3OOH-
Ka x Kb Kw
This relationship is true for any conjugate
acid-base pair.
64
Sample Problem 18.12
Determining the pH of a Solution of A-
SOLUTION
65
Sample Problem 18.12
5.6x10-10 M
so x OH- 1.2x10-5 M
Checking the assumption
66
Sample Problem 18.12
8.3x10-10 M
pH -log (8.3x10-10) 9.08
67
Acid Strength of Nonmetal Hydrides

• For nonmetal hydrides (E-H), acid strength
  depends on
• the electronegativity of the central nonmetal
  (E), and
• the strength of the E-H bond.

Across a period, acid strength increases. Electron
egativity increases across a period, so the
acidity of E-H increases.
Down a group, acid strength increases. The length
of the E-H bond increases down a group and its
bond strength therefore decreases.
68
Figure 18.10
The effect of atomic and molecular properties on
nonmetal hydride acidity.
69
Acid Strength of Oxoacids
All oxoacids have the acidic H bonded to an O
atom.

• Acid strength of oxoacids depends on
• the electronegativity of the central nonmetal
  (E), and
• the number of O atoms around E.

For oxoacids with the same number of O atoms,
acid strength increases as the electronegativity
of E increases.
For oxoacids with different numbers of O atoms,
acid strength increases with the number of O
atoms.
70
The relative strengths of oxoacids.
Figure 18.11
71
Hydrated Metal Ions
Some hydrated metal ions are able to transfer an
H to H2O. These metal ions will form acidic
solutions.
Consider a metal ion in solution, Mn
Mn(aq) H2O(l) ? M(H2O)xn(aq)
If Mn is small and highly charged, it will
withdraw enough e- density from the O-H bonds of
the bound H2O molecules to release H
72
Figure 18.12
The acidic behavior of the hydrated Al3 ion.
73
Salts that Yield Neutral Solutions
A salt that consists of the anion of a strong
acid and the cation of a strong base yields a
neutral solution.
NaNO3
This solution will be neutral, because neither
Na nor NO3- will react with H2O to any great
extent.
74
Salts that Yield Acidic Solutions
A salt that consists of the anion of a strong
acid and the cation of a weak base yields an
acidic solution.
NH4Cl
This solution will be acidic, because NH4 will
react with H2O to produce H3O
75
Salts that Yield Basic Solutions
A salt that consists of the anion of a weak acid
and the cation of a strong base yields a basic
solution.
CH3COONa
This solution will be basic, because CH3COO- will
react with H2O to produce OH-
76
Sample Problem 18.13
Predicting Relative Acidity of Salt Solutions
from Reactions of the Ions with Water
(a) Potassium perchlorate, KClO4 (b) Sodium
benzoate, C6H5COONa (c) Chromium(III) nitrate,
Cr(NO3)3
SOLUTION
(a) K is the cation of a strong base (KOH)
while ClO4- is the anion of a strong acid
(HClO4). This solution will be neutral.
77
Sample Problem 18.13
(b) Na is the cation of a strong base (NaOH)
while the benzoate anion (C6H5COO-) is the anion
of a weak acid (benzoic acid). The benzoate ion
will react with H2O to produce OH- ions
This solution will be basic.
(c) NO3- is the anion of a strong acid (HNO3)
and will not react with H2O to any great extent.
Cr3 is a small metal cation with a fairly high
charge density. It will become hydrated and the
hydrated ion will react with H2O to form H3O
ions
This solution will be acidic.
78
Salts of Weakly Acidic Cations and Weakly Basic
Anions
If a salt that consists of the anion of a weak
acid and the cation of a weak base, the pH of the
solution will depend on the relative acid
strength or base strength of the ions.
NH4CN
79
The reaction that proceeds farther to the right
determines the pH of the solution, so we need to
compare the Ka of NH4 with the Kb of CN-.
Since Kb of CN- gt Ka of NH4, CN- is a stronger
base than NH4 is an acid. A solution of NH4CN
will be basic.
80
Table 18.7 The Acid-Base Behavior of Salts in
Water
81
Sample Problem 18.14
Predicting the Relative Acidity of Salt Solutions
from Ka and Kb of the Ions
SOLUTION
Ka of Zn(H2O)62 1x10-9 (from Appendix C.)
Ka for Zn(H2O)62 gtgt Kb HCOO-, therefore the
solution is acidic.
82
The Leveling Effect
All strong acids and bases are equally strong in
water.
All strong acids dissociate completely to form
H3O, while all strong bases dissociate
completely to form OH-.
In water, the strongest acid possible is H3O and
the strongest base possible is OH-.
H2O exerts a leveling effect on any strong acid
or base.
83
The Lewis Acid-Base Definition
A Lewis base is any species that donates an
electron pair to form a bond.
A Lewis acid is any species that accepts an
electron pair to form a bond.
The Lewis definition views an acid-base reaction
as the donation and acceptance of an electron
pair to form a covalent bond.
84
Lewis Acids and Bases
A Lewis base must have a lone pair of electrons
to donate. Any substance that is a Brønsted-Lowry
base is also a Lewis base.
A Lewis acid must have a vacant orbital (or be
able to rearrange its bonds to form one) to
accept a lone pair and form a new bond. Many
substances that are not Brønsted-Lowry acids are
Lewis acids.
The Lewis definition expands the classes of acids.
85
Electron-Deficient Molecules as Lewis Acids
B and Al often form electron-deficient molecules,
and these atoms have an unoccupied p orbital that
can accept a pair of electrons
BF3 accepts an electron pair from ammonia to form
a covalent bond.
86
Lewis Acids with Polar Multiple Bonds
Molecules that contain a polar multiple bond
often function as Lewis acids
The O atom of an H2O molecule donates a lone pair
to the S of SO2, forming a new S?O s bond and
breaking one of the S?O p bonds.
87
Metal Cations as Lewis Acids
A metal cation acts as a Lewis acid when it
dissolves in water to form a hydrated ion
The O atom of an H2O molecule donates a lone pair
to an available orbital on the metal cation.
88
Figure 18.13
The Mg2 ion as a Lewis acid in chlorophyll.
89
Sample Problem 18.15
Identifying Lewis Acids and Bases
SOLUTION
(a) The H ion accepts the electron pair from
OH-. H is the Lewis acid and OH- is the Lewis
base.
(b) BCl3 accepts an electron pair from Cl-. Cl-
is the Lewis base and BCl3 is the Lewis acid.
(c) An O atom from each H2O molecule donates an
electron pair to K. H2O is therefore the Lewis
base, and K is the Lewis acid.