Chapter 17: Chemistry of Acids and Bases
Defining Acids and Bases (review)
There are three major ways to define acids and bases. They
were introduced by Lewis, Brønsted and Arrhenius:
1. A Lewis acid is a molecule that can accept an electron pair.
A Lewis base is a molecule that can donate an electron pair.
2. A Brønsted acid is a molecule that can donate H+.
A Brønsted base is a molecule that can accept H+.
3. An Arrhenius acid is a molecule that produces H+ (or H3O+)*
when dissolved in water.
An Arrhenius base is a molecule that produces OH- when
dissolved in water.
* Free protons (H+) do not exist in water. Every H+ is
solvated by water molecules. This is often represented as
the hydronium ion, H3O+ – but this is still a simplification.
The true formula is closer to H9O4+.
The Lewis definition of acids and bases is the
broadest. Every acid is a Lewis acid, but not
every acid is a Brønsted acid or an Arrhenius
acid. Note, however, that every Arrhenius acid is
both a Brønsted acid and a Lewis acid.
e.g. Nitric acid is an Arrhenius, a Brønsted and a Lewis acid.
Arrhenius:
Brønsted:
Lewis:
e.g. Ammonia is an Arrhenius, a Brønsted and a Lewis base.
Arrhenius:
Brønsted:
Lewis:
As in Chemistry 1000, we will focus primarily on the Arrhenius
acids; however, you should be aware of how the three
definitions interrelate – particularly if you plan to take any
further chemistry courses.
Compounds which can act as either an acid or a base are called
amphoteric (or amphiprotic). The most common example is
water. In a reaction between two water molecules, one acts as
an acid and the other acts as a base:
H ..
O
..
H
+
H
..O..
H
H
H
+
O.. H
-
+
..
.. H
:O
This is an equilibrium reaction that occurs in every aqueous
solution despite the fact that the equilibrium lies far to the left:
K = Kw = [H3O+][HO-] = 1.0 × 10-14 at 25 ˚C
where Kw stands for “equilibrium constant for water”.
Why is water not included in this equilibrium constant
expression?
Acids, Bases and Equilibria (Ka and Kb)
We define Arrhenius acids as strong or weak based on what
proportion of acid molecules “give up” H+ when dissolved in
water. This can be represented as an equilibrium reaction:
giving the equilibrium constant expression:
where Ka stands for “equilibrium constant for an acid”. Strong
acids have Ka > 1 while weak acids have Ka < 1.
Similarly, we define Arrhenius bases as strong or weak based on
what proportion of base molecules produce HO- when dissolved
in water. This can be represented as an equilibrium reaction:
giving the equilibrium constant expression:
where Kb stands for “equilibrium constant for a base”. Strong
bases have Kb > 1 while weak bases have Kb < 1.
When discussing acid-base chemistry, the term “ionization
constant” is frequently used instead of “equilibrium constant”.
e.g. Write an ionization constant expression for bicarbonate as
an acid in water.
Write an ionization constant expression for bicarbonate as a
base in water.
Acids which can only give up one proton are monoprotic acids.
Those which can give up more than one are polyprotic acids.
(The terms diprotic and triprotic are often used to specify acids
which can donate two or three protons respectively.) Note that
not every hydrogen atom in a molecule is a potential proton!
e.g. Acetic acid (CH3CO2H) is a monoprotic acid. Draw its
structure, and identify the hydrogen atom which can be
donated as H+. Justify your answer.
e.g. Phosphoric acid (H3PO4) is a triprotic acid. As such, it has
three ionization constants (Ka1, Ka2 and Ka3). Write a
reaction equation and an ionization constant expression for
each of the three sequential deprotonations.
Predict the relative magnitudes of Ka1, Ka2 and Ka3. Justify your
answer.
Recall that, since each of these reactions is reversible, this set of
reactions can just as easily be written as a set of protonations
(starting with PO43-):
Here, PO43-, HPO42- and H2PO4- are acting as bases while H3O+
is acting as an acid. This is where the terms conjugate base and
conjugate acid originate. For clarity, we will focus on the first
deprotonation of H3PO4:
In the forward reaction, H3PO4 is the acid. In the reverse
reaction, H2PO4- is the base. As such, H2PO4- is the conjugate
base of H3PO4. Similarly, H3O+ is the conjugate acid of H2O.
Any pair of compounds that differ only by the presence of
one H+ is a conjugate acid-base pair. The conjugate acid will
have one more H+ than the conjugate base.
What is the conjugate acid of HPO42-?
What is the conjugate base of HPO42-?
One of the compounds in the “deprotonation of phosphoric acid”
sequence cannot have a conjugate base. Which one? Why?
Looking at the conjugate base of an acid can give us an idea of
how strong it is. Write the conjugate base for each of the six
common strong acids:
HCl + H2O →
+ H3O+
HNO3 + H2O →
+ H3O+
HBr + H2O →
+ H3O+
H2SO4 + H2O →
+ H3O+
HI + H2O →
+ H3O+
HClO4 + H2O →
+ H3O+
Note that they are all very stable anions.
A weak acid, on the other hand, will have a less stable conjugate
base. Which should be a stronger acid, HOCl or HCN?
For a conjugate acid-base pair, there is a useful mathematical
relationship between the Ka of the acid and the Kb of the base.
This stems from the fact that each produces the other when
reacted with water.
e.g. CH3CO2H and CH3CO2- are a conjugate acid-base pair:
This means that any acid with a large Ka will have a conjugate
base with a small Kb. In other words, the stronger the acid, the
weaker its conjugate base. A classic example is hydrochloric
acid (HCl), a strong acid whose conjugate base (Cl-) is so weak
that it rarely acts as a base (never in water!).
Similarly, any base with a large Kb will have a conjugate acid
with a small Ka.
e.g. The Ka and Kb of water are both 1.0 × 10-14 at 25 ˚C.
Calculate the Ka of H3O+ and the Kb of OH- at 25 ˚C.
Any acid whose Ka is greater than that of H3O+ is a strong acid
in water. Any base whose Kb is greater than that of OH- is a
strong base in water. This is a symptom of solvent leveling.
In practice, no acid can act as a stronger acid than the conjugate
acid of the solvent in which it is dissolved.
e.g. HCl no longer exists in aqueous solution – it is completely
converted to H3O+ and Cl-. Similarly, an aqueous solution
of HI contains no HI – only H3O+ and I-. Despite the fact
that HI is nominally 10,000 times more acidic than HCl, the
two solutions will have the same acidity because they are
both solutions in which the active acid is H3O+.
By the same logic, no base can act as a stronger base than the
conjugate base of the solvent in which it is dissolved (hydroxide
for aqueous solutions).
The following page lists ionization constants for several
common acids and bases. Several of them should be familiar
from your background in nomenclature. You will need to learn
any strong acids and strong bases that you don’t already know.
You should also recognize whether the other compounds listed
are acids, bases or both. Finally, note the following trends:
1. The metal hydroxides are not the only strong bases – just
the most common ones. Add sulfide, ethoxide, amide and
hydride to your list of strong bases!
2. The conjugate base of a multiprotic acid is also an acid –
but much weaker. Its Ka is typically 100,000 times smaller.
This means that H2SO4 is a strong acid but HSO4- is not.
3. Hydrated metal ions such as [Fe(OH2)6]3+ are acidic.
4. As a general rule, anions are basic (or amphiprotic).
Anions with no hydrogen atoms can’t be acids – they have
no H+ to donate!
5. Compounds containing a -CO2H group are acids
(carboxylic acids, to be precise). The second oxygen atom
is necessary for acidity. Alcohols (-COH) are not acidic.
Ionization Constants for Some Acids and their Conjugate Bases
Acid Name
Hydriodic acid
Acid
Ka
HI
Conj. Base
~ 10
11
Br
I
–
Base Name
very small
iodide ion
Hydrobromic acid
HBr
~ 10
9
very small
bromide ion
Perchloric acid
HClO4
~ 10
7
ClO4
very small
perchlorate ion
Cl
–
very small
chloride ion
ClO3
very small
chlorate ion
very small
hydrogen sutfate ion
very small
nitrate ion
Hydrochloric acid
HCl
~ 10
7
Chloric acid
HClO3
~ 10
3
2
Sulfuric acid
H2SO4
~ 10
Nitric acid
HNO3
~ 20
+
–
Kb
–
–
HSO4
NO3
Hydronium ion
H3O
Urea acidium ion
(NH2)CONH3
6.6 X 10
Iodic acid
HIO3
1.6 X 10
1.0
+
9.1 X 10
[Fe(OH)(H2O)5]
ClCH2CO2
F
Nitrous acid
HNO2
4.5 X 10
Formic acid
HCO2H
1.8 X 10
Benzoic acid
C6H5CO2H
6.5 X 10
NO2
HCO2
–5
C6H5CO2
C2O
N3
1.9 X 10
[Al(OH)(H2O)5]
C5H5N
–7
HCO
–
3
–7
[Cu(OH)(H2O)5]
–8
HS
4.2 X 10
1.6 X 10
9.1 X 10
–
Hypochlorous acid
HClO
Hexaaqualead(II) ion
[Pb(H2O)6]
HPO4
SO3
2+
Hexaaquacobalt(II) ion
[Co(H2O)6]
Boric acid
B(OH)3(H2O)
Ammonium ion
NH4
+
5.6 X 10
Hydrocyanic acid
HCN
4.0 X 10
Hexaaquairon(II) ion
[Fe(H2O)6]
Hydrogen carbonate ion
HCO3
Hexaaquanickel(II) ion
[Ni(H2O)6]
2+
–
2–
2+
B(OH)4
hydrogen sulfide ion
–7
hydrogen phosphate ion
–7
sulfite ion
–7
hypochlorite ion
–7
pentaaquahydroxolead(II) ion
–6
–
pentaaquahydroxocoba[t(II) ion
–5
tetrahydroxo borate ion
–5
ammonia
–5
cyanide ion
–5
pentaaquahydroxoiron(II) ion
–4
carbonate ion
–4
pentaaquahydroxonickel(II) ion
–2
6.7 X 10
7.7 X 10
1.4 X 10
–10
NH3
1.8 X 10
–10
CN
–
2.5 X 10
–10
[Fe(OH)(H2O)5]
4.8 X 10
–11
CO3
2.5 X 10
–11
[Ni(OH)(H2O)5]
PO
OH
3.2 X 10
HPO4
3.6 X 10
H2O
1.0 X 10
–14
–
–19
C2H5OH
+
2–
2.8 X 10
phosphate ion
1.0
hydroxide ion
S
C2H5O
1 X 10
–
very small
NH
H2
very small
H
–
4.0 X 10
–
very small
NH3
+
3–
4
1 X 10
Hydrogen
3.1 X 10
2.1 X 10
2–
Ammonia
+
pentaaquahydroxocopper(II) ion
–7
2.9 X 10
+
[Co(OH)(H2O)5]
Water
HS
–
–10
Hydrogen phosphate ion
Ethanol
hydrogen carbonate ion
–8
6.25 X 10
1.6 X 10
–9
–13
Hydrogen sulfide ion*
pyridine
–8
1.6 X 10
–2
[Pb(OH)(H2O)5]
7.3 X 10
+
2–
ClO
1.3 X 10
pentaaquahydroxoaluminum ion
–9
1.3 X 10
2.4 X 10
–8
1.5 X 10
propanoate ion
–9
1.8 X 10
–8
3.5 X 10
2+
acetate ion
–10
1.1 X 10
–8
6.2 X 10
2+
–
–8
6.2 X 10
azide ion
–10
7.7 X 10
–6
5.6 X 10
oxalate ion
–10
5.6 X 10
–
–6
7.9 X 10
benzoate ion
5.3 X 10
–
formate ion
–10
2.9 X 10
–
CH3CH2CO2
1.3 X 10
–11
–10
1.6 X 10
2–
4
CH3CO2
1.8 X 10
CH3CH2CO2H
H2PO
5.6 X l10
–5
CH3CO2H
Propanoic acid
HSO3
2.2 X 10
–5
Acetic acid
Hydrogen sulfite ion
–
–
–5
6.3 X 10
HN3
7.1 X 10
–
–5
HC2O
–
1.6 X 10
1.4 X 10
–4
Hydrazoic
2+
–
–4
Hydrogen oxalate ion
Dihydrogen phosphate ion
1.3 X 10
–4
1.4 X 10
–
4
–
4
–3
7.2 X 10
H2S
6.7 X 10
H2PO
ClCH2CO2H
Hydrogen sulfide
1.7 X 10
–
–3
6.3 X 10
HF
2+
–
4
–3
Hydrofluoric acid
H2CO3
nitrite ion
–
Chloroacetic acid
[Cu(H2O)6]
fluoride ion
–11
8.3 X 10
ClO2
7.5 X 10
Hexaaquacopper(II) ion
chloroacetate ion
–11
SO
–2
1.1 X 10
Carbonic acid
pentaaquahydroxoiron(III) ion
–12
2–
4
1.2 X 10
+
dihydrogen phosphate ion
–12
–2
HClO2
[Al(H2O)6]
chlorite ion
–12
HSO3
HSO4
C5H5NH
sulfate ion
–13
HC2O
Chlorous acid
Pyridinium ion
hydrogen sulfite ion
–13
6.3 X 10
–2
Hydrogen sulfate ion
Hexaaquaaluminum ion
–
–2
–
3+
hydrogen oxalate ion
–13
IO3
1.5 X 10
–
4
iodate ion
–13
–1
5.9 X 10
3+
urea
–14
1.0 X 10
1.5 X 10
H2SO3
H3PO4
water
–14
H2O
H2C2O4
[Fe(H2O)6]
–14
(NH2)2CO
Sulfurous acid
Hexaaquairon(III) ion
–
–1
Oxalic acid
Phosphoric acid
–
–
2
5
sulfide ion
large
ethoxide ion
large
amide ion
large
hydride ion
pH, pOH, pKw, pKa and pKb
Recall that pH is a measure of the concentration of protons (or
solvated protons like H3O+) in a solution:
pH = –log[H+] = –log[H3O+]
Similarly, we used pOH to report the concentration of hydroxide
ions in an aqueous solution:
pOH = –log[OH-]
We can calculate pKw, pKa and pKb in the same way:
pKw = –logKw
pKa = –logKa
pKb = –logKb
For any aqueous solution, pH + pOH = pKw. At 25 ˚C, this is 14.
Note that, because pH, pOH, pKa, etc. use a logarithmic scale,
each unit of measurement represents an order of magnitude. In
other words, a solution with a pH of 0 is 1000 times more acidic
than a solution with a pH of 3. Also note that it is possible to
have negative values for pH, pOH, pKa, etc.
Give an example of an acidic solution with a negative pH.
Give an example of a basic solution with a negative pOH.
Recall that, when you take the logarithm of “x”, any numbers
before the decimal indicate the exponent from writing “x” in
scientific notation. The numbers after the decimal indicate the
significant figures. As such, the number of decimal places in a
pH should be the same as the number of significant figures in
the initial [H+]. When doing the inverse calculation, the number
of significant figures in [H+] should be the same as the number
of decimal places in the pH.
e.g. [Cu(OH2)5(OH)]+ has a Kb of 6.25 × 10-8. What is its pKb?
e.g. Acetic acid has a pKa of 4.74. What is its Ka?
e.g. Milk of magnesia is an aqueous solution with a pH of 10.5.
(a) What is the hydronium ion concentration of this solution?
(b) What is the hydroxide ion concentration of this solution?
(c) Is this solution acidic or basic?
e.g. Methylamine (CH3NH2) is a weak base. If the pH of a
0.065 M solution of methylamine is 11.70, what is its Kb?
e.g. In a 0.20 M aqueous solution of acetic acid, what are the
equilibrium concentrations of H3O+, CH3CO2H, and
CH3CO2-? What is the pH?
The Method of Iterative Approximation
When working with weak acid-base equilibria, using an iterative
approach can be easier than solving a quadratic or higher-order
polynomial. In this approach, we assume that x is so small that
it is safe to use x = 0 as an approximation. We can only do this
because we know that Ka or Kb is small so the amount of
reactants consumed will be negligible – or close to it.
(This approach can be applied to other equilibrium problems
but only if K is small.)
For the problem on the previous page, we arrived at:
1.8 × 10-5 =
x2 .
0.20 - x
which we then rearranged to a quadratic expression and used the
quadratic formula to solve for x.
Instead, we could have assumed that 0.20 – x = 0.20, giving:
1.8 × 10-5 = x2 .
0.20
Therefore,
x2 = 3.6 × 10-6
Therefore,
x = 1.9 × 10-3
When using this method, we must always check our answer by
plugging it back into the original equation and confirming that
we get an equivalent answer (to as many sig. fig. as we should
have).
1.8 × 10-5 =
x2
.
-3
0.20 – (1.9 × 10 )
Therefore,
x2 = 3.6 × 10-6
Therefore,
x = 1.9 × 10-3
***Use all the digits in your calculator to prevent rounding
error!!!***
e.g. Use the method of iterative approximation to calculate the
pH and the percent dissociation of 0.0046 M HF(aq).
e.g. Calculate the concentrations of all species present in a
0.0250 M aqueous solution of phosphoric acid.
Acid-Base Reactions
As we have seen, the reaction between an acid and a base
produces a conjugate base and a conjugate acid. Technically, all
acid-base reactions are equilibrium reactions. We can predict
the direction in which the equilibrium lies by comparing the
strength of the reactants and the products. The stronger acid and
stronger base will react more readily than the weaker acid and
weaker base. As such, the equilibrium will lie on the side with
the weaker acid and weaker base.
e.g. HNO3(aq) +
H2O(l)
NH3(aq) +
H2O(l)
NO3-(aq) + H3O+(aq)
NH4+(aq) + OH-(aq)
Reacting a Strong Acid with a Strong Base
By definition, strong acids and strong bases are fully ionized in
solution. If we mix HCl(aq) and NaOH(aq), we get a mixture of
water, sodium ions and chloride ions:
The net ionic equation is:
As we saw in Chemistry 1000, this is the net ionic equation for
any aqueous strong acid-strong base reaction. This type of
reaction is sometimes called a neutralization reaction because
the product is a neutral aqueous solution.
***When predicting the pH of a salt solution, look at the ions.
Conjugate bases of strong acids are neutral; other anions are
basic. Conjugate acids of strong bases are neutral; other
cations are acidic.***
Reacting a Weak Acid with a Strong Base
Consider the reaction between acetic acid (CH3CO2H) and
sodium hydroxide (fully dissociated to Na+ and OH-):
CH3CO2H(aq) + OH-(aq)
CH3CO2-(aq) + H2O(l)
______________ is a much stronger acid than ________, and
______________ is a much stronger base than ____________.
The equilibrium lies far to the right, and the reaction can be
considered to essentially go to completion. To calculate exactly
how close to completion, we use Ka for acetic acid and Kw:
CH3CO2H + H2O
CH3CO2- + H3O+
+
2 H 2O
H 3O + + OH -
CH3CO2H + OH-
Ka = 1.8 x 10-5
1/Kw = 1.0 x 1014
CH3CO2- + H2O
Knet = (Ka) x (1/Kw)
Knet = 1.8 x 109
The product of a weak acid-strong base reaction is a basic salt
solution. In this case, the salt is sodium acetate (which
dissociates to the neutral sodium ion and the basic acetate ion).
Reacting a Strong Acid with a Weak Base
Consider the reaction between hydrochloric acid (fully reacted
with water to give H3O+ and Cl-) and ammonia:
H3O+(aq) + NH3(aq)
H2O(l) + NH4+(aq)
______________ is a much stronger acid than ________, and
______________ is a much stronger base than ____________.
The equilibrium lies far to the right, and the reaction can be
considered to essentially go to completion. To calculate exactly
how close to completion, we use Kb for ammonia and Kw:
NH3 + H2O
+
NH4+ + OH-
H3O+ + OH-
2 H 2O
NH3 + H3O+
NH4+ + H2O
Kb = 1.8 x 10-5
1/Kw = 1.0 x 1014
Knet = (Kb) x (1/Kw)
Knet = 1.8 x 109
The product of a strong acid-weak base reaction is an acidic salt
solution. In this case, the salt is ammonium chloride (dissociates
to the acidic ammonium ion and the neutral chloride ion).
Reacting a Weak Acid with a Weak Base
Consider the reaction between acetic acid and ammonia:
CH3CO2H(aq) + NH3(aq)
CH3CO2-(aq) + NH4+(aq)
Here, it is not so easy to predict the direction of reaction just by
looking at the reaction. Acetic acid is a stronger acid than
ammonium, but ammonia is a stronger base than acetate. To
find whether the reaction is product- or reactant-favoured:
CH3CO2H + H2O
NH3 + H2O
+
H3O+ + OH-
CH3CO2H + NH3
CH3CO2- + H3O+
NH4+ + OH2 H 2O
CH3CO2- + NH4+
Ka = 1.8 x 10-5
Kb = 1.8 x 10-5
1/Kw = 1.0 x 1014
Knet = Ka x Kb x (1/Kw)
Knet = 3.2 x 104
Thus, this particular weak acid-weak base reaction is ________favoured. While true for this example, this is not a general rule.
In summary:
acid
base
strong strong
strong
weak
weak
strong
weak
weak
complete reaction?
salt solution
yes
neutral
yes
acidic
yes
basic
depends on Ka and Kb depends on Ka and Kb
Calculate the pH of a solution prepared by mixing 25.00 mL of
0.0385 M hypochlorous acid with 10.00 mL of 0.0247 M
potassium hydroxide.
Important Concepts from Chapter 17
• definitions of acids and bases (Lewis, Brønsted and Arrhenius)
• conjugate acid-base pairs
• ionization constants (Ka, Kb, Kw) and ionization constant
expressions
• pH, pOH, pKw, pKa and pKb
• factors contributing to acidity
• solvent leveling
• the strong acids and strong bases (names and formulæ)
• acid-base reactions (strong-strong, strong-weak, weak-strong,
and weak-weak)
• acidity of salt solutions
• calculations and ICE tables
• method of iterative approximation (and when it’s appropriate
to use)