Chapter 15 Worksheet 1
Bronsted-Lowry definition of acids and bases, pH scale, strong acids and bases
Arrhenius’ definition of acids and bases:
Acid: Substance that produces aqueous H + (protons) when dissolved in water.
Hydrochloric acid:
HCl(aq) → H +
(aq) + Cl
-
(aq) K eq
is large; strong acid
Acetic acid: CH
3
COOH(aq) = H + (aq) + CH
3
COO (aq) K eq
= 1.8 x 10 -5 ; weak acid
Base: Substance that produces aqueous OH when dissolved in water.
Sodium hydroxide:
NaOH(aq) → Na +
(aq) + OH
-
(aq) K eq
is large; strong base
(Notice that all metal hydroxides are Arrhenius Bases)
Bronsted-Lowry definition of acids and bases
An acid is a proton donor and a base is a proton acceptor. An acid-base reaction involves the transfer of a proton from an acid to a base. A reaction between an acid and a base always produces another acid and another base.
Consider the reaction of a generic monoprotic acid (HA) with water:
HA(aq) + H
2
O(l) = H
3
O
+
(aq) + A
-
(aq) K a
= [H
3
O
+
] eq
[A
-
] eq
/[HA] eq acid 1 base 1 acid 2 base 2
K a
is the equilibrium constant for the reaction of an acid with water. It is called the acid-ionization constant. The size of K a
is a measure of acid strength.
Often, H
+
(hydrogen ion) is used as shorthand for H
3
O
+
(hydronium ion) and acid ionization reactions are written as:
HA(aq) = H
+
(aq) + A
-
(aq)
Examples:
HCl (aq) + H
2
O (l) → H
3
O
+
(aq) + Cl
-
(aq) K a
is large; strong acid
acid 1 base 1 acid 2 base 2
CH
3
COOH (aq) + H
2
O (l) = H
3
O
+
(aq) + CH
3
COO
-
(aq) K a
= 1.8 x 10
-5
; weak acid acid 1 base 1 acid 2 base 2
1

Consider the reaction of a generic base (A ) with water
A
-
(aq) + H
2
O (l) = HA (aq) + OH
-
(aq)
K b
= [HA] eq
[OH
-
] eq
/ [A
-
] eq
K b
is the equilibrium constant for the reaction of a base with water. It called the base-ionization constant. The size of K b
is a measure of base strength.
Examples:
H
-
(aq) + H
2
O (l) → H
2
(aq) + OH
-
(aq) K b is large, strong base base 1 acid 1 acid 2 base 2
NH
3
(aq) + H
2
O(l) = NH
4
+
(aq) + OH
-
(aq) K b
= 1.8 x 10
-5
; weak base
base 1 acid 1 acid 2 base 2
Notice that water can act as an acid or a base! Substances of this type are called “amphiprotic” or
“ amphoteric” .
Of course, any acid can react with any base. For example:
CH
3
COOH(aq) + NH
3
(aq) = NH
4
+
(aq) + CH
3
COO
-
(aq)
acid 1 base 1 acid 2 base 2
In every acid-base reaction, the position of the equilibrium favors transfer of the proton from the stronger acid to the stronger base.
An acid and base that differ only in the presence or absence of a proton are called a conjugate acid-base pair.
2

1. Complete the table and circle all amphiprotic substances:
Note: Amphiprotic substances are in colored italic s. HSO
4
is not amphoteric because is not really a base. OH is not amphoteric because it is not really an acid. Notice that amphoteric substances are conjugate bases of polyprotic weak acids.
Acid strength
Conjugate acid
HCl
H
2
SO
4
HNO
3
K a
∞
∞
~20
Conjugate base
Cl -
HSO
4
-
NO
3
-
K b
0
0
~5 x 10 -16
Base strength
H
3
O +
1.0
H
2
O 1.0 x 10 -14
HSO
4
-
HF
1.2 x 10 -2
7.2 x 10 -4
SO
4
2-
H
3
PO
4
7.5 x 10 -3 H
2
PO
4
-
F -
8.3 x 10 -13
1.3 x 10 -12
1.4 x 10 -11
CH
3
COOH 1.8 x 10 -5 CH
3
COO
-
5.5 x 10 -10
H
2
CO
3
4.2 x 10 -7 HCO
3
2.4 x 10 -8
-7
H
2
PO
4
-
6.2 x 10 -8 HPO
4
21.6 x 10
NH
4
+ 5.5 x 10 -10
HCO
3
-
4.8 x 10 -11
HPO
4
2-
3.6 x 10 -13
NH
3
1.8 x 10 -5
CO
3
22.1 x 10 -4
PO
4
32.7 x 10 -2
H
2
O 1.0 x 10 -14 OH -
1.0
OH -
H
2
0
0
O 2-
H -
∞
∞
2.
What do you notice about the relative strength of an acid and its conjugate base?
As the strength of an acid gets stronger, the strength of the conjugate base gets weaker (and vice versa)
Types of acids and bases
Notice that an acid can be a cation, an anion, or have no charge. Only uncharged acids are named with the word “acid”.
There are two types of weak bases:
1. Anions that are conjugate bases of weak acids (CH
3
COO , HPO
4
2, F , etc.)
2. Uncharged molecules that contain lone pairs of electrons. Many weak bases contain nitrogen (NH
3
, amines). The proton binds through the lone pair on the nitrogen. Their conjugate acids are cations.
Notice that the conjugate base of a polyprotic acid is amphiprotic (amphoteric).
3

3.
Complete the following acid base reactions, indicate the conjugate acid-base pairs, and state whether the reaction has a large or small equilibrium constant.
Note: conjugate acid-base pairs are color coded a.
CH
3
COOH (aq) + NH
3
(aq) = CH
3
COO (aq) + NH
4
+ (aq)
The reactants are the stronger acid and base so K eq
is very large!
b.
H
2
CO
3
(aq) + NO
3
(aq) = HCO
3
(aq) + HNO
3
(aq)
The products are the stronger acid and base so K eq
is very small! c.
H
2
CO
3
(aq) + H
2
O (l) = HCO
3
(aq) + H
3
O + (aq) K eq
= K a
for H
2
CO
3
= 4.2 x 10 -7
The products are the stronger acid and base so K eq
is very small! d.
HCO
3
(aq) + H
2
O (l) = CO
3
2 (aq) + H
3
O + (aq)
OR
HCO
3
(aq) + H
2
O (l) = H
2
CO
3
(aq) + OH - (aq)
K eq
= K a
for HCO
3
= 4.8 x 10 -11
K eq
= K b
for HCO
3
= 2.4 x 10 -8
Both reactions have small equilibrium constants? Which reaction occurs more readily? Will the solution be acidic or basic? HCO
3
is a much stronger base than it is an acid so the second reaction will predominate and the solution will be basic. e.
NH
3
(aq) + H
2
O (l) = NH
4
+ (aq) + OH - (aq) K eq
= K b
for NH
3
= 1.8 x 10 --5
The products are the stronger acid and base so K eq
is very small!
4.
a. The equilibrium constant for which of the above reactions is an example of either a K a
(acid ionization constant) or a K b
(base ionization constant)?
The reactions of an acid or base with water (c,d,e) a.
Write the balanced equation for the reaction whose equilibrium constant is the K a
for phosphoric acid.
H
3
PO
4
(aq) + H
2
O (l) = H
2
PO
4
(aq) + H
3
O + (aq) b.
Write the balanced equation for the reaction whose equilibrium constant is the K b
for the dihydrogen phosphate ion.
H
2
PO
4
(aq) + H
2
O (l) = H
3
PO
4
(aq) + OH - (aq)
4

Autoionization (dissociation) of water and the pH scale:
H
2
O(l) + H
2
O(l) = H
3
O
+
(aq) + OH
-
(aq) [also written as: H
2
O(l) = H
+
(aq) + OH
-
(aq)]
K w
= [H
3
O + ] eq
[OH ] eq
= 1.0 x 10 -14 (at 25 o C) MEMORIZE THIS!!
K w
is called the “ionization constant” or “ ion-product constant” for water
For ANY solution, if you know the concentration of either the hydrogen ion or the hydroxide ion then you know the concentration of the other! They are ALWAYS related by the equation above! pH = -log[H
3
O + ] pOH = -log[OH ] MEMORIZE THIS!!
Taking the negative log of both sides of the K w
expression gives: pH + pOH = 14 MEMORIZE THIS!!
In pure water at 25 o C:
[H
3
O + ] = [OH ] = 10 -7
Thus, pH = 7
If [H
3
O + ] >[OH ], then pH < 7 and the solution is acidic
If [H
3
O + ] <[OH ], then pH > 7 and the solution is basic
If [H
3
O + ] =[OH ], then pH = 7 and the solution is neutral
5.
Complete the table (red numbers were given):
[H
3
O
+
] (M) pH pOH [OH
-
] (M) Acidic or
Basic?
3.2 x 10 -8 7.49 6.51 3.1 x 10 -7 Basic
6.3 x 10 -5
3.2 x 10 -9
4.20
8.50
9.80
5.50
1.6 x 10
3.2 x 10
-10
-6
Acidic
Basic
1.3 x 10 -13 12.89 1.11 7.8 x 10 -2 Basic
5

Strong acids and bases
According to the Bronsted-Lowry definition, the reactions of strong acids and bases with water go to completion (very large equilibrium constants).
Some common strong acids (MEMORIZE THESE!!):
Hydrochloric Acid HCl
Hydrobromic Acid HBr
Hydroiodic Acid HI
(HF is a weak acid; we’ll disuss this later)
Chloric Acid HClO
3
Perchloric Acid
Nitric Acid
HClO
4
HNO
3
Sulfuric Acid H
2
SO
Moderately strong acid:
4
(Only first ionization goes to completion)
Hydronium ion H
3
O +
Some common strong bases:
Hydride ion
Oxide ion
H -
O 2-
Moderately strong base:
Hydroxide ion OH -
Note: According to the Arrhenius definition of a base, soluble metal hydroxides (NaOH, KOH, etc.) are classified as strong bases since they are strong electrolytes. According to the Bronsted-Lowry definition, they are not bases at all! It is the resulting OH ion that is the base and it is only a moderately strong base.
6. Consider what happens when the strong acid, nitric acid (HNO
3
), reacts with water.
a.
Write the balanced equation for the ionization reaction . (There are two ways to write it.)
HNO
3
(l) + H
2
O (l) → NO
3
(aq) + H
3
O + (aq)
Shorthand version: HNO
3
(l) → NO
3
(aq) + H + (aq) b.
Write the two expressions for K a
.
K a
=
[ NO
3

][ H
3
O

]
[ HNO
3
]
K a
=
[ NO
3

][ H

]
[ HNO
3
]
6

c.
What can we say about the size of K a
for this reaction?
Very large (essentially infinite). Strong acids dissociate completely in water. d.
What is the pH of a 3.25 x 10
-3
M solution of nitric acid?
Since the reaction goes to completion and the stoichiometry is 1:1 . . .
[H
3
O + ] = 3.25 mM = 3.25 x 10 -3 M pH = -log(3.25 x 10 -3 )= 2.488
Note: For a log, only the digits after the decimal place are significant. The whole numbers only tell you where the decimal point was in the original number. Since the original number had 3 sig. figs., then so must the log. 2.488 has 3 sig figs. The 2 is not significant. e.
What is the concentration of nitric acid if the pH is 1.5?
[H
3
O + ] = 10 -1.5
= 3 x 10 -2 M (one sig fig)
7

7. Consider what happens when Ca(OH)
2,
dissolves in water. a.
Write the balanced equation for the reaction.
Ca(OH)
2
(s) → Ca 2+ (aq) + 2 OH (aq)
So where is the reaction with water? The dissociation of calcium hydroxide (an ionic compound) produces the base OH which subsequently reacts with water:
OH (aq) + H
2
O (l) = H
2
O (l) + OH - (aq) b.
What can we say about the size of the equilibrium constant for this reaction?
The dissociation reaction has a very large equilibrium constant. The subsequent base ionization reaction has an equilibrium constant of 1! Do you see why? c.
What is the [OH
-
] in a 3.25 mM solution of calcium hydroxide? pOH?
To calculate the [OH
-
] we only need to consider the dissociation of calcium hydroxide because the subsequent reaction does not change the hydroxide ion concentration.
Since the reaction goes to completion:
[OH ] = 2 [Ca(OH)
2
] o
= 2(3.25 mM) = 6.50 mM pOH = -log (6.50 x 10 -3 ) = 2.187 d.
What is the [H
+
] in the above solution? pH?
[H
3
O + ] = 1.0 x 10 -14 / 6.50 x 10 -3 = 1.54 x 10 -12 M pH = -log(1.54 x 10 -12 )= 11.813 or pH = 14.000 – 2.187 = 11.813 e.
What is the concentration of a calcium hydroxide solution with pH = 9.25? pOH = 14.00 – 9.25 = 4.75
[OH ] = 10 -4.75
= 1.8 x 10 -5 M
[Ca(OH)
2
] = ½ [OH ] = 9.0 x 10 -6 M
8