Chapter 16
Acid - Base Equilibria
Acids and Bases: Definitions
CHEMISTRY
T HE C ENTRAL S CIENCE
Arrhenius Definition of Acids and Bases
Acids are substances which increase the concentration of H+ ions
when dissolved in water.
Chapter 16
Acid - Base Equilibria
• An acid is a substance that produces H+ when dissolved in
water.
Professor Angelo R. Rossi
Department of Chemistry
Bases are substances which increase the concentration of OHions when dissolved in water.
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• A base is a substance that produces OH- when dissolved in
water
But the Arrhenius definition of acids and bases is the limited to
water solutions
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Chapter 16
Acid - Base Equilibria
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Chapter 16
2
Acid - Base Equilibria
Brønsted-Lowry Acids and Bases
Brønsted-Lowry Acids and Bases
Brønsted-Lowry Definition of Acids and Bases
Proton - Transfer Reactions
The basic concept is that acid-base reactions involve the transfer of
H+ ions from one substance to another.
When HCl dissolves in water, the following reaction occurs:
HCl (g) + H2 O (l)
This involves a more general definition of acids and bases.
+
We see that the HCl molecule actually transfers a H+ ion to a water
molecule.
The H Ion in Water
The H+ ion interacts with H2 O by attaching itself to one of the lone
pairs surrounding the O atom to yield H3 O+ (aq).
+
H2 O (l) + H (aq)
Definitions
A Brønsted-Lowry acid is a molecule or ion that can donate a
proton to another molecule or ion.
−→ H3 O+ (aq)
A Brønsted-Lowry base is a molecule or ion that can accept a
proton from another molecule or ion.
• Chemists often use H+ (aq) for simplicity and convenience when
+
in fact, the more realistic structure is H3 O .
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⇌ H3 O+ (aq) + Cl− (aq)
3
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Chapter 16
Acid - Base Equilibria
Chapter 16
Acid - Base Equilibria
Brønsted-Lowry Acids and Bases
Conjugate Acid-Base Pairs
Using Acid-Base Definitions
Acid-Base Conjugate Pairs are two species that differ by a proton.
Every acid has a conjugate base formed by removing H+ from the acid.
Consider the following reaction:
NH3 (aq) + H2 O (l)
A conjugate acid is the species that contains the proton that is transferred.
Every base has a conjugate acid formed by adding H+ to the base.
⇌ NH4 (aq) + OH (aq)
+
−
A conjugate base is the species formed by loss of the proton.
• NH3 is an Arrhenius base because it leads to an increase in
OH− ions in water.
HNO2 (aq) + H2 O (l)
acid
• NH3 is an Brønsted-Lowry base because it accepts a proton
• To be a Brønsted-Lowry base, a molecule or ion must have a
nonbonding pair of electrons that can be used to bind to the H+
ion.
Chapter 16
base
HCl
H2 SO4
HSO4 −
NH4 +
H3 O+
H2 O
Cl−
HSO4 −
SO4 2−
NH3
H2 O
OH−
acid
⇌ NH4 + (aq) + OH− (aq)
acid
base
H2 O/H3 O+ and H2 O/OH− are also conjugate acid-base pairs.
5
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Chapter 16
Acid - Base Equilibria
Relative Strengths of Acids and Bases
Examples of Conjugate Acid-Base Pairs
Conjugate Base
acid
NH4 + /NH3 is called a conjugate acid-base pair because they differ only in the
presence or absence of a proton.
Acid - Base Equilibria
Conjugate Acid
base
NH3 (aq) + H2 O (l)
Substances which can act as either a Brønsted-Lowry base or
acid are called amphoteric.
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⇌ NO2 − (aq) + H3 O+ (aq)
HNO2 /NO2 − is called a conjugate acid-base pair because they differ only in the
presence or absence of a proton.
from H2 O.
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base
The stronger a conjugate acid −→ the weaker its conjugate base
The stronger a conjugate base −→ the weaker its conjugate acid.
The position of the equilibrium in every acid-base reaction favors the transfer of
the proton to the stronger base:
HC2 H3 O2 (aq) + H2 O (l)
↼
⇁
H3 O
+
(aq) + C2 H3 O2
−
(aq)
With the above comments, it is possible to group acids and bases into three broad
categories based on their interaction with H2 O:
1. Strong Acids completely transfer protons to water leaving no
undissociated molecules in solution.
H2 O is amphoteric and acts both as an acid and as a base.
2. Weak Acids only partly dissociate in aqueous solution and exist as a
mixture of undissociated molecules and ions from dissociated molecules.
3. Substances with negligible acidity which contain H but do not demonstrate
any acidic behavior.
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Chapter 16
Acid - Base Equilibria
Chapter 16
Acid - Base Equilibria
The Autoionization of Water
The Ion Product of Water
One molecule of H2 O can donate a proton to another H2 O molecule:
Because the autoionization of H2 O is an equilibrium process, it can
be written as an equilibrium constant expression:
H2 O (l) + H2 O (l)
⇌ H3 O+ (aq) + OH− (aq)
Kw
and this process is called the autoionization of water.
Although only about 2 out of every 109 H2 O molecules are ionized at
room temperature, the autoionization process is very important.
= [H3 O+ ][OH− ] = 1.0 x 10−14 at 25◦ C
The following equilibrium for the dissociation of H2 O is used very
frequently:
+
−
H2 O (l) ⇌ H (aq) + OH (aq)
The following equilibrium expression can be written for the ion
product of water:
Kw
= [H+ ][OH− ] = 1.0 x 10−14 at 25◦ C
The above equation is valid for any dilute aqueous solution.
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Chapter 16
9
Acid - Base Equilibria
Neutral, Acidic, and Basic Solutions
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Chapter 16
Acid - Base Equilibria
The pH Scale
Since the molar concentration of [H+ ] is very small, it can be
expressed in terms of pH which is given as
• If [H+ ] = [OH− ], the solution is neutral.
• If [H+ ] > [OH− ], the solution is acidic.
+
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pH
−
• If [H ] < [OH ], the solution is basic.
For a neutral solution, [H+ ]
= -log[H+ ]
= [OH− ].
[H+ ][OH− ] = [H+ ]2 = 1.0 x 10−14
[H+ ] = 1 x 10−7 ;
Solution Type
Acidic
Neutral
Basic
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[H+ ]M
−7
> 1.0 x 10
= 1.0 x 10−7
< 1.0 x 10−7
pH
=7
[OH− ]M
< 1.0 x 10−7
= 1.0 x 10−7
> 1.0 x 10−7
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pH value
< 7.00
= 7.00
> 7.00
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Chapter 16
Acid - Base Equilibria
The pOH Scale
Chapter 16
Acid - Base Equilibria
Relation Between pH and pOH
−
The negative log can also be used to express the OH
concentration:
−
pOH = -log[OH ]
Taking the negative log of both sides of the equation
[H+ ][OH− ] = 1.0 x 10−14 = Kw
yields
+
-log[H ]
| {z }
pH
+ -log[OH− ] = 14
| {z }
pOH
pH + pOH
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= 14
pH + pOH
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Chapter 16
13
Acid - Base Equilibria
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= 14
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Chapter 16
14
Acid - Base Equilibria
The pH Scale
The pH Scale
Measuring pH with pH Meter
Measuring pH - Acid-Base Indicators
A pH Meter measures voltage by placing two electrodes into a solution. The
voltage varies as pH.
Acid-Base Indicators are usually dyes which are themselves weak
acids and change color depending on whether they are in acidic or
basic solution. This property enables them to be used to measure
pH.
An acid-base indicator is also a base which changes color
depending on whether the acid form (HIn) or base form (In− ) is the
predominant species in solution.
HIn (aq)
⇌ H+ (aq) + In− (aq)
Ka
=
[H+ ][In− ]
[HIn]
Ka
[In− ]
= +
[HIn] [H ]
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Chapter 16
Acid - Base Equilibria
Chapter 16
Acid - Base Equilibria
Some Common Acid-Base Indicators
Strong Acids
The pH ranges for the color changes of some common acid-base indicators are
given in the figure below:
Strong acids are strong electrolytes and exist is solution entirely as
ions.
The seven most common strong acids include the following:
• HCl, HBr, HI, HNO3 , HClO3 , HClO4 , and H2 SO4 .
The typical behavior of a strong acid can be illustrated by the
following:
HNO3 (aq) + H2 O (l)
→ NO3 − (aq) + H3 O+ (aq)
Note that equilibrium arrows were not used in the above equation
because it lies completely to the right.
For example, a 0.20 M HNO3 produces
+
[H ]
= [NO3 − ] = 0.20M
Most indicators have a useful range of about 2 pH units.
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Chapter 16
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Acid - Base Equilibria
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Chapter 16
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Acid - Base Equilibria
Weak Acids
Strong Bases
Weak acids are only partially ionized in aqueous solution.
Strong bases are strong electrolytes and exist is solution entirely
as ions.
If a general weak acid is represented by HA, the reaction for its ionization can be
expressed in the following ways:
The most common soluble strong bases include
HA (aq) + H2 O (l)
• Hydroxides of the Group 1A alkali metals (e.g. NaOH, KOH).
• Hydroxides of the Group 2A alkaline earth metals (e.g.
or
HA (aq)
Ca(OH)2 ).
⇌ H+ (aq) + A− (aq)
An equilibrium constant can be used for weak acids to indicate the extent to which
it ionizes.
[H+ ][A− ]
Ka =
[HA]
For example, a 0.20 M NaOH produces
[Na+ ]
⇌ H3 O+ (aq) + A− (aq)
= [OH− ] = 0.20M.
• Ka is called the acid-dissociation constant and indicates the ionization
constant for the dissociation of a weak acid.
• The magnitude of Ka provides a measure of the relative tendency of a weak
acid to ionize in water: the larger the value of Ka , the stronger the acid.
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Chapter 16
Acid - Base Equilibria
Chapter 16
Acid - Base Equilibria
Percent Ionization vs Concentration of Weak Acids
Strong acids are better conductors of electricity than weak acids.
The percent ionization of a weak acid decreases as the concentration of the acid
increases as shown below:
Percent Ionization
Conductivity of Strong and Weak Acids
5
4
3
2
1
0
0
0.05
0.10
0.15
Acid Concentration (M)
• The [H+ ] is only a small fraction of the weak acid that is dissolved in solution.
• The percent ionization of weak acid at a particular temperature depends on
both the identity of the acid and its concentration.
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Chapter 16
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Chapter 16
Acid - Base Equilibria
Weak Acids: Example of Percent Ionization
Weak Acids: Example of Calculating Ka from pH
A 0.020 M solution of niacin (one of the B vitamins) has a pH of 3.26
(b) What is the acid-dissociation-constant, Ka , for niacin?
(a) What percentage of the acid is ionized in this solution?
C5 H4 N-COOH (aq)
C5 H4 N-COOH (aq) ⇌ H+ (aq) + C5 H4 N-COO− (aq)
⇌ H (aq) + C5 H4 N-COO (aq)
−
+
[H+ ][C5 H4 N-COO− ]
Ka =
[C5 H4 N-COOH]
pH
+
[H ]
percent ionization
Spring Semester
=
= -log[H+ ] = 3.26;
−3.26
= 10
0.74
= 10
[H+ ]
initial conc. C5 H4 N-COOH
+
[H ]
· 10
−4
Initial
Change
Equilibrium
= 10−3.26
C5 H4 N-COOH (aq)
0.020 M
-5.50 x 10−4 M
(0.020 - 5.50 x 10−4 ) M
Ka
−4
= 5.50 x 10
× 100 % =
5.50 x 10−4
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0.020
Ka
× 100 % = 2.8 %
23
Spring Semester
=
=
H+ (aq)
0.000 M
+5.50 x 10−4 M
5.50 x 10−4 M
C5 H4 N-COO− (aq)
0.000 M
+5.50 x 10−4 M
5.50 x 10−4 M
[H+ ][C5 H4 N-COO− ]
[C5 H4 N-COOH]
(5.50 x 10−4 )(5.50 x 10−4 )
= 1.6 x 10−5
(0.020 - 5.50 x 10−4 )
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Chapter 16
Acid - Base Equilibria
Chapter 16
Acid - Base Equilibria
Weak Acids: Example of Using Ka to Calculate pH
Polyprotic Acids
The Ka for niacin is 1.6 x 10−5 . What is the pH of a solution of a 0.010 M?
Polyprotic acids are those acids that have more than one ionizable proton. For
example, sulfurous acid (H2 SO3 ):
C5 H4 N-COOH (aq) ⇌ H+ (aq) + C5 H4 N-COO− (aq)
Initial
Change
Equilibrium
H+ (aq)
0.000 M
+xM
xM
C5 H4 N-COOH (aq)
0.010 M
-xM
(0.010 - x) M
C5 H4 N-COO− (aq)
0.000 M
+xM
xM
H2 SO3 (aq)
[H+ ][C5 H4 N-COO− ]
x2
=
= 1.6 x 10−5
[C5 H4 N-COOH]
(0.010 - x)
Assume x is negligible with respect to 0.010; this is OK, if x < 5 % of initial value.
Ka
=
0.010 -x
x2
0.010
HSO3
≃ 0.010
−
⇌ H+ (aq) + HSO3 − (aq);
Ka1
=
[H+ ][HSO3 − ]
= 1.7 x 10−2
[H2 SO3 ]
⇌ H+ (aq) + SO3 2− (aq);
Ka2
=
[H+ ][SO3 2− ]
= 6.4 x 10−8
[HSO3 − ]
(aq)
Ka2 << Ka1 : in a polyprotic acid, it is always easier to remove the first proton
than the second.
≈ 1.6 x 10−5
= [H+ ] = 4.0 x 10−4 ; pH = -log(4) + (-log(10−4 ) = 3.40
Check to make sure that x < 5% of 0.010. Yes.
x
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Chapter 16
25
Acid - Base Equilibria
Weak Bases
Kb
Kb
Spring Semester
=
Acid - Base Equilibria
These substances include ammonia (NH3 ) and a related class
of compounds called amines.
[BH+ ][OH− ]
Amines can be derived from ammonia (H-NH2 ) by taking away
a hydrogen atom and replacing it by a large organic group.
[B]
Kb is called the base-dissociation constant and refers to the equilibrium between
the base B reacting with water and the conjugate acid (BH+ ) and hydroxide ion
(OH− ).
Ammonia (NH3 ) is the most commonly encountered weak base:
NH3 (aq) + H2 O (l)
Chapter 16
26
1. Neutral molecules containing an atom with a nonbonding pair of
electrons that can serve as a proton acceptor.
⇋ BH+ (aq) + OH− (aq)
=
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Types of Weak Bases
Weak bases react with H2 O and abstract H+ to form the conjugate acid of the
base and OH− ions.
B (aq) + H2 O (l)
Spring Semester
Thus, methylamine (CH3 - NH2 ) is formed by replacing one H
atom with a methyl group (CH3 )
⇋ NH4 + (aq) + OH− (aq)
[NH4 + ][OH− ]
[NH3 ]
= 1.8 x 10−5
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Chapter 16
Acid - Base Equilibria
Types of Weak Bases
Chapter 16
Acid - Base Equilibria
Example Problem Involving Weak Base Calculation
A solution of NH3 in H2 O has a pH of 10.50. What is the molarity of the solution?
2. Anions of weak acids are also weak bases.
NH3 (aq) + H2 O (l)
Consider sodium fluoride (NaF) or sodium hypochlorite (NaClO).
Both of these ionic compounds are strong electrolytes and
dissolve completely in H2 O to yield Na+ , F− and Na+ , ClO− ,
respectively.
pOH = 14.00 - pH = 14.00 - 10.50 = 3.50
pOH
No reaction occurs for Na+ in H2 O.
= -log[OH− ]; [OH− ] = 10−3.50 = 100.50 · 10−4 = 3.16 x 10−4
The same amount of hydroxide and ammonium ions are formed:
However, both F− and ClO− are anions of weak acids and will
act as weak bases in water:
−
⇋ HClO (aq) + OH− (aq)
−
⇋ HF (aq) + OH− (aq)
ClO (aq) + H2 O (l)
F (aq) + H2 O (l)
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Chapter 16
−
[OH ]
29
Acid - Base Equilibria
NH3 (aq) + H2 O (l) ⇋ NH4 (aq) + OH (aq)
xM —
0.000 M
0.000 M
-3.16 x 10−4 M — +3.16 x 10−4 M +3.16 x 10−4 M
(x - 3.16 x 10−4 ) M —
3.16 x 10−4 M
3.16 x 10−4 M
+
Kb
=
[NH4 + ][OH− ]
[NH3 ]
=
(3.16 x 10−4 )2
x - 3.16 x 10−4
Spring Semester
= [NH4 + ] = 3.16 x 10−4
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Chapter 16
Acid - Base Equilibria
Relationship Between Ka and Kb
Example Problem Involving Weak Base Calculation
Initial
Change
Equilibrium
⇋ NH4 + (aq) + OH− (aq)
To illustrate the relationship between Ka and Kb , the following two equations can
be added together:
−
NH4
= 1.8 x 10−5
+
(aq)
⇋ NH3 (aq) + H+ (aq);
NH3 (aq) + H2 O (l)
⇋ NH4 + (aq) + OH− (aq);
Ka
=
Kb
[NH3 ][H+ ]
=
[NH4 + ]
[NH4 + ][OH− ]
[NH3 ]
Adding the above two equations gives:
−4
x - 3.16 x 10
x
[NH3 ]
Spring Semester
=
−4 2
(3.16 x 10
−5
1.8 x 10
)
≈x
H2 O (l)
This turns out to be the ion-product of H2 O (Kw ).
The product of the acid-dissociation constant for an acid and the
base-dissociation constant for its conjugate base is equal to the ion product of
water.
+ +
4
3 ][H ]
[NH
[NH
][OH− ]
Ka x Kb =
·
= [H+ ][OH− ] = Kw
+
4
[NH
]
[NH
3]
= 5.6 x 10−3
= (x - 3.16 x 10−4 ) M ≈ 5.6 x 10−3 M
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⇋ H+ (aq) + OH− (aq)
31
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32
Chapter 16
Acid - Base Equilibria
(a) Which of the following bases has the largest base-dissociation constant: NO2 − ,
PO4 3− , or N3 − ?
From the product of acid-dissociation constant for an acid and the
base-dissociation-constant for the conjugate base,
= Ka x Kb
From Table 16.2, p.685 and Appendix D, p. 1126:
we can discern the following
• Because of the inverse relationship between Ka and Kb ,
Ka
=
Kw
Kb
Acid - Base Equilibria
Example Problem for Relationship Between Ka and Kb
Relationship Between Ka and Kb
Kw
Chapter 16
.
Anion
Ka
NO2 −
PO4 3−
N3 −
4.5 x 10−4
4.2 x 10−13
1.9 x 10−5
Kb
=
Kw
Ka
2.2 x 10−11
2.4 x 10−2
5.3 x 10−10
Clearly, PO4 3− has the largest base-dissociation constant.
the strength of an acid increases (larger Ka ) as the strength of
the conjugate base decreases (smaller Kb ):
• Ka for an acid can be calculated if Kb is known; likewise, Kb for
an acid can be calculated if Ka is known.
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Chapter 16
Acid - Base Equilibria
Example Problem for Relationship Between Ka and Kb
Ka = 10
= 10
The base-dissociation-constant is:
Kb
Spring Semester
=
Kw
Ka
=
−5
·10
1.0 x 10−14
1.26 x 10−5
Acid - Base Equilibria
The cations and ions may exhibit acid-base properties so that the
resulting solution can be acidic or basic.
−5
= 1.26 x 10
Hydrolysis is the reaction of ions in solution with H2 O to generate
H+ (aq) or OH− (aq).
= 7.9 x 10−10
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Chapter 16
34
When salts dissolve in water, they are completely dissociated into
ions in solution making them strong electrolytes.
pKa = -log Ka = 4.90
0.10
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Acid-Base Properties of Salt Solutions
(b) The conjugate acid of the base quinoline has a pKa = 4.90. What is the
base-dissociation constant of quinoline?
−4.90
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Chapter 16
Acid - Base Equilibria
Chapter 16
Acid - Base Equilibria
Acid-Base Properties of Salt Solutions
Acid-Base Properties of Salt Solutions
An Anion’s Ability to React with Water
An Anion’s Ability to React with Water
The ability of an anion to react with H2 O to produce OH− depends on the strength
of the conjugate acid of the anion.
To determine the conjugate acid of anion X− and assess its strength, first add a
add proton to X− to give HX:
−
If the acid (HX) is one of the seven strong acids, then X
to react with H2 O.
• There will be an equilibrium mixture of weak acid (HX), X− ,
OH− , and the solution will be basic.
will have little tendency
• X− will react with water to produce the weak acid and OH− ions
• The anion will not affect the pH of the solution, and the equilibrium will lie far
to the left:
Cl
−
−
(aq) + H2 O (l)←−HCl (aq) + OH
If the acid (HX) is not the one of seven strong acids, then X− is the
conjugate base of a weak acid.
raising the pH of the solution:
(aq)
C2 H3 O2
−
(aq) + H2 O (l)
⇋ HC2 H3 O2 (aq) + OH− (aq)
• An anion that is the conjugate base of a strong acid will not affect the pH of
a solution.
• An anion that is the conjugate base of a weak acid will
increase the pH of a solution.
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Chapter 16
37
Acid - Base Equilibria
Acid - Base Equilibria
One way to analyze the acid-base properties of salt solutions is to consider a two-step
process of dissolving the salt in water and then analyzing the resulting cation and anion in
solution.
+
1. Polyatomic cations such as NH4 will donate a proton to water
producing H3 O+ ions and lowering the pH:
(aq) + H2 O (l)
Chapter 16
38
Example: Dissolution of NaNO3 in Water
A Cation’s Ability to React with Water
NH4
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Acid-Base Properties of Salt Solutions
Acid-Base Properties of Salt Solutions
+
Spring Semester
Dissolve in water.
NaNO3 (s)
⇋ NH3 (aq) + H3 O (aq)
+
−→ Na+ (aq) + NO3 − (aq)
Analyze the effect of the resulting ions in solution.
NH4 + can be considered to the the conjugate acid of the weak
base NH3 , and its strength in inversely related to Kb .
• Na+ is a cation which does not react with H2 O.
• NO3 − in the anion of strong conjugate acid (HNO3 ) and doesn’t react with water.
• Thus, the NaNO3 solution has a neutral pH.
2. Many metal ions react with H2 O to decrease the pH of an
aqueous solution.
3. Exceptions are ions of Group 1A and heavier members of Group
2A (Ca2+ , Sr2+ , Ba2+ ).
For a solution containing a cation which is the conjugate acid of a weak base and an anion
which is the conjugate base of a weak acid, the ion with the largest ionization constant will
have the greatest influence on pH.
For example, ammonium carbonate, (NH4 )2 CO3 is basic.
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