Acids & Bases
CHAPTER 16
(& part of CHAPTER 17)
Chemistry: The Molecular Nature of Matter, 6th edition
By Jesperson, Brady, & Hyslop
CHAPTER 16: Acids & Bases
Learning Objectives:
 Define Brønsted-Lowry Acid/Base
 Define Lewis Acid/Base
 Evaluate the strength of acids/bases
 Strong vs weak acids/bases
 Periodic trends
 Conjugate acids/bases
 Identify likely compounds that will form acids and
bases from the periodic table
 Acidic metal ions
 Acid/Base equilibrium:
 pH, pOH
 Ka, Kb, pKa, pKb
 Kw of water
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CHAPTER 16: Acids & Bases
Lecture Road Map:
① Brønsted-Lowry Acids/Bases
② Trends in acid strength
③ Lewis Acids & Bases
④ Acidity of hydrated metal ions
⑤ Acid/Base equilibrium
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CHAPTER 16 Acids & Bases
Brønsted-Lowry
Acid/Base
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Arrhenius
Acid/Base
Definition
Acid produces H3O+ in water
Base gives OH–
Acid-base neutralization
– Acid and base combine to produce water and a salt.
e.g. HCl(aq) + NaOH(aq)  H2O + NaCl(aq)
H3O+(aq) + Cl–(aq) + Na+(aq) + OH–(aq)
 2H2O + Cl–(aq) + Na+(aq)
• Many reactions resemble this without forming H3O+ or OH–
in solution
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Arrhenius
Acid/Base
Definition
Gas Phase Acid/Base chemistry not covered
by Arrhenius definition
e.g. NH3(g) + HCl(g)  NH4Cl(s)
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BrønstedLowry
Definition
• Acid = proton donor
• Base = proton acceptor
• Allows for gas phase acid-base reactions
e.g. HCl + H2O  H3O+ + Cl–
– HCl = acid
• Donates H+
– Water = base
• Accepts H+
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BrønstedLowry
Conjugate Acid-Base Pair
• Species that differ by H+
e.g. HCl + H2O  H3O+ + Cl–
• HCl = acid
• Water = base
• H3O+
– Conjugate acid of H2O
• Cl–
– Conjugate base of HCl
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BrønstedLowry
Example: Formic Acid
• Formic acid (HCHO2) is a weak acid
• Must consider equilibrium
– HCHO2(aq) + H2O
CHO2–(aq) + H3O+(aq)
• Focus on forward reaction
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BrønstedLowry
Example: Formic Acid
Now consider reverse reaction:
• Hydronium ion transfers H+ to CHO2–
• Formate Ion is the Brønsted Base
conjugate pair
HCHO2 + H2O
acid
base
H3O+ + CHO2
acid
base
conjugate pair
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Group
Problem
• Identify the conjugate partner for each
conjugate base
conjugate acid
Cl–
HCl
NH3
NH4+
C2H3O2–
HC2H3O2
CN–
HCN
F–
HF
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Group
Problem
Write a reaction that shows that HCO3– is a
Brønsted acid when reacted with OH–
HCO3–(aq) + OH–(aq)
H2O + CO32–(aq)
Write a reaction that shows that HCO3– is a
Brønsted base when reacted with H3O+(aq)
HCO3–(aq) + H3O+(aq)
H2CO3(aq) + H2O
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Group
Problem
In the following reaction, identify the acid/base
conjugate pairs.
(CH3)2NH + H2SO4 → (CH3)2NH+ + HSO4–
A. (CH3)2NH / H2SO4 (CH3)2NH+ / HSO4–
B. (CH3)2NH / (CH3)2NH+ H2SO4 / HSO4–
C. H2SO4 / HSO4– (CH3)2NH+ / (CH3)2NH
D. H2SO4 / (CH3)2NH (CH3)2NH+ / HSO4–
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BrønstedLowry
Amphoteric Substances
• Can act as either acid or base
– Can be either molecules or ions
e.g. Hydrogen carbonate ion:
– Acid
HCO3–(aq) + OH–(aq)  CO32–(aq) + H2O
– Base
HCO3–(aq) + H3O+(aq)  H2CO3(aq) + H2O
[Amphiprotic substances can donate or accept a
proton. This is a subtle but important difference from
the word amphoteric]
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Group
Problem
Which of the following can act as an
amphoteric substance?
A. CH3COOH
B. HCl
C. NO2–
D. HPO42–
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CHAPTER 16 Acids & Bases
Trends in
Acid/Base
Strength
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Acid/Base
Trends
Strengths of Acids & Bases
Strength of Acid
– Measure of its ability to transfer H+
– Strong acids
• React completely with water e.g. HCl and HNO3
– Weak acids
• Less than completely ionized e.g. CH3COOH and
CHOOH
Strength of Base classified in similar fashion:
– Strong bases
• React completely with water e.g. Oxide ion (O2–) and OH–
– Weak bases
• Undergo incomplete reactions
e.g. NH3 and NRH2 (NH2CH3, methylamine)
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Acid/Base
Trends
Strength in Water
• Strongest acid = hydronium ion, H3O+
– If more powerful H+ donor added to H2O
– Reacts with H2O to produce H3O+
Similarly,
• Strongest base is hydroxide ion (OH–)
– More powerful H+ acceptors
– React with H2O to produce OH–
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Acid/Base
Trends
Acid/Base Equilibrium
• Acetic acid (HC2H3O2) is weak acid
– Ionizes only slightly in water
HC2H3O2(aq) + H2O
H3O+(aq) + C2H3O2–(aq)
weaker acid
weaker base
stronger acid
stronger base
• Hydronium ion
– Better H+ donor than acetic acid
– Stronger acid
• Acetate ion
– Better H+ acceptor than water
– Stronger base
• Position of equilibrium favors weaker acid and base
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Group
Problem
In the reaction:
HCl + H2O → H3O+ + Cl–
which species is the weakest base ?
A. HCl
B. H2O
C. H3O+
D. Cl–
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Group
Problem
Group
Problem
Identify the preferred direction of the following
reactions:
H3O+(aq) + CO32–(aq)
HCO3–(aq) + H2O
Cl–(aq) + HCN(aq)
HCl(aq) + CN–(aq)
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Acid/Base
Trends
General Trends
• Stronger acids and bases tend to react with
each other to produce their weaker conjugates
– Stronger Brønsted acid has weaker
conjugate base
– Weaker Brønsted acid has stronger
conjugate base
• Can be applied to binary acids (acids made
from hydrogen and one other element)
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Acid/Base
Trends
Binary Acid Trends
Binary Acids = HnX
X = Cl, Br, P, As, S, Se, etc.
1.
Acid strength increases from left to right within
same period (across row)
– Acid strength increases as electronegativity
of X increases
e.g. HCl is stronger acid than H2S which is
stronger acid than PH3
– or
PH3 < H2S < HCl
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Acid/Base
Trends
Binary Acid Trends
Binary Acids = HnX
X = Cl, Br, P, As, S, Se, etc.
2. Acid strength increase from top to bottom
within group
– Acid strength increases as size of X and
bond length increases
e.g. HCl is weaker acid than HBr which is
weaker acid than HI
– or HCl < HBr < HI
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Group
Problem
Which is stronger?
• H2S or H2O
• H 2S
• CH4 or NH3
• NH3
• HF or HI
• HI
Acid/Base
Trends
Oxoacid Trends
Oxoacids (HnX Om)
– Acids of H, O, and one other element
– HClO, HIO4, H2SO3, H2SO4, etc.
1. Acids with same number of oxygen atoms and differing X
a. Acid strength increases from
bottom to top within group
• HIO4 < HBrO4 < HClO4
b. Acid strength increases from left to
right within period as the electronegativity of the central
atom increases H3PO4 < H2SO4 < HClO4
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Acid/Base
Trends
Definition
Oxoacids (HnXOm)
2. For same X
– Acid strength increases with number of oxygen atoms
• H2SO3 < H2SO4
• More oxygens, remove more electron density from
central atom, weakening O—H bond make H more
acidic
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Group
Problem
Which is the stronger acid in each pair?
• H2SO4 or H3PO4
H SO
2
4
• HNO3 or H3PO3
HNO3
• H2SO4 or H2SO3
H2SO4
• HNO3 or HNO2
HNO3
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Group
Problem
Which corresponds to the correct order of
acidity from weakest to strongest acid ?
A. HBrO3, HBrO, HBrO2
B. HBrO, HBrO2, HBrO3
C. HBrO, HBrO3, HBrO2
D. HBrO3, HBrO2, HBrO
Acid/Base
Trends
Basicity
• Acid strength can be analyzed in terms of basicity
of anion formed during ionization
• Basicity
– Willingness of anion to accept H+ from H3O+
• Consider HClO3 and HClO4:
O
O
H
O
O
Cl
H
O
Cl
O
O
HClO3
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HClO4
30
Acid/Base
Trends
H
Basicity
O
O
O
Cl
O
H
O
Cl
O
O
HClO3
HClO4
• Lone oxygens carry most of the negative charge
– ClO4– has 4 O atoms, so each has –¼ charge
– ClO3– has 3 O atoms, so each has –1/3 charge
• ClO4– weaker base than ClO3–
– Thus conjugate acid, HClO4, is stronger acid
• HClO4 stronger acid as more fully ionized
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Group
Problem
Acid/Base
Trends
Organic Acid Trends
• Organic acid —COOH
• Presence of electronegative atoms (halide, nitrogen or
other oxygen) near —COOH group
– Withdraws electron density from O—H bond
– Makes organic acid, stronger acids
e.g.
CH3CO2H < CH2ClCO2H < CHCl2CO2H < CCl3CO2H
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Group
Problem
Which of the following is the strongest organic acid?
A
H
O
I
C
C
OH
B
H
O
Br
C
C
H
H
O
F
C
C
OH
E
H
O
Cl
C
C
H
H
O
H
C
C
H
H
D
H
OH
C
OH
OH
CHAPTER 16 Acids & Bases
Lewis Acid/Base
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Lewis
Acid/Base
Definition
• Broadest definition of species that can be
classified as either acid or base
• Definitions based on electron pairs
• Lewis acid
– Any ionic or molecular species that can accept
pair of electrons
– Formation of coordinate covalent bond
• Lewis base
– Any ionic or molecular species that can
donate pair of electrons
– Formation of coordinate covalent bond
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Lewis
Acid/Base
Lewis Neutralization
• Formation of coordinate covalent bond between electron
pair donor and electron pair acceptor
Addition Compound
• NH3BF3 = addition compound
– Made by joining two smaller molecules
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Lewis
Acid/Base
Lewis Acid-Base Reaction
Electrons in coordinate covalent bond come from O in
hydroxide ion
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Lewis
Acid/Base
Lewis Acids
1.
Molecules or ions with incomplete valence shells
e.g. BF3 or H+
2. Molecules or ions with complete valence shells, but with
multiple bonds that can be shifted to make room for
more electrons
e.g. CO2
3. Molecules or ions that have central atoms that can
expand their octets
– Capable of holding additional electrons
– Usually, atoms of elements in Period 3 and below
e.g. SO2
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Lewis
Acid/Base
Lewis Acid Example: SO2
O2–
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Lewis
Acid/Base
Lewis Bases
• Molecules or ions that have unshared electron pairs
and that have complete shells
– e.g. O2– or NH3
Lewis Definition is Most General
– All Brønsted acids and bases are Lewis acids and
bases
– All Arrhenius acids and bases are Brønsted acids
and bases
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Lewis
Acid/Base
Proton (H+) Transfer
H2O—H+ + NH3  H2O + H+—NH3
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Group
Problem
Identify the Lewis acid and base in the following:
• NH3 + H+
NH4+
Base Acid
• F– + BF3
Base Acid
BF4–
• SeO3 + O2–
Acid
Base
SeO42–
Group
Problem
Which of the following species can act as
a Lewis base ?
A. Cl–
B. Fe2+
C. NO2–
D. O2–
CHAPTER 16 Acids & Bases
Acidity of Oxides
& Hydrates
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Acidic Metal
Ions
Acid-Base Properties of Elements &
their Oxides
Nonmetal oxides
– React with H2O to form acids
– Upper right hand corner of periodic table
– Acidic Anhydrides
– Neutralize bases
– Aqueous solutions red to litmus
– SO3(g) + H2O  H2SO4(aq)
– N2O5(g) + H2O  2HNO3(aq)
– CO2(g) + H2O  H2CO3(aq)
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Acidic Metal
Ions
Acid-Base Properties of Elements &
their Oxides
Metal oxides
– React with H2O to form hydroxide (Base)
– Group 1A and 2A metals (left hand side of periodic table)
– Basic Anydrides
– Neutralize acids
– Aqueous solutions blue to litmus
– Na2O(s) + H2O  2NaOH(aq)
– CaO(s) + H2O  Ca(OH)2(aq)
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Acidic Metal
Ions
Metal Oxides
• Solids at room temperature
• Many insoluble in H2O
• Why?
– Too tightly bound in crystal
– Can't remove H+ from H2O
– Do dissolve in solution of strong acid
– Now H+ free, can bind to O2– and remove
from crystal
Fe2O3(s) + 6H+(aq)  2Fe3+(aq) + 3H2O
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Group
Problem
What is the acid formed by P2O3
when it reacts with water ?
A. H2PO4
B. H2PO2
C. H3PO4
D. H3PO3
•P2O3 + 3H2O → 2H3PO3
Acidic Metal
Ions
Metal Ions in Solution
• Exist with sphere of water molecules with their
negative poles directed toward Mn+
• Mn+(aq) + mH2O
Lewis Acid
Lewis Base
M(H2O)mn+(aq)
hydrated metal ion
= addition compound
– n = charge on metal ion
= 1, 2, or 3 depending on metal atom
– For now assume m = 1 (monohydrate)
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Acidic Metal
Ions
M(H2O)n+(aq) + H2O
Metal Hydrates are Weak Brønsted Acids
M(OH)n+(aq) + H3O+(aq)
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Acidic Metal
Ions
Metal Hydrates are Weak Brønsted Acids
• Electron deficiency of metal cations causes them to induce
electron density towards metal from water of hydration
• Higher charge density = more acidic metal
ionic charge
charge density 
ionic volume
• Acidity increases left to right across period
• Acidity decreases top to bottom down group
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Acidic Metal
Ions
Acidity of Hydrated Metal Ions
Degree to which M(H2O)mn+ produces acidic solutions
depends on:
1. Charge on Cation: As charge increases on Mn+, acidity
increases
– Increases metal ion’s ability to draw electron density to itself and
away from O—H bond
2. Cation’s Size: As size of cation decreases, acidity
increases
– Smaller, more concentrated charge
– Means greater pull of electron density from O—H bond
Net result: Very small, highly charged cations are very acidic
[Al(H2O)6]3+(aq) + H2O
[Al(H2O)5(OH)]2+(aq) + H3O+ (aq)
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Group
Problem
In the following list of pairs of ions, which
is the more acidic ?
Fe2+ or Fe3+; Cu2+ or Cu+; Co2+ or Co3+
A. Fe3+, Cu+, Co2+
B. Fe2+, Cu2+, Co3+
C. Fe3+, Cu2+, Co3+
D. Fe2+, Cu2+, Co2+
Acidic Metal
Ions
Trends in Acidity of Mn+
• Acidity increases up group (column) as cation size
decreases
• Acidity increases across period (row) as cation size
decreases
Alkali Metal Ions
(Li+, Na+, K+, Rb+, Cs+)
All weak
(+1, large size)
Be2+
Other Alkaline earth metals
(Ba2+, Ca2+ Sr2+, Mg2+)
Moderately weak
Very Weak
Transition metal ions, Al3(often +3,
Quite acidic
+4 charges)
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Group
Problem
Identify each of the following as acidic or basic and give their
reaction with water:
• P2O5 acidic
P2O5(s) + 3H2O
2H3PO4(aq)
2H3PO4(aq)
2H+(aq) + 2H2PO4–(aq)
• MnO2 basic
MnO2(s) + 2H2O
Mn2+(aq) + 4OH–(aq)
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CHAPTER 16 Acids & Bases
Acid/Base
Equilibrium
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Molecular Nature of Matter, 6E
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Acid/Base
Equilibrium
Weak Acids & Bases
• Incompletely ionized
• Molecules and ions exist in equilibrium
• HA = any weak acid; B = any weak base
HA(aq) + H2O
A–(aq) + H3O+(aq)
B (aq) + H2O
B H+(aq) + OH–(aq)
CH3COOH(aq) + H2O
HSO3–(aq) + H2O
NH4+(aq) + H2O
CH3COO–(aq) + H3O+(aq)
SO32–(aq) + H3O+(aq)
NH3 (aq) + H3O+ (aq)
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Acid/Base
Equilibrium
Weak Acids & Bases
• Often simplify as
• HA (aq)
A –(aq) + H+(aq)
-
+
[A ][H ]
Ka =
[HA]
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Acid/Base
Equilibrium
Weak Acids & Bases
Acid + Water
Or generally
HA(aq) + H2O
K c¢ =
Conjugate Base + Hydronium Ion
A–(aq) + H3O+(aq)
[ A - ][H3O+ ]
[HA ][H2O]
• But [H2O] = constant (55.6 M ) so rewrite as
K c¢ ´ [H2O] =
[ A ][H3O ]
-
[HA]
+
= Ka
• Where Ka = acid ionization constant
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Acid/Base
Equilibrium
Weak Acids & Bases
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Acid/Base
Equilibrium
Weak Acids & Bases
CH3COO–(aq) + H2O
NH4+(aq) + OH–(aq)
NH3(aq) + H2O
• Or generally
B (aq) + H2O
B H+(aq) + OH–(aq)
[BH ][OH ]
K c¢ =
[B ][H2O]
+
-
[BH ][OH ]
Kb =
[B ]
+
CH3COOH(aq) + OH–(aq)
But [H2O] = constant
so rewrite as
-
Where Kb = base ionization
constant
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Acid/Base
Equilibrium
Weak Acids & Bases
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Acid/Base
Equilibrium
pH
• Lots of weak acids and bases
– How can we quantify their relative strengths?
• Need reference
– Choose H2O
• Water under right voltage
– Slight conductivity
– Where does conductivity come from?
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Acid/Base
Equilibrium
pH
• Trace ionization  self-ionization of water
• H2O + H2O
H3O+(aq) + OH–(aq)
acid
base
acid
base
• Equilibrium law is:
Kc =
+
-
[H3O ][OH ]
[H2O]2
æ 1 mol ö
• But [H2O]pure = 1000 g ç
÷÷ = 55.6 M
ç
è 18.0 g ø
1.00 L
[H2O] = constant even for dilute solutions
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Acid/Base
Equilibrium
pH
H2O + H2O
H3O+(aq) + OH–(aq)
• Since [H2O] = constant, equilibrium law is
K w = [H3O ][OH ]
+
-
• K w = is called the ion product of water
• Often omit second H2O molecule and write
• H2O
H+(aq) + OH–(aq)
K w = [H ][OH ]
+
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Acid/Base
Equilibrium
Kw
H2O
H+(aq) + OH–(aq)
• For pure H2O at 25 °C
– [H+] = [OH–] = 1.0 × 10–7 M
– Kw = (1.0 × 10–7)(1.0 × 10–7) = 1.0 × 10–14
– See Table 17.1 for K w at various temperatures
• H2O auto-ionization occurs in all solutions
– When other ions present
• [H+] is usually NOT equal to [OH–]
• But Kw = [H+][OH–] = 1.0 × 10–14
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Acid/Base
Equilibrium
Definition of Acidic & Basic
• In aqueous solution,
– Product of [H3O+] and [OH–] equals K w
– [H3O+] and [OH–] may not actually equal each other
– Solutions are classified on the relative
concentrations of [H3O+] and [OH–]
Solution Classification
Neutral
[H3O+] = [OH–]
Acidic
[H3O+] > [OH–]
Basic
[H3O+] < [OH–]
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Acid/Base
Equilibrium
Weak Acids & Bases: Example
Ex. 1 In a sample of blood at 25 °C,
[H+] = 4.6  10–8 M. Find [OH–] and determine if the
solution is acidic, basic or neutral.
K w = [H ][OH ] = 1 ´10
+
-
[OH ] =
Kw
+
[H ]
-
=
1.0 ´ 10-14
4.6 ´ 10
-8
-14
= 2.2 ´ 10
-7
•So 2.2 × 10–7 M > 4.6 × 10–8 M
•[OH–] > [H3O+] so the solution is basic
Jesperson, Brady, Hyslop. Chemistry: The
Molecular Nature of Matter, 6E
69
Acid/Base
Equilibrium
pH
• Arrhenius (of kinetics fame)
– Sought an easy way to write the very small
numbers associated with [H+] and [OH–]
– Developed the “p” notation where p stands for
the –log mathematical operation
pX = -log X
– Result is a simple number
• pH is defined as:
+
pH = -log[H ]
– Define pOH as:
Jesperson, Brady,
Hyslop.
Chemistry: The
Molecular
Nature of Matter,
6E
-
pOH = -log[OH ]
– Define pKw as: pKw = -log K w = 14.00
• Take anti-log to obtain [H+], [OH–] or Kw
70
Acid/Base
Equilibrium
General Properties of Logarithms
log(a ´ b ) = log a + log b
log a b = b ´ log a
æa ö
log çç ÷÷ = log a - log b
èb ø
Using Logarithms
• Start with K w = [H+ ][OH- ]
• Taking –log of both sides of eqn. gives
-log([H+ ][OH- ]) = -log K w = -log(1.0 ´10-14 )
-log[H ] - log[OH ] = -log K w = -(-14.00)
+
-
• So at 25 °C:
pH + pOH = pK w = 14.00
Jesperson, Brady, Hyslop. Chemistry: The
Molecular Nature of Matter, 6E
71
Acid/Base
Equilibrium
Definition of Acidic and Basic
• As pH increases, [H+] decreases; pOH
decreases, and [OH–] increases
• As pH decreases, [H+] increases; pOH
increases, and [OH–] decreases
Neutral
pH = 7.00
Acidic
pH < 7.00
Basic
pH > 7.00
Jesperson, Brady, Hyslop. Chemistry: The
Molecular Nature of Matter, 6E
72
Acid/Base
Equilibrium
Measuring pH
1.
pH meter
– Most accurate
– Calibrate with solutions of known pH before use
– Electrode sensitive to [H+]
– Accurate to  0.01 pH unit
2. Acid-base indicator
– Dyes, change color depending on [H+] in solution
– Used in pH paper and titrations
– Give pH to  1 pH unit
3. Litmus paper
– Red pH  4.7 acidic
– Blue pH  4.7 basic
– Strictly acidic vs. basic
73
Jesperson, Brady, Hyslop. Chemistry: The
Molecular Nature of Matter, 6E
Acid/Base
Equilibrium
Jesperson, Brady, Hyslop. Chemistry: The
74
Acid/Base
Equilibrium
Example pH Calculations
Calculate pH and pOH of blood in Ex. 1.
We found [H+] = 4.6 × 10–8 M
[OH–] = 2.2 × 10–7 M
pH = –log(4.6 × 10–8) = 7.34
pOH = –log(2.2 × 10–7) = 6.66
14.00 = pKw
Or
pOH = 14.00 – pH = 14.00 – 7.34 = 6.66
Jesperson, Brady, Hyslop. Chemistry: The
Molecular Nature of Matter, 6E
75
Acid/Base
Equilibrium
Example pH Calculations
What is the pH of NaOH solution at 25 °C in
which the OH– concentration is 0.0026 M?
[OH–] = 0.0026 M
pOH = –log(0.0026) = 2.59
pH = 14.00 – pOH
= 14.00 – 2.59
= 11.41
Jesperson, Brady, Hyslop. Chemistry: The
Molecular Nature of Matter, 6E
76
Acid/Base
Equilibrium
Strong Acids
• Assume 100% dissociated in solution
– Good ~ if dilute
• Makes calculating [H+] and [OH] easier
• 1 mole H+ for every 1 mole HX
– So [H+] = CHX for strong acids
• Thus, if 0.040 M HClO4
• [H+] = 0.040 M
• And pH = –log (0.040) = 1.40
Jesperson, Brady, Hyslop. Chemistry: The
Molecular Nature of Matter, 6E
Strong
Acids
HCl
HBr
HI
HNO3
H2SO4
HClO3
HClO4
HX (general
term for a
strong acid)77
Acid/Base
Equilibrium
Strong Bases
Strong Bases
NaOH
KOH
LiOH
Ca(OH)2
Ba(OH)2
• 1 mole OH– for every 1 mole M OH
• [OH–] = CMOH for strong bases
• 2 mole OH– for 1 mole M(OH)2
• [OH–] = 2
for strong bases
C M (OH)
2
Sr(OH)2
Jesperson, Brady, Hyslop. Chemistry: The
Molecular Nature of Matter, 6E
78
Acid/Base
Equilibrium
Effect of Auto ionization of Water with
Strong Bases
• The auto-ionization of H2O will always add to [H+] and
[OH–] of an acid or base. Does this have an effect on the
last answer?
– The previous problem had 0.00022 M [OH–] from the
Ca(OH)2 but the [H+] must have come from water. If it
came from water an equal amount of [OH–] comes
from water and the total [OH–] is
– [OH–]total = [OH–]from Ca(OH)2 + [OH–]from H2O
– [OH–]total = 0.00022 M + 4.6 × 10–11 M
= 0.00022 M (when properly rounded)
Jesperson, Brady, Hyslop. Chemistry: The
Molecular Nature of Matter, 6E
79
Acid/Base
Equilibrium
Example pH Calculations
Kw
-14
1.0
´
10
-13
[OH ] = + =
= 5.0 ´ 10
0.0200
[H ]
– So [H+] from H2O must also be 5.0  10–13 M
• [H+]total = 0.020 M + (5.0  10–13 M)
= 0.020 M (when properly rounded)
• So we see that [H+]from H2O will be negligible except
in very dilute solutions of acids and bases
Jesperson, Brady, Hyslop. Chemistry: The
Molecular Nature of Matter, 6E
80
Acid/Base
Equilibrium
-
Looking at Weak Acids Again
+
[A ][H ]
Ka =
[HA]
pK a = -log K a
K a = 10
-pK a
pK b   logK b
What is the pKa of HF if Ka = 3.5 × 10–4?
HF(aq) + H2O
F–(aq) + H3O+(aq)
or
HF(aq)
F–(aq) + H+(aq)
-
+
[F ][H ]
Ka =
[HF]
= 3.5 × 10–4
pKa = –log Ka
= –log(3.5 × 10–4) = 3.46
K b  10 pK b
Jesperson, Brady, Hyslop. Chemistry: The
Molecular Nature of Matter, 6E
81
Acid/Base
Equilibrium
Conjugate Acid-Base Pairs
1. Consider ionization reaction of generic acid and water
HA(aq) + H2O
A–(aq) + H3O+(aq)
[A ][H ]
Ka =
[HA]
-
+
2. Consider reaction of a salt containing anion of this acid (its
conjugate base) with water
A–(aq) + H2O
HA(aq) + OH–(aq)
Kb =
[HA][OH- ]
[A - ]
Jesperson, Brady, Hyslop. Chemistry: The
Molecular Nature of Matter, 6E
82
Acid/Base
Equilibrium
Conjugate Acid-Base Pairs
HA(aq) + H2O
A–(aq) + H2O
2H2O

A–(aq) + H3O+(aq)
HA(aq) + OH–(aq)
H3O+(aq) + OH–(aq)


[A ][H ] [HA][OH ]


K a Kb 

 [H ][OH ]  K w

[HA]
[A ]
For any conjugate acid base pair:
K a  K b  K w  1.0  1014
Jesperson, Brady, Hyslop. Chemistry: The
Molecular Nature of Matter, 6E
(at 25 °C)
83
Acid/Base
Equilibrium
More About Logarithms
log(a ´ b ) = log a + log b
K a ´ K b = K w = 1.0 ´10
-14
• Then taking –log of both sides of equation gives:
 log(K a  K b )   logK w   log(1.0  1014 )
 logK a  logK b   logK w  (14.00)
So
pK a + pK b = pK w = 14.00
(at 25 °C)
• Earlier we learned the inverse relationship of conjugate acidbase strengths, now we have numbers to illustrate this.
• The stronger the conjugate acid, the weaker the conjugate
base.
84
Jesperson, Brady, Hyslop. Chemistry: The
Molecular Nature of Matter, 6E
Acid/Base
Equilibrium
•
Weak Acid Base Calculations
Need to develop strategy for dealing with weak
acid/base equilibrium calculations
Two general types of calculations:
1. Calculating Ka or Kb from initial concentrations
of acid or base and measured pH in solution
2. Calculating equilibrium concentrations given Ka
or Kb and initial concentrations
Jesperson, Brady, Hyslop. Chemistry: The
Molecular Nature of Matter, 6E
85