Transcript Chem 1202 - LSU Department of Chemistry

Acid-Base Equilibria
Chapter 16
Equilibrium, Part II
Watkins
Chem 1422, Chapter 16
1
Acids and Bases: A Brief Review (Ch 4)
• Acid
–
–
–
–
tastes sour
feels squeeky clean
strong acid with [acid] > 1 dissolves protein
detect: changes litmus to red
–
–
–
–
tastes bitter
feels slippery
strong base with [base] > 1 dissolves protein
detect: changes litmus to purple
• Base
• Arrhenius definition
– acids increase [H+] in water
– bases increase [OH-] in water
– acid + base → salt + water.
Watkins
Chem 1422, Chapter 16
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Acids and Bases: A Brief Review (Ch 4)
“H+” literally means a bare proton; single protons
cannot actually exist in water!
In water, the proton always attaches to one or more
water molecules to form proton clusters.
The simplest cluster is H3O+(aq). Larger clusters
such as H5O2+(aq), H7O3+(aq), etc. also exist.
Watkins
Chem 1422, Chapter 16
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Acids and Bases: A Brief Review (Ch 4)
These clusters are in
dynamic equilibrium with
one another in water:
H+ + H2O → H3O+
H3O+ + H2O ⇌ H5O2+
H5O2+ + H2O ⇌ H7O3+
...
H2n+1On+ + H2O ⇌ H2n+3On+1+
The symbols H+(aq) and
H3O+(aq) are synonymous
and represent all of the
possible proton clusters in
water, known collectively as
"hydronium ion".
Watkins
Chem 1422, Chapter 16
4
Acids and Bases
• Arrhenius definition
– acids increase [H+] in water
– bases increase [OH-] in water
– This hydronium/hydroxyl definition is restricted to
aqueous solutions
• Brønsted-Lowry definition
– An acid donates “H+” (to a base)
– A base accepts “H+” (from an acid)
– This proton transfer definition is not restricted to
aqueous solutions; but in this course, only acid/base
aqueous solutions will be studied.
Watkins
Chem 1422, Chapter 16
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Proton Transfer Reactions in Water
ionization
HCl(aq) + H2O(l) → Cl-(aq) + H3O+(aq) acid
reaction
HCl donates a proton to H2O. Therefore,
HCl is a BL acid.
H2O accepts a proton from HCl. Therefore,
H2O is a BL base.
hydrolysis
NH3(aq) + H2O(l) → NH4+(aq) + OH-(aq) base
reaction
H2O donates a proton to NH3. Therefore,
H2O is a BL acid.
NH3 accepts a proton from H2O. Therefore,
NH3 is a BL base.
Water is one of many amphoteric substances
which can behave as either an acid or a base.
Watkins
Chem 1422, Chapter 16
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Proton Transfer Equilibrium
In solution, the proton transfer reaction is in
equilibrium. A BL acid must have an ionizable
proton, and can be a
cation: NH4+(aq) + H2O(l) ⇌ NH3(aq) + H3O+(aq)
neutral: H3PO4(aq) + H2O(l) ⇌ H2PO4-(aq) + H3O+(aq)
anion: HCO3-(aq) + H2O(l) ⇌ CO32-(aq) + H3O+(aq)
A BL base can be a
neutral: NH3(aq) + H2O(aq) ⇌ NH4+(aq) + OH-(aq)
anion: SO42-(aq) + H2O(aq) ⇌ HSO4-(aq) + OH-(aq)
not a cation (why?)
Watkins
Chem 1422, Chapter 16
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Conjugate BL Acid-Base Pairs
acid
base
base
acid
HAz(aq) + H2O(l) ⇌ Az-1(aq) + H3O+(aq)
acid ionization reaction
base hydrolysis reaction
Bz(aq) + H2O(l) ⇌ HBz+1 + OH-(aq)
base
acid
acid
base
Every acid/base equilibrium has two conjugate pairs.
Some examples of conjugate acid/base pairs:
Acid
HCl
HC2H3O2
H3PO4
H2PO4HPO42Watkins
Base
ClC2H3O2H2PO4HPO42PO43-
Acid
H2SO4
HSO4H3O+
H2 O
HO-
monoprotic
diprotic
Base
HSO4SO42H2O
HOO2triprotic
Chem 1422, Chapter 16
Acid
NH4+
NH3
NH2NH2-
Base
NH3
NH2NH2N3-
tetraprotic
8
Relative BL Acid Strength
HAz(aq) + H2O(l) ⇌ Az-1(aq) + H3O+(aq)
acid ionization reaction
Keq
Equilibrium constant Keq = Kc is symbolized
as Ka after the name of the reaction:
[H+]eq [Az-1]eq
Keq = Kc = Ka =
[HAz]eq
Ka is sometimes called the “acid dissociation
constant”. Values of Ka for some weak acids are
listed in Appendix Table D-1.
Watkins
Chem 1422, Chapter 16
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Relative BL Acid Strength
HAz(aq) + H2O(l) ⇌ Az-1(aq) + H3O+(aq)
acid ionization reaction
Ka
The value of Ka is a measure of the strength of HAz
(relative to base H2O(l)):
Weak acid: equilibrium lies far to the left (Ka << 1)
Moderate acid: equilibrium is midway (Ka ≈ 1)
Strong acid: equilibrium lies far to the right (Ka >> 1)
There are only 7 common neutral acids which donate
almost all (>99.99%; Ka > 104) of their protons to H2O:
Strong Acids
HCl, HBr, HI, HNO3, HClO3, HClO4, H2SO4
Watkins
Chem 1422, Chapter 16
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Relative BL Base Strength
H2O(l) + Bz(aq) ⇌ OH-(aq) + HBz+1(aq) Keq = Kb
base hydrolysis reaction
[HBz+1]eq [OH-]eq
Kb =
[Bz]eq
The strongest BL bases have Kb >> 1:
Strong Bases: O2-, NH2-, NH2-, N3-, S2-, HOH- (from soluble hydroxides), is moderately strong.
Kb is sometimes called the “base hydrolysis
constant”. Values of Kb for a few weak bases
are listed in Appendix Table D-2.
Watkins
Chem 1422, Chapter 16
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The Autoionization of Water
Water is amphoteric, so in all aqueous solutions,
including pure water, the following equilibrium is always
established:
H2O(l) + H2O(l)
H3O+(aq) + OH-(aq)
Kc = Kw = [H+][OH-]
“water ionization constant”
At 25 oC (“room temperature”), Kw = 1.0 × 10-14.
However, the autoionization of water is endothermic, so
for example, at 37 oC, Kw = 2.36 × 10-14 (in accordance
with LeChatelier's principle).
Watkins
Chem 1422, Chapter 16
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The Autoionization of Water
Water is amphoteric, so in all aqueous solutions,
including pure water, the following equilibrium is always
established:
H2O(l) + H2O(l)
H3O+(aq) + OH-(aq)
Kc = Kw = [H+][OH-] = 1×10-14
“water ionization constant”
In aqueous chemistry, many numbers (e.g., equilibrium
constants, concentrations) are very small, so a shorthand has been invented for small numbers.
Watkins
Chem 1422, Chapter 16
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The p Scale
Define: pH = – log10[H+] so [H+] = 10-pH (“anti-log”)
The symbol "p" in pH means "negative power of 10"
You can calculate the negative log (and anti-log) of any
number:
pOH = – log[OH-]
[OH-] = 10-pOH
pKw = – log Kw
Kw = 10-pKw
pKa = – log Ka
Ka = 10-pKa
pKb = – log Kb
Kb = 10-pKb
On most calculators, the log x and 10x functions are
together.
Watkins
Chem 1422, Chapter 16
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The p Scale
H2O(l) + H2O(l) ⇌ H3O+(aq) + OH-(aq)
Kw = [H+][OH-]
pKw = -log{[H+][OH-]} = {-log[H+]} + {-log[OH-]}
In all aqueous solutions
pKw = pH + pOH
In pure water and all other neutral aqueous solutions:
[H+] = [OH-] and pH = pOH
Kw = [H+][OH-] = x2, x = Kw , pH = pOH = ½pKw
At 25 oC, pKw = 14.00 so in a neutral solution
pH = pOH = 7.00
At 37 oC, pKw = 13.63 so in a neutral solution
pH = pOH = 6.81
Watkins
Chem 1422, Chapter 16
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pH Scale
pH @ 25 oC
Acids and bases
are common in our
everyday life, and
[H+] is a very
important factor
in bio-metabolism.
Thus, the pH of
household items is
vital information.
Watkins
Chem 1422, Chapter 16
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pH Scale
pH @ 25 oC
The pH and pOH
scales do not end
at 0 and 14. For
example, a 10 M
HCl solution has a
pH of -1 and a
pOH of 15.
Watkins
Chem 1422, Chapter 16
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Conjugate Acid/Base Pairs
Consider the conjugate acid base pair HAz and Az-1.
acid ionization reaction
HAz(aq) + H2O(l) ⇌ H3O+(aq) + Az-1(aq)
Ka
base hydrolysis reaction
Az-1(aq) + H2O(l) ⇌ HAz(aq) + OH-(aq)
Kb
Kw = KaKb
H2O(l) + H2O(l) ⇌ H3O+(aq) + OH-(aq)
For any conjugate acid/base pair: KaKb = Kw
For any conjugate acid/base pair: pKa + pKb = pKw
Example: for HS-, Ka = 1×10-19 (appendix D-1)
so for S2-, Kb = Kw/Ka = 1×105 (a strong base)
Watkins
Chem 1422, Chapter 16
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Strengths of Conjugate Pairs in Water
The stronger the acid,
the weaker its conjugate base.
KaKb=Kw
For the 7 strong acids, their conjugate bases are so weak
that, for 6 of them, their reactions with water are
negligible (Kb ≈ 0) and they are called spectator ions:
Cl-, Br-, I-, NO3-, ClO3-, ClO4Exception: HSO4- is also a very weak base, but it is not a
spectator because it is also a weak acid (Ka = 1.2×10-2).
Watkins
Chem 1422, Chapter 16
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Strengths of Conjugate Pairs in Water
The stronger the base,
the weaker its conjugate acid.
KaKb=Kw
The soluble IA and IIA metal hydroxides are strong
bases. Their conjugate acids, the IA and IIA metal ions,
are so weak (Ka ≈ 0) they are spectator ions:
Li+, Na+, K+, Rb+, Cs+, Ca2+, Sr2+, Ba2+
By contrast, the rest of the metal hydroxides are weak
bases, so their conjugate acids (the metal ions
themselves) are relatively strong acids (Al3+ is quite a
strong acid!). More about this later.
Watkins
Chem 1422, Chapter 16
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Strength of Hydroxyl
OH-(aq) is a strong base, but how strong is it?
Consider the following equations involving the conjugate
pair HA/A- and their constants Ka and Kb:
1 H2O(l) + HA(aq) ⇌ H3O+(aq) + A-(aq) Ka
2 OH-(aq) + HA(aq) ⇌ H2O(l) + A-(aq)
Kb-1 = KaKw-1
Equation 1 defines the strength Ka of acid HA with
respect to base H2O, but it also defines the strength of
base H2O with respect to acid HA: “Kb(H2O)”.
Equation 2 defines the strength “Kb(OH-)” of base OHwith respect to acid HA.
Watkins
Chem 1422, Chapter 16
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Strength of Hydroxyl
OH-(aq) is a strong base, but how strong is it?
Consider the following equations involving the conjugate
pair HA/A- and their constants Ka and Kb:
1 H2O(l) + HA(aq) ⇌ H3O+(aq) + A-(aq) Ka
2 OH-(aq) + HA(aq) ⇌ H2O(l) + A-(aq)
Kb-1 = KaKw-1
“Kb(H2O)” = Ka
“Kb(OH-)” = KaKw-1
Since the two “Kb” values are in reference to the same
acid HA, they can be compared directly:
“Kb(OH-)”
= Kw-1
“Kb(H2O)”
Watkins
Hyroxyl is a stronger base
than water by a factor of Kw-1
Chem 1422, Chapter 16
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pH Measurement
pH is measured most accurately with a pH meter.
Watkins
Chem 1422, Chapter 16
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pH Measurement
pH is measured most accurately with a pH meter.
Certain dyes (called
indicators) change color
as pH changes.
Indicators are less
precise than pH
meters, because they do
not show a sharp color
change as pH changes.
Watkins
Chem 1422, Chapter 16
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pH Calculations
The pH of any aqueous solution can be
calculated, but the method of calculation depends
on what is dissolved in the solution.
Each of the following requires a slightly different
method:
•Strong acids
•Weak acids
•Strong bases
•Weak bases
•Salts
Watkins
Chem 1422, Chapter 16
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pH Calculations - Strong Acids
The seven common strong acids are HCl, HBr, HI,
HNO3, HClO3, HClO4, and H2SO4.
All of these acids are monoprotic (even H2SO4 is treated
as monoprotic in calculations).
Strong acids are strong electrolytes because they ionize
“completely” in solution. That is, equilibrium lies so far
to the right that the acid ionization reaction is treated as
a completion reaction:
HNO3(aq) + H2O(l) → H3O+(aq) + NO3-(aq)
or
Watkins
HNO3(aq) → H+(aq) + NO3-(aq)
Chem 1422, Chapter 16
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pH Calculations - Strong Acids
For a strong monoprotic acid, [H+] is equal to the
molarity of the acid.
Example: HCl(aq) → H+(aq) + Cl-(aq)
For a 0.0346 M hydrochloric acid solution:
[Cl-] = [H+] = 0.0346 M and pH = -log(0.0346) = 1.46
Example: H2SO4(aq) → H+(aq) + HSO4-(aq)
What is the concentration of a sulfuric acid solution
with a pH of 3.26?
The concentration of each ion is equal to the initial
concentration of the acid:
[H+] = [HSO4-] = 10-3.26 = 5.49 × 10-4 M
(Note: weak acid HSO4- contributes an insignificant
amount of H+ to the solution).
Watkins
Chem 1422, Chapter 16
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pH Calculations - Strong Bases
• Soluble Hydroxide salts:
– IA metal hydroxides of Li, Na, K, Rb, Cs
– IIA metal hydroxides of Ca, Sr, Ba (not Be, Mg)
– All other metal hydroxides are only slightly soluble
and pH depends on their solubility (chapter 17).
• Soluble hydroxides are strong electrolytes which
dissolve completely in solution
NaOH(aq) → Na+(aq) + OH-(aq)
Ca(OH)2(aq) → Ca2+(aq) + 2 OH-(aq)
Watkins
Chem 1422, Chapter 16
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pH Calculations - Strong Bases
The pH of a strong base is derived from the initial [OH-]
and pOH: pH = pKw – pOH.
Example: 0.0346 M KOH ([OH-] = 0.0346 M)
pOH = -log(0.0346) = 1.46
at 25 oC, 14 - 1.46 = 12.54 = pH
Example: 0.0346 M Ca(OH)2 ([OH-] = 2×0.0346 M)
pOH = -log(0.0692) = 1.16
at 25 oC, pH = 12.84
Watkins
Chem 1422, Chapter 16
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pH Calculations - Strong Bases
Other strong bases include oxide ion, sulfide ion, etc.
Example: 0.0346 M Na2O(aq)
Na2O(aq) → 2Na+(aq) + O2-(aq)
O2-(aq) + H2O(l) → 2OH-(aq)
pOH = -log(2×0.0346) = 1.16
at 25 oC, pH = 12.84
Watkins
Chem 1422, Chapter 16
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pH Calculations - Weak Acids
Weak acids are only partially ionized in aqueous
solution; un-ionized acid molecules are in equilibrium
with hydronium ions and the conjugate base:
HAz(aq)
H+(aq) + Az-1(aq)
[H+] [Az-1]
Ka =
[HAz]
Values of Ka are found in Appendix table D-1.
Watkins
Chem 1422, Chapter 16
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pH Calculations - Weak Acids
Watkins
Chem 1422, Chapter 16
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pH Calculations - Weak Acids
Use the ICE table to calculate the pH of a monoprotic
weak acid solution, initial concentration Ca.
H+(aq) + A-(aq)
HA(aq)
[HA]
[H+]
[A-]
[ ]i
Ca
0
0
[ ]
-x
+x
+x
[ ]f
Ca-x
x
x
0 < x < Ca
Watkins
Qi = 0
Ka << 1
x2
Ka 
Ca  x
x 2  K a x  K a Ca  0
x
 K a  K a2  4Ka Ca
Chem 1422, Chapter 16
2
pH = -log(x)
33
pH Calculations - Weak Acids
Approximation: if Ka < 10-2 then x will be small,
and if Ca is much (> 102 times) larger than Ka,
then x << Ca so Ca-x  Ca
Ca >> Ka
H+(aq) + A-(aq)
HA(aq)
Ka << 1
[ ]i
Ca
0
0
x2
x2
Ka 

Ca  x Ca
[ ]
-x
+x
+x
[H+] = x  K a C a
[ ]f
Ca-x
x
x
+
[HA] [H ]
-
[A ]
For example: calculate 0.15 - 0.00005
= 0.14995 = 0.15 to 2 sig figs
Watkins
Chem 1422, Chapter 16
pH = -log(x)
BIG ±
small
≈ BIG
34
Sample Problems
1. Calculate the pH of a 0.158 M solution of butanoic acid.
Ca = 0.158, Ka = 1.5 ×10-5
(from appendix D)
Since Ca >> Ka, we can use
the approximation
[HA]
[H+]
[A-]
I
Ca
0
0
C
-x
+x
+x
E
Ca-x
x
x

[H ]  K aCa
[H  ]  (1.5  10 -5 )(0.158)  1.54 10 -3
pH = -log(1.54×10-3) = 2.81
compare this to the precise values:
[H+] = 1.532×10-3, pH = 2.8147
Watkins
Chem 1422, Chapter 16
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Sample Problems
2. A solution of HF has pH 2.15. What is Ca?
Appendix D: Ka = 6.8×10-4
[HA]
I
Ca
x = [H+] = 10-2.15 = 7.08×10-3
C
-x
2
Ka = x /(Ca - x)
E
Ca-x
Ca = (x2 /Ka) + x
Ca = {(7.08×10-3)2 / 6.8×10-4} + 7.08×10-3
[H+]
[A-]
0
0
+x
+x
x
x
= 0.0808 M
No approximation necessary
Watkins
Chem 1422, Chapter 16
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Sample Problems
3. The pH of a 0.172 M weak acid solution is 4.81. What
is Ka for this acid?
[HA] [H+] [A-]
Ca = 0.172
x = [H+] = 10-4.81 = 1.55×10-5
I
Ca
0
0
C
-x
+x
+x
E
Ca-x
x
x
Ka = x2/(Ca - x)
= (1.55×10-5)2/(0.l72 - 1.55×10-5)
= 1.40×10-9
No approximation necessary
Watkins
Chem 1422, Chapter 16
37
Weak Acids
Percent ionization of a monoprotic acid is defined as the
ratio of [H+]eq to Ca
x
%I  100 
Ca
HA(aq)
H+(aq) + A-(aq)
+
-
[HA]
[H ]
[A ]
I
Ca
0
0
C
-x
+x
+x
E
Ca-x
x
x
K aCa
%I  100 
Ca
Ka
%I  100 
Ca
For example:
0.05 M acetic acid, %I = 1.90%
0.15 M acetic acid, %I = 1.10%
Watkins
Chem 1422, Chapter 16
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Weak Acids
%I of Acetic Acid
Watkins
Chem 1422, Chapter 16
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Polyprotic Acids
Polyprotic acids have more than one ionizable proton.
• The protons are removed in successive equilibria:
H2SO3(aq) ⇌ H+(aq) + HSO3-(aq)
Ka1 = 1.7 × 10-2
HSO3-(aq) ⇌ H+(aq) + SO32-(aq)
Ka2 = 6.4 × 10-8
H3PO4(aq) ⇌ H+(aq) + H2PO4-(aq)
Ka1 = 7.5 × 10-3
H2PO4-(aq) ⇌ H+(aq) + HPO42-(aq)
Ka2 = 6.2 × 10-8
HPO42-(aq) ⇌ H+(aq) + PO43-(aq)
Ka3 = 4.2 × 10-13
Watkins
Chem 1422, Chapter 16
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Polyprotic Acids
Polyprotic acids have more than one ionizable proton.
• The protons are removed in successive equilibria:
H2SO3(aq) ⇌ H+(aq) + HSO3-(aq)
Ka1 = 1.7 × 10-2
HSO3-(aq) ⇌ H+(aq) + SO32-(aq)
Ka2 = 6.4 × 10-8
• In polyprotic acids it is increasingly difficult to
remove successive protons: Ka1 > Ka2 > Ka3 etc.
• Usually Ka1 >> Ka2, so approximately all of the [H+]eq
comes from the first ionization.
• In problems, treat any polyprotic acid
(including H2SO4) as a monoprotic acid.
Watkins
Chem 1422, Chapter 16
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Polyprotic Acids
Note that the first two dissociation contants of citric
acid are similar in magnitude, so citric acid cannot be
treated as monoprotic; pH calculation of a citric acid
solution involves coupled equilibria.
Watkins
Chem 1422, Chapter 16
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Weak Bases
Weak bases accept a few protons from water:
NH3(aq) + H2O(l)
NH4+(aq) + OH-(aq) Kb << 1
Watkins
Chem 1422, Chapter 16
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Types of Weak Bases
• Neutral bases have lone pairs to attract and attach
protons. A huge number of these contain nitrogen;
nitrogenous bases are called amines.
– Amines are related to ammonia (NH3) with one or more
H atoms replaced with C groups: CH3NH2 (methylamine),
(CH3)2NH (dimethylamine), (CH3)3N (trimethylamine).
– Plants produce amines (alkaloids) such as caffeine, nicotine,
opium, heroin, cocaine, etc.
– Amines in the brain are neurotransmitters and CNS drugs
– Amines in the blood act as hormones
– About 20 amino acids (with -NH2 groups and –COOH
groups) make up all proteins.
– Amines called nucleic acids make up the genetic coding
molecules DNA, RNA, tRNA, etc.
Watkins
Chem 1422, Chapter 16
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Types of Weak Bases
• Neutral bases have lone pairs to attract and attach
protons. A huge number of these contain nitrogen;
nitrogenous bases are called amines.
H
H
H
N
OH
N
H
H
H
H
H 3C
H 3C
N
N
Watkins
N
H
CH3
H2 N
N
N
N
H
H
O
N
NH
H
Aniline
H 3C
CH3
H
H
N
CH3
Pyridine
Cytosine
Chem 1422, Chapter 16
45
H
Types of Weak Bases
• Neutral bases have lone pairs to attract and attach
protons.
H+
H+
N
N
H
H
N
N
<name>amine
<name>ammonium cation is a conjugate acid
Watkins
Chem 1422, Chapter 16
46
Types of Weak Bases
• Anionic bases have lone pairs and negative charges to
attract and attach protons.
• Anionic bases are the conjugates of weak acids.
• Example: OCl- (hypochlorite) is the conjugate base of
weak acid HOCl (hypochlorous acid):
HOCl(aq) + H2O(l)
OCl-(aq) + H+(aq)
OCl-(aq) + H2O(l)
HOCl(aq) + OH-(aq)
Ka = 3.0×10-8
Kb = ?
Kb = Kw/Ka = 1.0×10-14/ 3.0×10-8 = 3.3×10-7
For a conjugate acid/base pair, KaKb = Kw
Watkins
Chem 1422, Chapter 16
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Types of Weak Bases
• Anionic bases have lone pairs and negative charges to
attract and attach protons.
• Anionic bases are the conjugates of weak acids.
• Example: CO32- is the conjugate base of HCO3which is the conjugate base of H2CO3
H2CO3(aq) + H2O(l)
HCO3-(aq) + H+(aq)
Ka1 = 4.3×10-7
HCO3-(aq) + H2O(l)
CO32-(aq) + H+(aq)
Ka2 = 5.6×10-11
CO32-(aq) + H2O(l)
HCO3-(aq) + OH-(aq)
Kb1 = Kw/Ka2
HCO3-(aq) + H2O(l)
H2CO3(aq) + OH-(aq) Kb2 = Kw/Ka1
Identify the correct conjugate pair!
Watkins
Chem 1422, Chapter 16
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Weak Base Problems
B(aq) + H2O(l)
HB+(aq) + OH-(aq)
A-(aq) + H2O(l)
HA(aq) + OH-(aq)
Quadratic equation?
2
x
x2
Kb 
Graphing calculator?

Cb  x Cb
[B]
[HB+] [OH-]
I
Cb
0
0
x  [OH - ]  K bCb
C
-x
+x
+x
pOH = -log(x)
E
Cb-x
x
x
pH = 14 - pOH
If Kb < 10-2 and Cb > ~100Kb (very common)
then x << Cb so Cb - x is  Cb
Watkins
Chem 1422, Chapter 16
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Weak Bases
Percent ionization is defined as:
100 times the ratio of [OH-] to Cb
B(aq) + H2O(l)
A-(aq) + H2O(l)
HB+(aq) + OH-(aq)
HA(aq) + OH-(aq)
x
%I  100
where x = [OH-]
Cb
If the approximation is valid, then
%I  100
K bCb
Cb
Kb
%I  100
Cb
0.1 M NH3(aq) (“NH4OH”, Kb = 1.8×10-5), %I = 1.3%
Watkins
Chem 1422, Chapter 16
50
Weak Base Problem
1. What is the pH of a 0.337 M solution of pyridine?
C5H5NH+(aq) + OH-(aq)
C5H5N(aq) + H2O(l)
Cb = 0.337
Kb = 1.7×10-9
(Appendix D)
Cb >> Kb, so ...
[OH  ]  (1.7 10 -9 )(0.337)  2.39 10 -5
pOH = -log(2.39×10-5) = 4.62
pH = 14 - pOH = 9.38
Watkins
Chem 1422, Chapter 16
51
Weak Base Problem
2. What is the pH of a 0.263 M hypochlorite solution?
ClO-(aq) + H2O(l)
HClO(aq) + OH-(aq)
Cb = 0.263 (ClO- is the conjugate base of HClO)
Ka of HClO is 3.0×10-8 (Appendix D)
Kb = Kw/Ka = 1.0×10-14/3.0×10-8 = 3.3×10-7
[OH  ]  (3.3 10 -7 )(0.263)  2.95 10 -4
pOH = 3.53; pH = 10.47
Watkins
Chem 1422, Chapter 16
52
Summary of Acid/Base Formulas
pH -log [H+]
pOH -log [OH-]
Aqueous Solns pH + pOH = pKw (= 14 (@ 25 oC)
Conjugate Pair Kw = KaKb
Strong Acids [H+] = Ca
IA Hydroxides [OH-] = Cb
IIA Hydroxides [OH-] = 2Cb
Weak Acids [H  ]  K aCa
Weak Bases [OH  ]  K bCb
if C >> K << 1
%Ionization %I  K C
(acid or base)
Watkins
Chem 1422, Chapter 16
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Acid-Base Properties of Salt Solutions
• Recall that "acid plus base yields salt plus water"
• There are four kinds of salts, with anions from either
a strong acid (SA) or a weak acid (WA), and cations
from either a strong base (SB) or a weak base (WB)
– SBSA WBSA
SBWA
WBWA
NaCl
NH4Cl
NaF
NH4F
NaOH and NH4OH and HCl and HF
• Soluble salts are strong electrolytes in water, forming
many ions in solution.
Watkins
Chem 1422, Chapter 16
54
Acid-Base Properties of Salt Solutions
• Recall that "acid plus base yields salt plus water"
• There are four kinds of salts, with anions from either
a strong acid (SA) or a weak acid (WA), and cations
from either a strong base (SB) or a weak base (WB)
– SBSA WBSA
SBWA
WBWA
• Acid-base properties of salt solutions are a
consequence of the reaction of the ions with water:
– the cation may be an acid
the anion may be a base.
– Each salt must be analyzed to determine its acidbase properties
Watkins
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Acid-Base Properties of Salt Solutions
SBSA - Salt from Strong Base & Strong Acid
NEUTRAL SOLUTION
(both ions are spectators)
NaCl (from NaOH & HCl):
Na+ + H2O → NR (cation of strong base is spectator ion)
Cl- + H2O → NR (anion of strong acid is spectator ion)
Ca(NO3)2 (from Ca(OH)2 & HNO3);
Ca2+ + H2O → NR (cation of strong base is spectator ion)
NO3- + H2O → NR (anion of strong acid is spectator ion)
Caution: salts formed from H2SO4 are not neutral;
HSO4- is an acid, and SO42- is a base.
Watkins
Chem 1422, Chapter 16
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Acid-Base Properties of Salt Solutions
SBWA - Salt from Strong Base & Weak Acid
BASIC SOLUTION
(anion = conjugate base of weak acid)
NaF (from NaOH & HF):
Na+ + H2O → NR (cation of strong base is spectator ion)
F- + H2O ⇌ HF + OH- (equilibrum problem)
Ba(C2H3O2)2 (from Ba(OH)2 & HC2H3O2);
Ba2+ + H2O → NR (cation of strong base is spectator ion)
C2H3O2- + H2O ⇌ HC2H3O2 + OH- (equilibrium problem)
Watkins
Chem 1422, Chapter 16
57
Acid-Base Properties of Salt Solutions
WBSA - Salt from Weak Base & Strong Acid
ACIDIC SOLUTION
(cation = conjugate acid of weak base)
NH4Cl (from NH4OH {NH3(aq)} & HCl)
Cl- + H2O → NR (anion of strong acid is spectator ion)
NH4+ ⇌ NH3 + H+ (equil. problem)
Al(NO3)3 (from Al(OH)3 & HNO3)
NO3- + H2O → NR (anion of strong acid is spectator ion)
[Al(H2O)6]3+ ⇌ [Al(H2O)5OH]2+ + H+ (equil. problem)
(many metal ions hydrolyze; MULTIPLE EQUILIBRIA)
Watkins
Chem 1422, Chapter 16
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Acid-Base Properties of Salt Solutions
WAWB - Salts from Weak Acid & Weak Base
ACID, NEUTRAL OR BASIC SOLUTION
(cation is weak acid, anion is weak base)
NH4F (from NH4OH & HF)
NH4+ ⇌ NH3 + H+
(cation of weak base is a conjugate weak acid)
F- + H2O ⇌ HF + OH(anion of weak acid is a conjugate weak base)
The relative amounts of H+ and OH- produced
depend on the values of the cation Ka and the
anion Kb. This is a coupled equilibrium problem.
Watkins
Chem 1422, Chapter 16
59
pH of Salt Solutions
Calculate the pH of a 0.123 M solution of BaBr2
1. BaBr2(s) + H2O(l) → Ba2+(aq) + 2Br-(aq)
2. Ba2+(aq) is a spectator ion (ignore it)
3. Br-(aq) is a spectator ion (ignore it)
4. No reactions: pH = 7.00
Watkins
Chem 1422, Chapter 16
60
pH of Salt Solutions
Calculate the pH of a 0.123 M solution of NaF
(Ka for HF = 6.8 × 10 -4)
1. NaF(s) + H2O(l) → Na+(aq) + F-(aq)
2. Na+(aq) is a spectator ion (ignore it)
3. F-(aq) is the conjugate base of weak acid HF
Kb = Kw/Ka = 1.47×10-11
Cb = 0.123 M
4. [OH-] ≈ KbCb = 1.34×10-6 M; pOH = 5.87
5. pH = 14 – 5.87 = 8.13
Watkins
Chem 1422, Chapter 16
61
pH of Salt Solutions
Calculate the pH of a 0.123 M solution of NH4Cl
(Kb for NH3 = 1.8 × 10 -5)
1. NH4Cl(s) + H2O(l) → NH4+(aq) + Cl-(aq)
2. Cl-(aq) is a spectator ion (ignore it)
3. NH4+(aq) is the conjugate acid of base NH3
Ka = Kw/Kb = 5.56×10-10
Ca = 0.123 M
4. [H+] ≈ KaCa = 8.27×10-6 M
5. pH = 5.08
Watkins
Chem 1422, Chapter 16
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pH of Salt Solutions
Calculate the pOH of a 0.225 M solution of analinium
chloride (Kb for analine = 4.3×10-10).
1. HAnCl(s) → HAn+(aq) + Cl-(aq)
2. Cl-(aq) is a spectator ion (ignore it)
3. HAn+(aq) is the conjugate acid of base analine
Ka = Kw/Kb = 2.33×10-5
Ca = 0.225 M
4. [H+] ≈ KaCa = 2.29×10-3 M; pH = 2.64
5. 14 – pH = pOH = 11.4
Watkins
Chem 1422, Chapter 16
63
Acid-Base Strength
In order for the binary compound HX to be a
Bronsted-Lowry acid:
• The H-X bond must be very polar with H+ and X(this means that X must be a non-metal*)
• The H-X bond must be weak enough to be broken.
• The conjugate base, X-, must be stable in solution.
*Note that if X is a metal then the bond polarity is
H- and X+, in which case HX will not be an acid.
Watkins
Chem 1422, Chapter 16
64
Acid-Base Strength
Periodic Trends for X in acid HX
Acid strength of HX increases left to right
LiH is a base: X+ – HCH4 is neither acidic nor basic: C–H is ~ non-polar.
HF is an acid: F- – H+
Acid strength of HX increases top to bottom because of
other factors such as atomic size.
Watkins
Chem 1422, Chapter 16
65
Acid-Base Strength
both
Watkins
Chem 1422, Chapter 16
66
Acid-Base Strength
Substances which contain H-O-Y bonds may be either
acids or bases (Y is an atom which may be bonded to
other atoms)
If Y is a metal, the substance is a base
H-O-Na is a base because in water the H-O (covalent) bond is
stronger than the O-Na (ionic) bond.
If Y is a non-metal, the substance is an acid
As the electronegativity of Y increases, the acid becomes
stronger
H-O-I is a weak oxyacid because I is not very electronegative.
H-O-Cl is a stronger oxyacid because the Cl is more
electronegative than I.
Watkins
Chem 1422, Chapter 16
67
Acid Strength
Hypochlorous Acid vs. Hypoiodous Acid
Watkins
Chem 1422, Chapter 16
68
Acid Strength
The strength of an oxyacid increases with increasing
electronegativity of Y:
H-O-I
Ka = 2.3×10-11 (hypoiodous weak)
H-O-Cl
Ka = 3.0×10-8 (hypochlorous stronger)
The effective electronegativity of Y increases as more
electronegative atoms (e.g., O) are bonded to Y:
H-O-Cl
Ka = 3.0×10-8 (hypochlorous weakest)
H-O-ClO Ka = 1.1×10-2 (chlorous less weak)
H-O-ClO2 Ka >> 1
(chloric stronger)
H-O-ClO3 Ka >>> 1
(perchloric strongest)
Watkins
Chem 1422, Chapter 16
69
Organic Acids
Organic acids are called carboxylic acids because they
contain the carboxyl group COOH:
O
where R can be any atom
or group of atoms.
R C
O H
When the proton is removed, the negative charge is
delocalized over the two resonance structures of the
carboxylate anion, the conjugate base:
O
R C
O
R C
O
Watkins
O
Chem 1422, Chapter 16
70
Organic Acids
The acid strength increases as the effective
electronegativity of R increases.
H
R = CH3
O
O H
H
F
R = CF3
F
O
Ka = 0.23
C C
F
Watkins
Ka = 0.000018
H C C
O H
Chem 1422, Chapter 16
71
Acid/Base Definitions
Arrhenius
acid increases [H+], base increases [OH-] in water
restricted to protons/hydroxyl ions and aqueous solutions
Brønsted-Lowry
acid donates H+, base accepts H+
restricted to protons
includes Arrhenius definition; not restricted to water.
Lewis
acid = electron pair acceptor, base = electron pair donor
no restrictions
most general definition - includes both Arrhenius and
Bronsted-Lowry definitions.
Watkins
Chem 1422, Chapter 16
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Lewis Acids and Bases
Lewis acid: any atom, ion or molecule with a
vacant valence shell orbital which can accept an
electron pair
?
examples: H+ (A & BL); BF3; all metal cations
Lewis base: any atom, ion or molecule with a
non-bonded (lone) pair of electrons to donate
examples: H2O (BL), OH- (A), NH3, RCOO-, PO43Lewis Structure Required!
Watkins
Chem 1422, Chapter 16
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Lewis Acids and Bases
Lewis structure of BF3 - a reminder (chapters 8 & 9)
1. Count valence shell electrons: B F F F
3 + 3(7) = 24 electrons, 12 pairs
F
F B F
2. Central atom = B, peripheral atoms = F
F
3. 3 bond pairs;
12 – 3 = 9 non-bonding pairs
F B F
4. 9 lone pairs on peripheral atoms
5. No resonance!
F
F B F
Lewis Acid
6. 3 electron domains around B;
trigonal planar geometry
sp2 hybridization on B, one empty 2p orbital on B
Watkins
Chem 1422, Chapter 16
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Lewis acid-base reactions
F
F B
F
F H
N H
H
general Lewis
F B N H
acid-base rx
F H
H+
OH-
HOH
H+
H
O
H
H+
HO
H
n+
M
Watkins
H
H
O
H
proton transfer
n+
[M(H2 O)]
Chem 1422, Chapter 16
metal ion
hydration
75
Metal Ion Hydration
• In aqueous solution, small, highly charged metal ions
(e.g., Al3+, Fe3+) are always hydrated and therefore are
Lewis acids; the complex ion thus formed is a
Bronsted-Lowry/Arrhenius acid.
[Fe(H2O)6]3+(aq) + H2O(aq) ⇌ [Fe(H2O)5(OH)]2+(aq) + H3O+(aq)
Kh1 = Ka = 2.0×10-3
0.1 M iron(III) nitrate
Fe(NO3)3(aq) → Fe3+(aq) + 3NO3-(aq)
spectator ion
[H+] ≈
Watkins
K a Ca = 0.0141 M, pH = 1.85
Chem 1422, Chapter 16
76
Metal Ion Hydration
• In aqueous solution, large, slightly charged metal ions
(e.g., Na+, Ca2+) are always hydrated and are also
Lewis acids. However, the hydrated complex is a
very weak Bronsted-Lowry/Arrhenius acid:
[Na(H2O)6]+
[Na(H2O)5(OH)] + H+(aq) Kh ≈ 0
[Na(H2O)6]+
NR (spectator ion)
Spectator metal ions
Li+, Na+, K+, Rb+, Cs+, Ca2+, Sr2+, Ba2+
All other metal ion hydrates are BL/A acids, with Ka
dependent on ionic charge and ionic size.
Watkins
Chem 1422, Chapter 16
77
A/BL/L Acids and Bases
A acid?
does pH decrease
when added to water?
HC2H3O2?
Acid?
A
Base?
BL L
A
BL L
BL acid? does it donate H+?
H3O+
Y
Y
Y
N
N
Y
L acid?
H2O
N
Y
N
N
Y
Y
OH-
N
Y
N
Y
Y
Y
=======================
O2-
N
N
N
Y
Y
Y
A base? does pH increase when
added to water?
NH3
N
Y
N
Y
Y
Y
HSO4-
Y
Y
Y
N
Y
Y
NH4+
Y
Y
Y
N
N
N
Fe3+
Y
N
Y
N
N
N
Fe[(H2O)6]3+
Y
Y
Y
N
N
N
does it accept a lone
pair?
BL base?does it accept
L base?
Watkins
H+?
does it have a lone
pair?
Chem 1422, Chapter 16
78