Chem 1721
Brief Notes: Chapters 15 and 16
Chapter 15: Acids and Bases; Chapter 16: Acid-Base Equilibria
Bronstsed-Lowry definitions of acids and bases are based on proton transfer
 acids are proton donors
 bases are proton acceptors
An acid-base reaction (neutralization reaction) is a proton transfer reaction: Acid + Base  Salt (+ water)
 ex.
HCl (aq) + NaOH (aq)  NaCl (aq) + H2O
HNO3 (aq) + NH3 (aq)  NH4Cl (aq)
Dissociaton (ionization) equations:
 acid dissociation equation: HA + H2O  H3O+ + A
base dissociation equation: B + H2O  BH+ + OH
note: acidic solutions are characterized by [H3O+]
note: basic solutions are characterized by [OH ]
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Strong acids and bases are completely ionized in aqueous solution; all in the form of H3O+ + A , or Bn+ + OH
⎯
Strong Acids
HCl
HNO3
HBr
HClO4
HI
H2SO4
⎯
Strong Bases
LiOH
Ca(OH)2
NaOH
Sr(OH)2
KOH
Ba(OH)2
RbOH
Mg(OH)2
CsOH
Weak acids and bases are only partially ionized in aqueous solution (frequently 1% or less); the majority of a weak acid or
weak base is in its unionized form (HA or B)
examples of weak acids
examples of weak bases
HF
NH3
HC2H3O2
N2H4
H3PO4
C5H5N
HNO2
NEt3 (where Et = CH2CH3)
HClO3
HNMe2 (where Me = CH3)
Conjugate acid/base pairs
 the conjugate base of an acid is the species that remains after the proton is donated
HF + H2O  F + H3O+; F is the conjugate base of HF; HF and F is a conjugate acid/base pair
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 the conjugate acid of a base is the species that is formed when a base accepts a proton
NH3 + H2O  NH4+ + OH ; NH4+ is the conjugate acid of NH3; NH3 and NH4+ is a conjugate acid/base pair
⎯
Weak acid dissociation (ionization) equilibria:
 for weak acids in aqueous solution an equilibrium is established:
HA (aq) + H2O (l) ↔ A (aq) + H3O+ (aq)
this (heterogeneous) equilibrium has an equilibrium constant, Ka – the acid dissociation (ionization) constant
[H3O+][A-]
Ka =
[HA]
⎯
Comparison of strong and weak acids:
Strong Acids
completely ionized
Ka is very large
equilibrium position very far to right
at equilibrium [H3O+] = [HA]0; [HA] ≈ 0
H2O is stronger base than A
HA is stronger acid than H3O+
⎯
Weak Acids
partially ionized
Ka is small to very small
equilibrium position very far to left
at equilibrium [H3O+] << [HA]0; [HA] > 0
A is stronger base than H2O
H3O+ is stronger acid than HA
⎯
Auto-dissociation (ionization) of water: H2O + H2O ↔ H3O+ + OH
⎯
 equilibrium constant, Kw – the water auto-dissociation constant; Kw = [H3O+][OH ]
at 25°C Kw = 1.0 x 10 14
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
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

For any aqueous solution at 25°C, [H3O+][OH ] = 1.0 x 10
neutral solution: [H3O+] = [OH ]
acidic solution: [H3O+] > [OH ]
basic solution: [OH ] > [H3O+]
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14
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 a few examples
ex. [H3O+] = 2.5 x 10 3 M in lemon juice at 25°C. Calculate [OH ]. Is lemon juice acidic, basic, or neutral?
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answer: [OH ] = 4.0 x 10 12 M;
acidic because [H3O+] > [OH ]
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ex.
At 50°C Kw = 5.5 x 10 14. What is [H3O+] in a neutral solution at 50°C?
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answer: [H3O+] = 2.3 x 10 7 M
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[H3O+] and pH
 pH is a special measure of [H3O+] in a solution
pH = ⎯log[H3O+]; OR [H3O+] = 10 pH
⎯
logarithmic scale so pH decreases by 1 unit as [H3O+] increases by factor of 10
 related values:
pOH = ⎯log[OH ]
pKa = ⎯logKa
pKb = ⎯logKb
⎯
 ex.
Consider a sample of lakewater contaminated by the chemicals associated with “acid rain”. The pH = 4.5;
calculate [H3O+] and [OH ].
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answer: [H3O+] = 3.2 x 10 5 M
[OH ] = 3.1 x 10 10 M
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ex.
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What is the pH of a sample of seawater with [OH ] = 1.58 x 10 6 M?
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answer: pH = 8.20
 note: relationship between pH and pOH
Kw = [H3O+][OH ]
take ⎯log of both sides: ⎯logKw = ⎯log[H3O+] ⎯ log[OH ]
at 25°C: 14.00 = pH + pOH
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pH calcualtions for solutions of strong and weak acids
 strong acid solutions
[H3O+] = [HA]0
solve for pH directly
 ex.
 weak acid solutions
[H3O+] << [HA]
equilibrium calculation; use Ka and equilibrium table
Calculate the pH of 0.025 M nitric acid.
answer: 1.60
Will the pH of 0.025 M nitrous acid be higher, lower, or equal to the pH of 0.025 M nitric acid?
ex.
Calculate [HBr] if the solution has pH = 1.06.
answer: 0.087 M
ex.
Calculate the pH of 0.10 M HCN (aq). For HCN Ka = 4.9 x 10 10.
⎯
a few considerations:
2 potential sources of H3O+: dissociation of HCN AND the auto-dissociation of water
[H3O+]tot = [H3O+]HCN-diss + [H3O+]H2O-diss
dominant source of H3O+ determined by larger K value; here Ka > Kw by 4 orders of magnitude
set up an equilibrium calculation based on the acid dissociation equilibrium of the weak acid, HCN:
Δ[]
⎯ x
----
+x
+x
equil [ ]
(0.10 ⎯ x) M
----
xM
xM
[H3O+][CN-]
H2O (l)
----
H3O+ (aq)
0
initial [ ]
Ka =
+
↔
HCN (aq)
0.10 M
4.9 x 10-10 =
[HCN]
(x)(x)
(0.10 - x)
+
CN (aq)
0
⎯
4.9 x 10-10 =
x2
0.10
answer: x = [H3O+] = 7.0 x 10 6 M;
pH = 5.15
note: here we use the simplifying assumption that the x in the [HCN]eq term is negligibly small; it is usually
safe to use this approximation when Ka is small (i.e. ~ 10 5 or smaller)
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to check if this approximation is valid:
x
[HA]0
< 5%
if the result of this calculation is > 5% the approximation is not valid; solve for x using the quadratic formula
 percent dissocation (ionization) in weak acid solutions
another measure of acid strength
extent of reaction in the forward direction
for strong acids, effectively 100%
for weak acids <<< 100%
related to Ka and concentration
 percent dissociaton = (Δ[HA]/[HA]0)*100
for weak acids – percent dissociation increases as concentration decreases
compare: 0.0250 M HC2H3O2 (aq) and 0.010 M HC2H3O2 (aq). For acetic acid Ka = 1.8 x 10 5.
⎯
0.250 M HC2H3O2 (aq)
6.71 x 10 4 M
3.17
2.68%
⎯
acid
[H3O+]
pH
% dissociation
0.0100 M HC2H3O2 (aq)
4.24 x 10 4 M
3.37
4.24%
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determination of Ka from experimental data:
 from pH or % dissociation
use date to determine x, then calculate Ka
ex.
The pH of a 0.250 M solution of HF (aq) is 2.036. Calculate Ka for HF.
if pH = 2.036, then [H3O+] = x = 9.20 x 10 3
⎯
use the value of x to calculate Ka
Ka =
[H3O+][F-]
x2
(0.250 - x)
Ka =
[HF]
Ka =
(9.20 x 10-3)2
(.250 - .0092)
answer: Ka = 3.51 x 10 4
⎯
ex.
A 0.340 M solution of HNO2 (aq) is 3.65% dissociated. Calculate Ka for HNO2.
if % diss = 3.65, then Δ[HNO2] = x = 0.0124
use to calculate Ka
answer: Ka = 4.69 x 10 4
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pH calculations for solutions of strong and weak bases; percent dissociation and Kb calculations for weak bases
 strong base solutions
 weak base solutions
calculate [OH ] based on solution concentration
equilibrium exists in solution
solve for pOH directly, then pH
B (aq) + H2O (l) ↔ BH+ (aq) + OH (aq)
base dissociation constant, Kb
[OH ] << [B]
 recall: at 25°C pH + pOH = 14.00
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
ex. Calculate the pH of 0.25 M NaOH (aq) and 0.25 M Ca(OH)2 (aq).
Before calculation . . . which do you expect to be more basic? Have the lower pH?
answer: NaOH pH = 13.40
Ca(OH)2 pH = 13.70
ex. Calculate the pH and % dissociation of 0.40 M NH3 (aq). For NH3, Kb = 1.8 x 10 5.
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think through this calculation in the same way as a weak acid problem
2 sources of OH ; NH3 base ionization and auto-ionization of water
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so [OH ]tot = [OH ]NH3 + [OH ]H2O ≈ [OH ]NH3
because Kb NH3 > Kw
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set up equilibrium calculation for the base dissociation of the weak base NH3
Δ[]
⎯ x
----
+x
+x
(0.40 ⎯ x) M
----
xM
xM
+][OH-]
Kb = [NH4
[NH3]
H2O (l)
----
NH4+ (aq)
0
initial [ ]
equil [ ]
+
↔
NH3 (aq)
0.40 M
1.8 x 10-5 =
(x)(x)
(0.40 - x)
+
OH
0
⎯
1.8 x 10-5 =
x2
0.40
x = [OH ] = 0.0027
⎯
answer: pH = 11.43; % diss = 0.68%
ex. Codeine (C18H21NO3) is a weak base. The pH of a 0.0012 M solution of codeine is 9.64. Calculate Kb.
answer: Kb = 1.6 x 10 6
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Polyprotic Acids
 acids with more than one acidic proton (H+)
 H+ dissociation is step-wise; one H+ dissociated per step
 each dissociation step has its own Ka value
 ex oxalic acid, H2C2O4; Ka1=5.9 x 10 2; Ka2 = 6.4 x 10 5
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1st dissociation step: H2C2O4 (aq) + H2O (l) ↔ HC2O4 (aq) + H+ (aq)
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2nd dissociation step: HC2O4 (aq) + H2O (l) ↔ C2O42 (aq) + H+ (aq)
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note: Ka1 > Ka2 – this is ALWAYS true for polyprotic acids; H2C2O4 stronger acid than HC2O4
loss of H+ from an anion is less favorable than loss of H+ from a charge-neutral species
⎯
 polyprotic acids are common ion solutions (more in Ch. 15); [H3O+] ≠ 0 in 2nd dissociation step (is = “x” from 1st
dissociation step)
 ex. Determine the equilibrium concentrations of [H2CO3], [HCO3 ], [CO32 ] and [H3O+] as well as the pH of 0.45
M H2CO3 (aq). For carbonic acid Ka1 = 4.3 x 10 7, Ka2 = 5.6 x 10 11.
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1st dissociation step:
initial [ ]
H2CO3
0.45 M
+
equil [ ]
(0.45 – x) M
↔
H2O
HCO3
0M
+
⎯
xM
H3O+
0M
xM
x = [HCO3 ] = [H3O+] = 4.4 x 10 4 M
[H2CO3] = .45 – x = 0.45 M
using Ka1:
⎯
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2nd dissociation step:
initial [ ]
HCO3
4.4 x 10 4 M
+
equil [ ]
(4.4 x 10 4 – x) M
⎯
H2O
⎯
↔
CO32
0M
x = [CO32 ] = 5.6 x 10
⎯
11
⎯
H3O+
4.4 x 10⎯4 M
(4.4 x 10 4 + x) M
xM
⎯
using Ka2:
+
⎯
⎯
M
finally: [H3O+] = 4.4 x 10 4 M; pH = 3.36
⎯
note: x is negligibly small in both the (4.4 x 10 4 – x) M and (4.4 x 10 4 + x) M terms
⎯
Acidic and Basic properties of salts
 Ionic compounds can be acidic, basic or neutral
 cations tend to be neutral or acidic
 anions tend to be neutral or basic

neutral cations and anions are related to the strong acids and bases
neutral cations: Li+, Na+, K+, Rb+, Cs+, Ca2+, Sr2+, Ba2+
neutral anions: Cl , Br , I , NO3 , ClO4
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
the conjugate acid of a weak base (i.e. BH+) is acidic: BH+ + H2O ↔ B + H3O+; Ka
ex. NH4+, C5H5NH+, N2H5+, C6H5NH4+

the conjugate base of a weak acid (i.e. A ) is basic: A + H2O ↔ HA + OH ; Kb
ex. F , ClO , PO43 , NO2 , C2H3O2
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
a small, highly charged metal cation may be acidic: M(H2O)xn+ + H2O ↔ M(H2O)x 1(OH)(n 1)+ + H3O+; Ka
ex. Zn2+, Al3+, Cr3+, Fe3+

an anion may be acidic if it is the conjugate base (by definition) of a polyprotic acid but still has an acidic H+
ex. HSO4 , HSO3 , HCO3 , H2PO4 , HPO42 ; H2PO4 + H2O ↔ HPO42 + H3O+
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a table to summarize the acid/base properties of ions:
Examples
Ion that participates in H+
transfer reactions with H2O
Solution is:
NaCl, KNO3, BaI2
neither
neutral
NH4Cl, (C5H5NH)Br,
(CH3)2NH2Cl
cation
acidic
Na(C2H3O2), KClO, LiF
anion
basic
NH4F, NH4CN
both cation and anion
neutral if Ka = Kb
acidic if Ka > Kb
basic if Ka < Kb
Salt
Cation – conjugate acid of
a strong base
Anion – conjugate base of
a strong acid
Cation – conjugate acid of
a weak base
Anion – conjugate base of
a strong acid
Cation – conjugate acid of
a strong base
Anion – conjugate base of
a weak acid
Cation – conjugate acid of
a weak base
Anion – conjugate base or
a weak acid

Ka and Kb of a conjugate acid/base pair are related: Ka*Kb = Kw; pKa + pKb = pKw

ex. Write the acid ionization equation for NH4+; write the Ka expression; calculate Ka for NH4+.
ex. Calculate the pH of 1.20 M NaNO2 (aq). For HNO2, Ka = 4.6 x 10 4.
⎯
initial [ ]
NO2 (aq)
1.20 M
equil [ ]
(1.20 ⎯x) M
⎯
+
H2O (l)
----
↔
HNO2 (aq)
0
----
+
OH (aq)
0
⎯
xM
xM
use Kb for NO2 ; Kb = Kw/Ka for HNO2 = 2.2 x 10 11
⎯
⎯
answer: x = [OH ] = 5.1 x 10 6; pH = 8.71
⎯
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ex. Calculate the pH of 0.88 M C5H5NBr (aq). For C5H5N, Kb = 1.7 x 10 9.
⎯
initial [ ]
C5H5NH+ (aq)
0.88 M
equil [ ]
(0.88 ⎯ x) M
+
+
H2O (l)
-------
use Ka for C5H5NH ; Ka = Kw/Kb = 5.9 x 10
↔
C5H5N (aq)
0
xM
+
H3O+ (aq)
0
xM
6
⎯
answer: x = [H3O+] = 2.3 x 10 3 M; pH = 2.64
⎯
ex. Calculate the pH of 0.097 M Al(H2O)63+ (aq). For Al(H2O)63+, Ka = 1.4 x 10 5.
⎯
initial [ ]
Al(H2O)63+
0.097 M
equil [ ]
(.097 ⎯ x) M
+
↔
H2O
-------
Al(H2O)5(OH)2+
0
+
xM
H3O+
0
xM
set this up like a normal weak acid calculation
answer: x = [H3O+] = 0.0012 M; pH = 2.92
Structure/Strength Relationships for Acids and Bases

acid strength is all about how vulnerable (i.e. donatable) the acidic H+ is; the more willing the acid (HA) is to
donate H+, the stronger the acid

factors that affect the strength of the H⎯A bond will affect the strength of the acid
weaker H⎯A bond  H+ donated more easily  stronger acid
stronger H⎯A bond  H+ donated less easily  weaker acid

binary acids, HA vs. oxoacids, HAOn

for a set of binary acids with A belonging to the same group of the periodic table, H⎯A bond strength decreases as
the atomic radius of A increases (top to bottom of periodic table)
acid
HF
ΔHBDE
567 kJ/mol
Ka
10 4
HCl
431 kJ/mol
very large
HBr
366 kJ/mol
very large
HI
299 kJ/mol
very large
⎯
note: of the strong hydrohalic acids HCl, HBr, and HI, bond strength data suggests that HI should be the strongest

for a set of binary acids with A belonging to the same period of the periodic table, H⎯A bond strength is related to
the polarity of the bond
as the electronegativity of A increases, the polarity of the H⎯A bond increases, and the acid strength increases
the more electronegative A, the more A is attracted to the electron density in the H⎯A bond; as the electron density
in the bond is pulled toward A (electrons not shared equally between H and A), the H⎯A bond is weakened

substance, HA
CH4
electronegativity of A
2.5
acidic?
NO
NH3
3.0
NO, a weak base
H2O
3.5
weakly amphoteric
HF
4.0
weak acid, Ka = 10
4
⎯
oxoacids, HAOn
structurally, the central atom A is always bonded to one or more hydroxyl (OH) group
the acidic proton(s) in an oxoacid are the H’s of the OH group(s)
below, structures of carbonic, nitric and sulfuric acids
O
O
C
H-O
N
O-H
H2CO3
O-H
O
O
H-O
S
O
HNO3
O-H
H2SO4

for oxoacids with the same number of oxygens, but a different central atom, A, acid strength increases with
increasing electronegativity of A
the more electronegative A pulls electron density away from the H creating a more polarized O⎯H bond

for oxoacids with the same A but a different number of oxygens, acid strength increases with an increasing number
of oxygen atoms
2 factors to consider:
1.
O’s are electronegative, so the more O’s the more the general flux of electron density is away from H,
weakening the O⎯H bond
2.
the more O’s, the more stable the resulting oxoanion (conjugate base of the acid)
acid
electronegativity of A
Ka
acid
# of O’s
Ka
11
⎯
HClO
1
3.5 x 10 8
HOI
2.5
2.3 x 10
HOBr
2.8
2.0 x 10 9
HClO2
2
1.2 x 10 2
HOCl
3.0
3.5 x 10 8
HClO3
3
~1
HClO4
4
very large
⎯
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⎯
⎯
Lewis definitions of acids and bases

Lewis acid/base definitions are related to electron pairs donated and accepted
a Lewis acid is an electron pair acceptor
a Lewis base is an electron pair donor
some examples:
Al3+ (aq) + H2O (l) ↔ Al(H2O)3+; Al3+ Lewis acid, H2O Lewis base
Cu2+ (aq) + NH3 (aq) ↔ Cu(NH3)2+; Cu2+ Lewis acid, NH3 Lewis base
H
Al3+
+
[Al-OH2]3+
O
Cu2+
+
[Cu(NH3)]2+
NH3
H
acidic and basic oxides

two general guildelines:
1. oxides of nonmetals are acidic
2.

oxides of metals are basic
acidic and basic behavior of oxides can be viewed in terms of Lewis acid-base definitions
ex. SO3 (g) + H2O (l)  H2SO4 (aq); SO3 (S - Lewis acid) accepts an e pair from H2O (O - Lewis base)
⎯
ex. MgO (s) + H2O (l)  Mg2+ (aq) + 2 OH (aq); oxide ion (O2 Lewis base) donates an e pair to H2O
⎯
(H – Lewis acid)
⎯
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