Chapter 15:Aqueous Equilibria: Acids and Bases

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Chapter 15Aqueous EquilibriaAcids and Bases
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The Arrhenius Acid-Base Theory

• Generalized Arrhenius Acid HA(aq) ?
  H(aq) A-(aq)
• Acids are substances that dissociate in water to
  produce hydrogen ions
• Generalized Arrhenius Base MOH(aq) ?
  M(aq) OH-(aq)
• Bases are substances that dissociate in water to
  yield hydroxide ions
•  
• Acid-base-reaction HA MOH ? MA H2O
• acid base ? salt water
• Arrhenius theory has limitations
• 1.      Restricted to aqueous solutions
• 2.      Doesnt account for the basicity of
  substances like ammonia (NH3) that dont contain
  OH groups
• NH3 H2O ? NH4 OH-

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The Bronsted-Lowry Theory

• 1.  Acid is any substance that can transfer a
  proton (H ion) to another substance
• Acid proton donor
• 2.   Base is any substance that can accept a
  proton
• Base proton acceptor
• NH3 H2O ? NH4 OH-
• NH3 is a proton acceptor base
• H2O is a proton donor acid
• NH4 is a proton donor acid
• OH- is a proton acceptor base

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•   Acid-base reactions are proton-transfer
  reactions
•    The products of a Bronsted-Lowry acid-base
  reaction are
• themselves acids and bases

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HCl H2O
H3O Cl- Acid
Base Acid
Base NH3 H2O
NH4 OH- Base
Acid Acid
Base
Water can be both, acid or base Note all
Bronsted-Lowry bases have one or more lone
electron pairs Unshared pair of electrons are
used for bonding of the proton
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Example 1

• A) Write a balanced equation for the
  dissociation of each of the following
  Bronsted-Lowry acids in water
• What is the conjugate base of the acid in each
  case?
• 1. H2SO4(aq)
• 2. HSO4-(aq)
• 3. H3O(aq)
• 4. NH4(aq)

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Example 2

• What is the conjugate acid of each of the
  following Bronsted-Lowry Bases?
• HCO3-(aq)
• CO32-(aq)
• OH-(aq)
• H2PO4-(aq)

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Acid Strength and Base Strength Different acids
differ in their ability to donate protons HA
H2O ? H3O A- Acid
base acid base In
this case two bases, H2O and A- are competing for
protons If H2O is the stronger base (stronger
proton acceptor) than A- then the H2O molecules
will get the protons and reaction will shift to
the right. If A- is the stronger base than H2O,
then A- gets the protons and the reaction will
shift to the left The proton is always
transferred to the stronger base
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Strong acids are almost completely dissociated in
water perchloric acid HClO4 hydrochloric acid
HCl hydrobromic acid HBr hydroiodic acid
HI nitric acid HNO3 sulfuric acid H2SO4 In
this case, water is the stronger base than the
conjugate base Weak acids are only partially
dissociated in water, the aqueous solution
contains mainly undissociated molecules. hydroflu
oric acid HF acetic acid CH3COOH nitrous acid
HNO2 phosphoric acid H3PO4 Here, water is the
weaker base than the conjugate base
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Acid Strength and Base Strength

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Hydrated Protons and Hydronium Ions We often
write the dissociation of an acid as HA
H A- Example HCl
H Cl- H is simply one proton which
does not exist under normal conditions (only in
ultra high vacuum) H is always bonded to a lone
electron pair of oxygen H3O hydronium
ion Actually, this hydronium ion is associated
with additional water molecules H(H2O)n
n 2,3,4
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Dissociation of Water

• Most important property of water is its ability
  to act as an
• acid and a base
• In the presence of a base water acts as an acid
• In the presence of an acid water acts like a
  base
• In pure water one molecule can donate one proton
  to another molecule
• H2O(l) H2O ? H3O(aq) OH-(aq)
• Acid Base Acid
  Base
• Called dissociation of water

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Dissociation of Water

• Dissociation of water
• a)      2 H2O(l) ? H3O(aq) OH-(aq)
• b)      Kw H3OOH- Equilibrium equation
• c)      Kw ion-product constant for water
• d)      Kw 1 x10-14 _at_ 25?C
• equilibrium constants are affected by temp

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Kw H3O OH- 1 x 10-14 Since
H3O OH- We can write H3O2
1 x 10-14 H3O 1 x 10-7
mol/L Compared to the concentration of
undissociated water with 55.4 mol/L the
concentration of H3O (which equals the
concentration of OH-) is extremely small!
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Kw H3O OH- 1 x 10-14 is valid in all
aqueous solutions In pure water H3O
OH- 1 x 10-7 mol/L In acidic solutions If
we add an acid which dissociates into H3O
ions H3O gt 1 x 10-7 mol/L OH- lt 1 x 10-7
mol/L In basic solutions If we add a base which
dissociates into OH- ions H3O lt 1 x 10-7
mol/L OH- gt 1 x 10-7 mol/L
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e)      H3O gt OH- acidic f)       H3O
OH- neutral g)      H3O lt OH- basic

Always H3O OH- Kw 1.0 x 10-14
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The concentration of H3O is an important figure
which will tell us if the solution is neutral,
basic or acidic. Instead of writing H3O in
moles/L it is more convenient to express it on a
logarithmic scale, known as the pH scale
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The pH Scale

• pH Latin potentia hydrogenii (power of
  hydrogen)
• Definition the pH is the negative logarithm of
  the H3O concentration
• pH -log H3O H3O 10-pH pOH -log OH-
• Pure water H3O 10-7 pH 7.00
•  
• pH pOH 14 kw H3O OH- 1.0 x10-14
• Acidic solution pH lt 7 Neutral solution pH 7
• Basic solution pH gt 7

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Example 4

• The concentration of OH- in a sample of seawater
  is 5 x 10-6 M. Calculate the concentration of
  H3O ions, and classify the solution as acidic,
  neutral, or basic.

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In boiling water (1000C) H3O 1 x
10-6 Can you explain that?
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Example 6

• Calculate the concentrations of H3O and OH- of
  the following solution
• Human blood pH 7.40

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Measuring pH

• Acid-base indicator
• 1.    The approximate pH of a solution can be
  determined by using an acid-base indicator
• a. A substance that changes color in a specific
  pH range
• b. HIn abbreviated
• c.  Exhibit pH-dependent color change
• The indicators are weak acids and have different
  colors in their acid (HIn) and conjugate base
  (In-) forms
• HIn H20
  H3O In-
• Color A
  Color B

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Measuring pH

•  
• 2.   More accurate pH measurements can be made
  by using a pH meter
• a) A device that measures the pH-dependent
  electrical potential of the test solution

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The pH in Solutions of Strong Acids and Strong
Bases

• Strong acids are nearly 100 dissociated in
  aqueous solution
• a) H3O and A- concentrations are equal to the
  initial concentration of the acid HA
  H3O
• (H3O coming from the dissociation of water
  can be neglected)
• b) Concentration of undissociated HA molecules
  is essentially zero
• c) The pH of a solution of a strong monoprotic
  acid is calculated from the H3O concentration
• pH -logH3O -logHA

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The pH in Solutions of Strong Acids and Strong
Bases

• Calculation of the pH of a diprotic (H2SO4)
  solution is more complicated because 100 of the
  H2SO4 molecules dissociate to give H3O and HSO4-
  ions
• 1. Less than 100 of the resulting HSO4- ions
  dissociate to give H3O and SO42- ions
• 2. Majority of H3O comes from first
  dissociation

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The pH in Solutions of Strong Bases

• The most familiar Strong bases are alkali metal
  hydroxides, MOH, (NaOH, KOH)
• a) Strong bases are nearly 100 dissociated in
  aqueous solution
• b) The pH of a strong base solution can be
  found
•      Example 0.01 M NaOH
  

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Equilibria in Solutions of Weak Acids

• Introduction
• 1. A weak acid is not the same as a dilute
  solution of a strong acid
• 2. A strong acid is 100 dissociated in aqueous
  solution
• 3. A weak acid is only partially dissociated

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Equilibria in Solutions of Weak Acids

• The dissociation of a weak acid in water is
  characterized by an equilibrium equation
• HA(aq) H2O(l) ? H3O(aq) A-(aq)
• H3O A-
• Ka -------------- Ka is the
  acid-dissociation constant
• HA
• pKa -log Ka
• Larger the Ka the stronger the acid
• Smaller the pKa the weaker the acid

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Question How can you obtain Ka for a weak
acid? Answer prepare a certain molar solution
and measure the pH Example A 0.25 M
hydrofluoric acid has a pH of 2.036 HF H2O
H3O F- H3O F- Ka
-------------- HF H3O F-
can be calculated from the measured pH HF the
undissociated part can be calculated from
the initial concentration minus the
concentration of dissociated part
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H3O 10-2.036 9.2 x 10-3 M F- Now we
calculate HF at equilibrium From the initial
concentration 0.25 M 9.2 x 10-3 is
dissociated HF 0.25 - 9.2 x 10-3 0.241
M undissociated 9.2 x 10-3 x 9.2 x
10-3 Ka -----------------------------
3.52 x 10-4 0.241
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Calculating Equilibrium Concentrations in
Solutions of Weak Acids

• Once the Ka value for a weak acid has been
  measured it can be used to calculate equilibrium
  concentrations and the pH in a solution of the
  acid
• Example 8 There are 8 steps (x is negligible)
• General equation HCN H2O ? H3O CN-
• 0.10 M HCN (hydrocyanic acid)

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HCN H2O H3O CN- Ka 4.9
x 10-10 H2O H2O H3O OH-
Kw 1.0 x 10-14 Simplifications H3O
CN- HCN HCNinitial
H3O CN- H3O2 Ka
----------------- ------------ 4.9 x
10-10 HCN
HCNinitial H3O2 Ka x
HCNinitial H3O v Ka x
HCNinitial
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What is the pH of a 0.1 M HCN?
_______________ H3O v Ka x
HCNinitial _____________
________ H3O v4.9 x 10-10 x 0.1
v4.9 x 10-11 H3O 7 x 10-6 pH
5.15
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Percent Dissociation in Solutions of Weak Acids

• HA dissociated
• dissociation ----------------- x 100
• HA initial
• 1. The higher the dissociation the stronger
  the acid
• 2. dissociation increases as Ka increases
• 3. dissociation in weak acids increases as
  dilution increases

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Calculation of the percent dissociation of a
1.00 M acetic acid which has a pH 2.38 H3O
10-2.38 4.2 x 10-3 M CH3COO-
4.2 x 10-3 M dissociation --------------- x
100 0.42 1.0 M
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For a 1 molar acetic acid the dissociation is
only 0.42 And we can make the simplification CH3
COOH at equilibrium CH3COOHinit (only
0.42 is dissociated) H3O
CH3COO- Ka ----------------------- 1.8 x
10-5 CH3COOHinit Now we
can calculate the pH of a given concentration
H3O2 Ka ------------------
solving for H3O CH3COOHinit
_______________ H3O vKa
CH3COOHinit
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For a weak acid, the dissociation increases
with increasing dilution!! A 0.01 M CH3COOH has
a pH of 3.38 H3O 10-3.38 4.2 x 10-4
CH3COOHdissociated H3O
dissociation -------------------------
-------------------- CH3COOHinitial
CH3COOHinitial 4.2 x 10-4
dissociation ------------ 4.2
0.01 Now we cannot make the simplification any
more CH3COOH at equilibrium CH3COOHinit
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H3OCH3COO-
x2 Ka ----------------------- 1.8 x 10-5
--------- CH3COOH
0.01 x x2 1.8 x 10-7 (1.8 x
10-5) x x2 (1.8 x 10-5) x - 1.8 x 10-7
0 This is a quadratic equation which has 2
solutions
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For a quadratic equation ax2 bx c
________ -b
v b2 4 ac the solution is x
----------------------- 2a In our case the
quadratic equation is x2 (1.8 x 10-5) x - 1.8 x
10-7 0
_______________________ - (1.8 x 10-5)
v(1.8 x 10-5)2 4 (-1.8 x 10-7) x
--------------------------------------------------
---- 2 x1
4.2 x 10-4 x2 - 4.3 x 10-4 Only the
positive value of x has physical meaning
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x 4.2 x 10-4 H3O pH - log H3O
3.38 Now we can calculate the other
concentrations CH3COO- x 4.2 x
10-4 CH3COOH 0.01 x 0.01 (4.2 x 10-4
) 0.0096
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Polyprotic Acids

• Acids that contain more than one dissociable
  proton
• dissociate in a stepwise manner
• H2SO4 H HSO4-
• HSO4- H SO42-
  
• Each dissociation has its own Ka labeled Ka1
  Ka2 etc.
• Ka1 gt Ka2 gt Ka3 it is harder to take a
  hydrogen from a compound that is already
  electron rich, proton deficient
• The principal reaction is the first
  dissociation
• Essentially all the H3O in the solution
  comes from the first dissociation .

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Example carbonic acid H2CO3 H2O
H3O HCO3- Ka1 4.3 x
10-7 HCO3- H2O H3O
CO3- Ka2 4.3 x 10-11
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Equilibria in Solutions of Weak Bases

• Weak bases accept a proton from water to give the
  conjugate acid of the base and OH- ions
• NH3(aq) H2O(l) ? NH4(l) OH-(aq)
• Equilibrium Expression
• NH4 OH-
• Kb -------------------
• NH3
• Kb base-dissociation Constant

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Relation between Ka and Kb Ka strength of an
acid Kb strength of a base For a conjugate
acid-base pair the two equilibrium constants
are related
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Relation Between Ka and Kb

• NH4(aq) H2O(l) ? H3O(aq) NH3(aq) Ka
  H3O NH3
• NH4
•  
• NH3(aq) H2O(l) ? NH4(l) OH-(aq)
  Kb NH4OH-
• NH3
•  
• Net 2 H2O(l) ? H3O(aq) OH-(aq)
  
• Kw H3OOH- 1 x 10-14
• Ka x Kb Kw for conjugate acid-base pairs
  only!!!

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Acid-base Properties of Salts

• Introduction
• When an acid neutralizes a base, an ionic
  compound called a salt is formed.
• Salt solutions can be neutral, acidic, or basic
• 3. The pH depends on the acid-base properties of
  the cations and anions that result from the
  reaction
• a) Strong acid strong base ? Neutral solution
• b) Strong acid weak base ? Acidic solution
• c) Weak acid strong base ? Basic solution

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Acid-base Properties of Salts

• a) Salts that yield neutral solutions
• The following ions do not react appreciably with
  water to produce either H3O or OH- ions
• Cations from strong bases
• 1. Alkali metal cations of group 1A (Li, Na,
  K)
• 2. Alkaline earth cations of group 2A (Ca2,
  Sr2, Ba2) except for Be2
• Anions from strong monoprotic acids
• 1. Cl-, Br-, I-, NO3-, CLO4-
• Salts that contain only these ions give neutral
  solutions in pure water

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• Salts that yield basic solutions
• The cation is from a strong base and the anion is
  from a weak acid, like NO2-, F-, CH3CO2-, CO2- ,
  CN-
• Dissolve KCN in water
• KCN K CN-
  proceeds to completion
• However, CN- is always at equilibrium with
  undissociated
• HCN!
• CN- H2O HCN OH-
• OH- is formed and thus the solutions becomes
  basic

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What is the pH of a 0.1 M KCN solution? CN-
H2O HCN OH- HCN
OH- Kw 10-14 Kb
----------------- ---- ------------
2.0 x 10-5 CN- Ka
4.9 x10-10 Simplifications HCN
OH- CN- CN-initial OH-2 -----
---- 2.0 x 10-5 CN-initial
___________ OH- v2 x 10-5 x 0.1 1.4 x
10-3 M H3O Kw / 1.4 x 10-3 7.1 x 10-12
M pH 11.15
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Acid-base Properties of Salts

• Salts that yield Acidic solutions
• The anion is from a strong acid. But cation is
  from a weak base.
• Example NH4Cl NH4 Cl-
• NH4 H2O NH3 H3O
• NH3H3O Kw 10-14
• Ka --------------- -------- -----------
  5.56 x 10-10
• NH4 Kb
  1.8 x 10-5

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Factors that Affect Acid Strength

• Hydrohalic acids

The variation in polarity in this series is much
less important than the variation in bond
strength, HF 567 kJ/mol to HI 299 kJ/mol In
general for binary acids in the same group of the
periodic table, the H-A bond strength is the most
important determinant of acidity.
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Factors that Affect Acid Strength

• The H-A bond strength generally decreases with
  increasing size of element A down a group, so
  acidity increases. Size of halogens F-small
  get bigger down the group, bond strength
  decreases and acidity increases from HF to HI.

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Factors that Affect Acid Strength

• For binary acids of elements in the same row of
  the periodic table, changes in the H-A bond
  strength are smaller, and the polarity of the H-A
  bond is the most important determinant of acid
  strength.

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Lewis acids and Lewis bases
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Lewis general definition of Acids and Bases

• Lewis acid An electron pair acceptor
• Lewis base- An electron pair donor
• NH3 is a Bronsted/Lowry base because it accepts a
  proton NH3 H2O NH4 OH-
• H
  H
• H N H H N
  H
• H
  H
• NH3 is a Lewis base too because it is an electron
  pair donor

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• Lewis acid An electron pair acceptor
• Lewis base- An electron pair donor
• All Bronstedt-Lowry bases are Lewis bases
• since all proton acceptors have an unshared pair
  of electrons
• Lewis acid is more general than the
  Bronsted-Lowry
• (all Lewis acids are not also Bronsted-Lowry
  acids)
• Lewis acids include not only protons (H) but
  also all other
• cations and neutral molecules having vacant
  valence orbitals
• to accept a pair of electrons from a Lewis base

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Example Most heavy metal ions are hydrated in
water Cu(H2O)52 Cu2 5 O-H
Cu O-H H
H Lewis Lewis acid
base
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Lewis Acids and Bases
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Example 11

• For each of the following reactions, identify the
  Lewis acid and the Lewis base
• AlCl3 Cl- ? AlCl4-
• 2 NH3 Ag ? Ag(NH)2
• SO2 OH- ? HSO3-
• 6 H2O Cr3 ? Cr(OH2)63

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