This document discusses acid-base equilibria, including definitions of acids and bases according to Bronsted-Lowry theory. It covers water's behavior as both an acid and a base, pH calculations, strong and weak acids/bases, and polyprotic acids. Key points addressed are: the autoionization of water, conjugate acid-base pairs, the relationship between Ka and Kb, and using Ka or Kb values to determine pH or calculate concentrations.

1. 9/12/2022
ACID-BASE EQUILIBRIA
Grade 12 STEM – Chem 2

2. Learning Objectives
At the end of our discussion, you should be able to:
1. Define Bronsted-Lowry acids and bases;
2. Discuss the acid-base property of water;
3. Calculate the pH from the concentration of hydrogen ion or
hydroxide ions in aqueous solutions; and,
4. Determine the pH of a solution of a weak acid or weak
base

3. • Acids: taste sour and cause dyes to change color.
• Bases: taste bitter and feel soapy.
• Arrhenius: acids increase [H+]; bases increase [OH-] in
solution.
• Arrhenius: acid + base  salt + water.
• Problem: the definition confines us to aqueous solution.
Acids and Bases: A Brief Review

4. The H+ Ion in Water
• The H+(aq) ion is simply a proton with no electrons. (H
has one proton, one electron, and no neutrons.)
• In water, the H+(aq) form clusters.
• The simplest cluster is H3O+(aq). Larger clusters are
H5O2
+ and H9O4
+.
• Generally we use H+(aq) and H3O+(aq) interchangeably.
Brønsted-Lowry Acids and Bases

5. Proton Transfer Reactions
Brønsted-Lowry: acid donates H+ and base accepts H+.
• Brønsted-Lowry base does not need to contain OH-.
• Consider HCl(aq) + H2O(l)  H3O+(aq) + Cl-(aq):
– HCl donates a proton to water. Therefore, HCl is an acid.
– H2O accepts a proton from HCl. Therefore, H2O is a base.
• Water can behave as either an acid or a base.
• Amphoteric substances can behave as acids and bases.
Brønsted-Lowry Acids and Bases

6. Conjugate Acid-Base Pairs
• Whatever is left of the acid after the proton is donated is
called its conjugate base.
• Similarly, whatever remains of the base after it accepts a
proton is called a conjugate acid.
• Consider:
– After HA (acid) loses its proton it is converted into A- (base).
Therefore HA and A- are conjugate acid-base pairs.
– After H2O (base) gains a proton it is converted into H3O+ (acid).
Therefore, H2O and H3O+ are conjugate acid-base pairs.
• Conjugate acid-base pairs differ by only one proton.
Brønsted-Lowry Acids and Bases
HA(aq) + H2O(l) H3O+(aq) + A-(aq)

7. Relative Strengths of Acids and Bases
• The stronger the acid, the weaker the conjugate base.
• H+ is the strongest acid that can exist in equilibrium in
aqueous solution.
• OH- is the strongest base that can exist in equilibrium in
aqueous solution.
Brønsted-Lowry Acids and Bases

9. The Ion Product of Water
• In pure water the following equilibrium is established
• at 25 C
• The above is called the autoionization of water.
The Autoionization of Water
H2O(l) + H2O(l) H3O+(aq) + OH-(aq)
14
-
3
-
3
2
2
2
2
-
3
10
0
.
1
]
OH
][
O
H
[
]
OH
][
O
H
[
]
O
H
[
]
O
H
[
]
OH
][
O
H
[










w
eq
eq
K
K
K

10. The Autoionization of Water
• [H+] = [OH-] neutral
• [H+] > [OH-] acidic ( [H+] > 1.0x10-7 M )
• [H+] < [OH-] basic ( [H+] < 1.0x10-7 M )

11. Calculate [H+] in an aqueous solution in which [OH-] is 1.8x10-9 M. Is this an acidic
or basic solution at 25oC?

12. • In most solutions [H+(aq)] is quite small.
• We define
• In neutral water at 25 C, pH = pOH = 7.00.
• In acidic solutions, [H+] > 1.0  10-7 M , so pH < 7.00.
• In basic solutions, [H+] < 1.0  10-7 M , so pH > 7.00.
• The higher the pH, the lower the pOH, the more basic the
solution.
The pH Scale
]
OH
log[
pOH
]
H
log[
]
O
H
log[
pH -
3 




 

pOH
pH
OH
H






10
]
[
10
]
[

13. • Most pH and pOH values fall between 0 and 14.
• There are no theoretical limits on the values of pH or pOH. (e.g.
pH of 2.00 M HCl is -0.301.)
• Number of decimals in the log equals number of sig. figs. in the
original number.
• [Number of decimals in p-scale equals number of sig. figs. in
the concentration value.]
The pH Scale

14. 1. Calculate the pH of an aqueous solution for which (a) [H+] = 1.0x10-7 M ;
(b) [H+] = 1.4x10-3 M; (c) [OH-] = 2.0x10-3 M .
2. An antacid tablet has a pH of 9.18. Calculate the hydrogen ion
concentration.

16. Other “p” Scales
• In general for a number X,
• For example, pKw = -log Kw.
The pH Scale
X
log
X
p 

 
14
pOH
pH
14
]
OH
log[
]
H
log[
14
]
OH
][
H
[
log
pK
10
0
.
1
]
OH
][
H
[
-
-
w
14
-
















w
K

17. Measuring pH
• Most accurate method to measure pH is to use a pH
meter.
• However, certain dyes change color as pH changes.
These are indicators.
• Indicators are less precise than pH meters.
• Many indicators do not have a sharp color change as a
function of pH.
• Most indicators tend to be red in more acidic solutions.
The pH Scale

18. The pH Scale

19. Strong Acids
• The strongest common acids are HCl, HBr, HI, HNO3,
HClO3, HClO4, and H2SO4.
• Strong acids are strong electrolytes.
• All strong acids ionize completely in solution:
HNO3(aq) + H2O(l)  H3O+(aq) + NO3
-(aq)
• Since H+ and H3O+ are used interchangeably, we write
HNO3(aq)  H+(aq) + NO3
-(aq)
Strong Acids and Bases

20. What is the concentration of the acid for an aqueous solution of HNO3 that
has a pH of 2.34 ?

21. Strong Bases
• Most ionic hydroxides are strong bases (e.g. NaOH,
KOH, and Ca(OH)2).
• Strong bases are strong electrolytes and dissociate
completely in solution.
• The pOH (and hence pH) of a strong base is given by the
initial molarity of the base. Be careful of stoichiometry.
Strong Acids and Bases
1. Calculate pH of 0.029 M NaOH.
2. Calculate [Ca(OH)2] for which the pH is 11.68 .

22. 1. Calculate pH of 0.029 M NaOH.
2. Calculate [Ca(OH)2] for which the pH is 11.68 .

23. 1. Calculate pH of 0.029 M NaOH.
2. Calculate [Ca(OH)2] for which the pH is 11.68 .

24. • Weak acids are only partially ionized in solution.
• There is a mixture of ions and unionized acid in solution.
• Therefore, weak acids are in equilibrium:
Weak Acids
HA(aq) + H2O(l) H3O+(aq) + A-(aq)
HA(aq) H+
(aq) + A-
(aq)
]
HA
[
]
A
][
O
H
[ -
3


a
K
]
HA
[
]
A
][
H
[ -


a
K

25. • Ka is the acid dissociation constant.
• Note [H2O] is omitted from the Ka
expression. (H2O is a pure liquid.)
• The larger the Ka the stronger the acid
(i.e. the more ions are present at
equilibrium relative to unionized
molecules).
• If Ka >> 1, then the acid is completely
ionized and the acid is a strong acid.
Weak Acids
Ka Samples

26. Calculating Ka from pH
• Weak acids are simply equilibrium calculations.
• The pH gives the equilibrium concentration of H+.
• Using Ka, the concentration of H+ (and hence the pH) can be calculated.
– Write the balanced chemical equation clearly showing the equilibrium.
– Write the equilibrium expression. Find the value for Ka.
– Write down the initial and equilibrium concentrations for everything except
pure water. We usually assume that the change in concentration of H+ is x.
• Substitute into the equilibrium constant expression and solve. Remember to turn
x into pH if necessary.
Weak Acids
Niacin, one of the B-vitamins, is a 0.020 M solution of niacin, has a pH of 3.26 .
(a) What is the Ka ?
(b) What % of acid was ionized in the solution?

27. Niacin, one of the B-vitamins, is a 0.020 M solution of niacin, has a pH of 3.26 .
1. What is the Ka ?
2. What % of acid was ionized in the solution?

28. Using Ka to Calculate pH
• Percent ionization is another method to assess acid
strength.
• For the reaction
Weak Acids
HA(aq) + H2O(l) H3O+(aq) + A-(aq)
100
]
HA
[
]
O
H
[
ionization
%
0
3



eqm
Calculate the pH of a 0.20 M HCN solution. Ka(HCN) = 4.9x10-10

29. Calculate the pH of a 0.20 M HCN solution. Ka(HCN) = 4.9x10-10

31. Using Ka to Calculate pH
• Percent ionization relates the equilibrium H+
concentration, [H+]eqm, to the initial HA concentration,
[HA]0.
• The higher percent ionization, the stronger the acid.
• Percent ionization of a weak acid decreases as the
molarity of the solution increases.
• For acetic acid, 0.05 M solution is 2.0 % ionized whereas
a 0.15 M solution is 1.0 % ionized.
Weak Acids

32. 100
]
[
%
2
1
x
HA
Ka
I
o










33. Polyprotic Acids
• Polyprotic acids have more than one ionizable proton.
• The protons are removed in steps not all at once:
• It is always easier to remove the first proton in a
polyprotic acid than the second.
• Therefore, Ka1 > Ka2 > Ka3 etc.
Weak Acids
H2SO3(aq) H+(aq) + HSO3
-(aq) Ka1 = 1.7 x 10-2
HSO3
-(aq) H+(aq) + SO3
2-(aq) Ka2 = 6.4 x 10-8

34. Polyprotic Acids
Weak Acids
• The solubility of CO2 in pure water at 25oC and 0.1 atm is 0.0037 M. Assume
the formation of H2CO3 (carbonic acid), (A) What is the pH of a 0.0037 M solution
of H2CO3? (B) What is the CO3
2- concentration?
• Answers: (A) 4.40 (B) 5.6x10-11 M

35. • The solubility of CO2 in pure water at 25oC and 0.1 atm is 0.0037 M. Assume
the formation of H2CO3 (carbonic acid), (A) What is the pH of a 0.0037 M solution
of H2CO3? (B) What is the CO3
2- concentration?
• Answers: (A) 4.40 (B) 5.6x10-11 M

36. • The solubility of CO2 in pure water at 25oC and 0.1 atm is 0.0037 M. Assume
the formation of H2CO3 (carbonic acid), (A) What is the pH of a 0.0037 M solution
of H2CO3? (B) What is the CO3
2- concentration?
• Answers: (A) 4.40 (B) 5.6x10-11 M

37. • Weak bases remove protons from substances.
• There is an equilibrium between the base and the
resulting ions:
• Example:
• The base dissociation constant, Kb , is defined as
Weak Bases
Weak base + H2O conjugate acid + OH-
NH3(aq) + H2O(l) NH4
+(aq) + OH-(aq)
]
NH
[
]
OH
][
NH
[
3
-
4


b
K

38. Types of Weak Bases
• Bases generally have lone pairs or negative charges in order to
attack protons.
• Most neutral weak bases contain nitrogen.
• Amines are related to ammonia and have one or more N-H bonds
replaced with N-C bonds (e.g., CH3NH2 is methylamine).
• Anions of weak acids are also weak bases. Example: OCl- is the
conjugate base of HOCl (weak acid):
Weak Bases
ClO-(aq) + H2O(l) HClO(aq) + OH-(aq) Kb = 3.3 x 10-7
• Calculate [OH-] and pH of a 0.15 M solution of NH3 . (Kb = 1.8x10-5)

40. • Calculate [OH-] and pH of a 0.15 M solution of NH3 . (Kb = 1.8x10-5)
Ans: pH = 11.22
Solution

42. • We need to quantify the relationship between strength of
acid and conjugate base.
• When two reactions are added to give a third, the
equilibrium constant for the third reaction is the product
of the equilibrium constants for the first two:
Reaction 1 + reaction 2 = reaction 3
has
Relationship Between Ka and Kb
2
1
3 K
K
K 


43. For a conjugate acid-base pair
• Therefore, the larger the Ka, the smaller the Kb. That is,
the stronger the acid, the weaker the conjugate base.
• Taking negative logarithms:
Relationship Between Ka and Kb
b
a
w K
K
K 

b
a
w pK
pK
pK 

• Calculate Kb for F- ; given: Ka(HF) = 6.8x10-4
• Calculate Ka for NH4
+ ; given: Kb(NH3) = 1.8x10-5

44. • Calculate Kb for F-; given: Ka(HF) = 6.8x10-4
• Calculate Ka for NH4
+ ; given: Kb(NH3) = 1.8x10-5

45. • Calculate Kb for F-; given: Ka(HF) = 6.8x10-4
• Calculate Ka for NH4
+ ; given: Kb(NH3) = 1.8x10-5

46. Relationship Between Ka and Kb

47. Preview
• Neutral Solution – produced by salts that are made from
Cations of Strong Bases and Anions of Strong Acids.
• Basic Solution – formed if Anion of salt is the conjugate
base of a weak acid.
• Acidic Solution – formed if Cation of salt is the
conjugate acid of a weak base or if salt contains a highly
charged metal ion.
• If salt contains cation and anion that can both affect
pH, then compare Ka and Kb.
Acid-Base Properties of Salt Solutions

48. • Nearly all salts are strong electrolytes.
• Therefore, salts exist entirely of ions in solution.
• Acid-base properties of salts are a consequence of the
reaction of their ions in solution.
• The reaction in which ions produce H+ or OH- in water is
called hydrolysis.
• Anions from weak acids are basic.
• Anions from strong acids are neutral.
Acid-Base Properties of Salt Solutions

49. An Anion’s Ability to React with Water
• Anions, X-, can be considered conjugate bases from
acids, HX.
• IF X- comes from a strong acid, then it is neutral.
• If X- comes from a weak acid, then
• The pH of the solution can be calculated using
equilibrium!
Acid-Base Properties of Salt Solutions
X-(aq) + H2O(l) HX(aq) + OH-(aq)
Example: Calculate the pH of a 0.15 M Sodium Acetate solution.
Give: Kb(C2H3O2
-) = 5.6x10-10 Answer:8.96

50. Example: Calculate the pH of a 0.15 M Sodium Acetate solution.
Give: Kb(C2H3O2
-) = 5.6x10-10 Answer:8.96

51. An Cation’s Ability to React with Water
• Polyatomic cations with ionizable protons can be
considered conjugate acids of weak bases.
• Some metal ions react in solution to lower pH.
Combined Effect of Cation and Anion in Solution
• An anion from a strong acid has no acid-base properties.
• An anion that is the conjugate base of a weak acid will
cause an increase in pH.
Acid-Base Properties of Salt Solutions
NH4
+(aq) + H2O(l) NH3(aq) + H3O+(aq)

52. Combined Effect of Cation and Anion in Solution
• A cation that is the conjugate acid of a weak base will
cause a decrease in the pH of the solution.
• Metal ions will cause a decrease in pH except for the
alkali metals and alkaline earth metals.
• When a solution contains both cations and anions from
weak acids and bases, use Ka and Kb to determine the
final pH of the solution.
Acid-Base Properties of Salt Solutions
Qualitatively: If Ka > Kb acidic; If Ka < Kb basic;
If Ka = Kb neutral

53. Summary
• Neutral Solution – produced by salts that are made from
Cations of Strong Bases and Anions of Strong Acids.
• Basic Solution – formed if Anion of salt is the conjugate
base of a weak acid.
• Acidic Solution – formed if Cation of salt is the
conjugate acid of a weak base or if salt contains a highly
charged metal ion.
• If salt contains cation and anion that can both affect
pH, then compare Ka and Kb.
Acid-Base Properties of Salt Solutions

54. Acid-Base Properties of Salt Solutions

55. Factors that Affect Acid Strength
Consider H-X. For this substance to be an acid we need:
• H-X bond to be polar with H+ and X- (if X is a metal
then the bond polarity is H-, X+ and the substance is a
base), [ i.e. Large Electronegativity ]
• the H-X bond must be weak enough to be broken, [ i.e.
Small Bond Strength ]
• the conjugate base, X-, must be stable. [ i.e. Weak base ]
Acid-Base Behavior and Chemical Structure

56. Binary Acids
• Acid strength increases across a period [ EN ] and down
a group [ bond strength, size ]
• Conversely, base strength decreases across a period and
down a group.
• HF is a weak acid because the bond energy is high.
• The electronegativity difference between C and H is so
small that the C-H bond is non-polar and CH4 is neither
an acid nor a base.
Acid-Base Behavior and Chemical Structure

57. Binary Acids
Acid-Base Behavior and Chemical Structure

58. Oxyacids
• Oxyacids contain O-H bonds.
• All oxyacids have the general structure Y-O-H.
• The strength of the acid depends on Y and the atoms
attached to Y.
– If Y is a metal (low electronegativity), then the substances are
bases.
– If Y has intermediate electronegativity (e.g. I, EN = 2.5), the
electrons are between Y and O and the substance is a weak
oxyacid.
Acid-Base Behavior and Chemical Structure

59. Oxyacids
Acid-Base Behavior and Chemical Structure

60. Carboxylic Acids
• Carboxylic acids all contain the COOH group.
• All carboxylic acids are weak acids.
• When the carboxylic acid loses a proton, it generate the
carboxylate anion, COO-.
Acid-Base Behavior and Chemical Structure
R
C
OH
O

61. • Brønsted-Lowry acid is a proton donor.
• Focusing on electrons: a Brønsted-Lowry acid can be
considered as an electron pair acceptor.
• Lewis acid: electron pair acceptor.
• Lewis base: electron pair donor.
• Note: Lewis acids and bases do not need to contain
protons.
• Therefore, the Lewis definition is the most general
definition of acids and bases.
Lewis Acids and Bases

62. • Lewis acids generally have an incomplete octet (e.g.
BF3).
• Transition metal ions are generally Lewis acids.
• Lewis acids must have a vacant orbital (into which the
electron pairs can be donated).
• Compounds with p-bonds can act as Lewis acids:
H2O(l) + CO2(g)  H2CO3(aq)
Lewis Acids and Bases

63. Hydrolysis of Metal Ions
• Metal ions are positively charged and attract water
molecules (via the lone pairs on O).
• The higher the charge, the smaller the metal ion and the
stronger the M-OH2 interaction.
• Hydrated metal ions act as acids:
• The pH increases as the size of the ion increases (e.g.
Ca2+ vs. Zn2+) and decreases as the charge increases (Na+
vs. Ca2+ and Zn2+ vs. Al3+).
Lewis Acids and Bases
Fe(H2O)6
3+(aq) Fe(H2O)5(OH)2+(aq) + H+(aq)
Ka = 2 x 10-3

64. Hydrolysis of Metal Ions
Lewis Acids and Bases

65. Acid-Base Equilibria
Arrhenius
Definition
Autoionization
of Water
Bronsted-Lowry
Acids-Bases
pH Scale
Weak Acids Weak Bases
Strong
Acids/Bases
Chemical
Structure
Salt Solutions
Lewis
Acids/Bases
14
-
10
0
.
1
]
OH
][
H
[ 




w
K ]
H
log[
pH 


14
pOH
pH 

]
HA
[
]
A
][
H
[ -


a
K
100
]
HA
[
]
H
[
I
%
0



eqm
b
a
w K
K
K 

Conjugate Acid-Base Pairs