Relating pH to Acid and Base
Concentrations
AP CHEMISTRY
Acid-Base Chemistry and pH
 The chemistry of an aqueous solution often depends
critically on pH
 It is therefore important to examine how pH relates
to acid and base concentrations

The simplest cases are those involving strong acids and bases
Calculating pH for Strong Acids
 Remember, strong acids are strong electrolytes
 Aqueous solutions of strong acids consists entirely of conjugate
base ions and H3O+ ions
 Equilibrium lies very far to the right so LARGE Ka
 The acid is the only significant source of H+ ions
 As a result, calculating the pH of a solution of a strong acid is
straight forward because [H+] equals the original
concentration of acid
Strong Acid Animation
Steps for Calculating pH of Strong Acids
THINK – Strong acid, complete dissociation!
2. WRITE – Dissociation equation
3. WRITE – Major species at equilibrium
1.

H+, A-, H2O
4. THINK – At equilibrium:
 [HA] ≈ 0.0 M, [H+] = [A-] = [HA]0
5. WRITE – pH = -log[H+]
 [H+] from the autoionization of water is 1.0 x 10-7 which is
very small relative to [H+] from the acid, so neglect it!
Practice!
 #1 on Ka Practice WS
Calculating pH for Weak Acids
 Remember, weak acids only partially ionize in aqueous
solution


Aqueous solutions of weak acids are equilibria systems
At equilibrium, solutions consist almost entirely of acid molecules
with only relatively few H3O+ and conjugate base ions

Ka is much smaller than 1
Weak Acid Animation
 We can use the equilibrium constant for the ionization
reaction to express the extent to which a weak acid
ionizes

As a result, calculating the pH of a weak acid solution always
represents an equilibrium condition
Steps for Calculating pH of Weak Acid Solutions
THINK – Weak acid, incomplete dissociation!
2. WRITE – Equilibrium equation
3. WRITE – Major species at equilibrium
1.

4.
HA and H2O
THINK – Do not know equilibrium conditions so use
ICE table and Ka expression to solve for [H+] ([H3O+] )
 Make assumption that [HA]int – x = [HA]eq = [HA]int if Ka
<< 1
WRITE – pH = -log[H+]
5.

[H+] from the autoionization of water is 1.0 x 10-7 which is very small
relative to [H+] from the acid, so neglect it!
Practice!
Let’s take a look at AP FRQ #18 WS!
Using % Ionization to Measure Acid Strength
 We have seen that the magnitude of Ka indicates the
strength of a weak acid
 Another measure of acid strength is percent
ionization, and it is mathematically defined as:
[H+ ]equilibrium
Percent Ionization =
× 100
[HA]initial
Solving Weak Acid Equilibrium Problems
Calculating Percent Ionization
THINK – Weak acid, incomplete dissociation!
2. WRITE – Equilibrium equation
3. WRITE – Major species at equilibrium
1.

HA and H2O
4. THINK – Do not know equilibrium conditions so
use ICE table and Ka expression to solve for [H+]
([H3O+] )
 Make assumption that [HA]int – x = [HA]eq = [HA]int if
Ka << 1
5. WRITE – %dissociation =
[H+ ]
[HA]0
× 100
Practice!
 #11 on Ka Worksheet!
Weak Base Equilibria
The Strength of Bases
 If a base completely dissociates to produce OH- ions in
solution, it is a STRONG BASE
BOH (aq) → B+ (aq) + OH- (aq)
 Solution consists almost entirely of OH- ions and
conjugate acid ions with a negligible concentration of
base molecules
Because the reaction lies very far to the right, the equilibrium
constant, Kc, is much greater than 1


More products than reactants at equilibrium
Solving Strong Base Equilibrium Problems
Calculating pH
THINK – Strong base, complete dissociation!
2. WRITE – Dissociation equation
3. WRITE – Major species at equilibrium
1.

BH+, OH-, H2O
4. THINK – At equilibrium:
 [B] ≈ 0.0 M, [BH+] = [OH-] = [B]0
5. WRITE – pOH = -log[OH-]; pH = 14 - pOH
 [OH-] from the autoionization of water is 1.0 x 10-7 which is
very small relative to [OH-] from the base, so neglect it!
Weak Base Equilibria
 Weak bases react with water by abstracting protons from water
 Products include a conjugate acid and hydroxide ion (OH-)
B (aq) + H2O (l) ↔ BH+ (aq) + OH- (aq)
Because the reaction lies mostly to the left, the equilibrium constant Kc is much
less than 1


More reactants than products at equilibrium

Major species at equilibrium are B and H2O
 The equilibrium constant, K, has a specific notation for basic solutions, called the
base-dissociation constant:
Kb

Equilibrium expression is written the same as Kc:
[BH + ][OH − ]
Kb =
[B]
Solving Weak Base Equilibrium Problems
Calculating pH
THINK – Weak base, incomplete dissociation!
2. WRITE – Equilibrium equation
3. WRITE – Major species at equilibrium
1.

B and H2O
4. THINK – Do not know equilibrium conditions so
use ICE table and Kb expression to solve for [OH-]
 Make assumption that [B]int – x = [B]eq = [B]int if Kb <<
1
5. WRITE – pOH = -log[OH-]; pH = 14 - pOH
 [OH-] from the autoionization of water is 1.0 x 10-7 which is
very small relative to [OH-] from the base, so neglect it!
Practice!
 #5 on Kb worksheet!
Relationship Between Ka and Kb
 We have seen in a qualitative way that the stronger the
acid, the weaker its conjugate base
 The quantitative relationship that describes this
relationship is as follows:
K a × K b = K w = 1.0 × 10−14
 As the strength of the acid increases (Ka gets larger), the
strength of its conjugate base much decrease (Kb gets
smaller) so that the product K a × K b remains
1.0 × 10−14
Introducing pKa and pKb
 Recall that we often express [H+] as pH
pH = -log [H+]
 This “p” nomenclature is often used for other very
small numbers such as pKa and Kb
pKa = -log Ka
pKb = -log Kb
pKa + pKb = 14
Acids and Bases Tutorial
Solving Acid and Base pH Problems Tutorial