AP Chemistry 8.3 Weak Acid and Base Equilibria Study Notes - New Syllabus Effective fall 2024

AP Chemistry 8.3 Weak Acid and Base Equilibria Study Notes- New syllabus

AP Chemistry 8.3 Weak Acid and Base Equilibria Study Notes – AP Chemistry – per latest AP Chemistry Syllabus.

LEARNING OBJECTIVE

Explain the relationship among pH, pOH, and concentrations of all species in a solution of a monoprotic weak acid or weak base.

Key Concepts:

Acid-Base Reactions

AP Chemistry-Concise Summary Notes- All Topics

8.3.A.1 Ionization of Weak Acids in Water:

1. Weak Acid Ionization and Equilibrium:

A weak acid is one that does not ionize completely in water. Rather, it establishes a reversible equilibrium between the undissociated acid and its ionized products. The general equation for the ionization of a weak acid HA in water is: $H A (a q) + H_{2} O (l) ⇌ H_{3} O^{+} (a q) + A^{-} (a q)$

* HA = weak acid
* H3O = hydronium ion
* A = conjugate base of the acid

Unlike strong acids, which fully dissociate, weak acids produce only a low concentration of hydronium ions, and hence solutions of them are more basic (higher pH) than equivalent solutions of strong acids.

ii. Equilibrium Constant (Ka):

The strength of a weak acid is quantified by its acid dissociation constant Ka, which is given by:

$K_{a} = \frac{[H_{3} O^{+}] [A^{-}]}{[H A]}$

* A larger Ka means the acid ionizes more → stronger weak acid.
* A smaller Ka means less ionization → weaker acid.

2. Acid Strength and Ka:

The strength of an acid is a measure of the ability of the acid to donate protons (H⁺) in an aqueous solution. For weak acids, that is expressed in terms of the acid dissociation constant, Ka.

i. Definition of Ka:

For a representative weak acid HA dissolved in water: $H A (a q) + H_{2} O (l) ⇌ H_{3} O^{+} (a q) + A^{-} (a q)$

The acid dissociation constant is: $K_a = \frac{[H_3O^+][A^-]}{[HA]}$

ii. Interpreting Ka:

Large Ka → more ionization → stronger weak acid
Small Ka → less ionization → weaker acid

> For example, acetic acid has a of $1.8 \times 10^{-5}$ , which means that very few acetic acid molecules donate protons in water.

iii. Comparison Table:

Acid	$K_a$ value	Strength
Hydrochloric acid (HCl)	Very large (>>1)	Strong acid
Acetic acid (CH₃COOH)	$1.8 \times 10^{-5}$	Weak acid
Formic acid (HCOOH)	$1.8 \times 10^{-4}$	Stronger than acetic
Phenol (C₆H₅OH)	$1.1 \times 10^{-10}$	Very weak acid

iv. Key Takeaway:

The smaller the Ka, the less the acid ionizes, which is to say fewer hydronium ions are formed, and the acid is weaker.

8.3.A.2 Equilibrium and pH of Weak Acid Solutions:

1. Acid-Base Equilibrium and Ka/pKa:

Weak acids only partially ionize in water, establishing an equilibrium: $HA + H_2O \rightleftharpoons H_3O^+ + A^-$

This equilibrium is described by the acid dissociation constant Ka: $K_a$ $K_a = \frac{[H_3O^+][A^-]}{[HA]}$ To simplify comparison, we use pKa: $\text{p}K_a = -\log K_a$

Lower pKa = Stronger acid

Higher pKa = Weaker acid

Quick Conversion:

$K_a = 10^{-\text{p}K_a}$

This relationship helps predict acid strength and calculate pH.

2. pH Calculation of Weak Acids:

To calculate the pH of a weak acid:

Write the ionization equation:
$HA \rightleftharpoons H_3O^+ + A^-$
Set up the ICE table (Initial, Change, Equilibrium).
Use the Ka expression:
$K_a = \frac{x^2}{[HA]_0 – x}$
Where x is the concentration of H3O+
Solve for x then calculate pH:
$\text{pH} = -\log [H_3O^+]$

8.3.A.3 Ionization of Weak Bases in Water:

1. Ionization of Weak Bases:

Weak bases partially ionize when dissolved in water, releasing hydroxide ions (OH⁻) and their conjugate acid at equilibrium.

The general equation for ionization of a weak base B in water is: $B (aq) + H_2O (l) \rightleftharpoons BH^+ (aq) + OH^- (aq)$

B = weak base
BH = conjugate acid
OH = hydroxide ion

2. Base Dissociation Constant (Kb):

The ionization is explained by the base dissociation constant Kb: $K_b = \frac{[BH^+][OH^-]}{[B]}$

A larger means more ionization → stronger weak base.
A smaller means less ionization → weaker base $\text{pH} = -\log [H_3O^+]$

8.3.A.4 Equilibrium and pH of Weak Base Solutions:

1. Equilibrium of Weak Bases:

Weak bases partially ionize when dissolved in water, forming an equilibrium between the un-ionized base B and its conjugate acid BH with hydroxide ions OH formed.

The equation for ionization is: $B (a q) + H_{2} O (l) ⇌ B H^{+} (a q) + O H^{-} (a q)$

At equilibrium, the concentrations of B, BH, and OH are constant.

2. Base Dissociation Constant (Kb):

The degree of ionization is characterized by the base dissociation constant Kb: $K_b = \frac{[BH^+][OH^-]}{[B]}$

* A larger Kb indicates more ionization → stronger weak base.
* A smaller Kb indicates less ionization → weaker base. $\text{pH} = -\log [H_3O^+]$

8.3.A.5 Calculating Percent Ionization of Weak Acids and Bases:

1. Definition and Importance of Percent Ionization:

Percent ionization measures how much a weak acid or base ionizes in solution:

$\text{Percent Ionization} = \left( \frac{[\text{Ionized form}]}{[\text{Initial acid/base}]} \right) \times 100$

For a weak acid: $\text{Percent Ionization} = \left( \frac{[H_3O^+]}{[HA]_0} \right) \times 100$

ii. Consequence of What’s Important:

Indicates acid/base strength: Greater ionization at higher percent ionization.
Represents concentration comparisons: Concentration differences are revealed.
Helpful in equilibrium problems: Assists in checking assumptions (e.g. whether $x \ll [HA]_0$ is valid).

iii. Key Point: Percent ionization is especially helpful for weak acids and bases because they do not dissociate fully, unlike strong acids and bases.

2. Calculation Methods:

i. Using Equilibrium Concentrations

$\text{Percent Ionization} = \left( \frac{[\text{Ionized form at equilibrium}]}{[\text{Initial concentration}]} \right) \times 100$

For a weak acid: $\text{Percent Ionization} = \left( \frac{[H_3O^+]}{[HA]_0} \right) \times 100$

ii. Using pKa (or pKb) and Initial Concentration

Use an ICE table and the Ka or pKa to solve for [H3O+] or [OH−]at equilibrium.
Then apply the percent ionization formula.

$\text{pH} = -\log [H_3O^+]$

8.3.A.6 Relationship Between Ka and Kb for Conjugate Acid-Base Pairs:

1. Conjugate Acid-Base Pairs and Ionization Constants:

A conjugate acid-base pair is two species that differ by one proton (H⁺):

* Acid ⇌ Conjugate base + H⁺
* Base + H⁺ ⇌ Conjugate acid

ii. Relationship Between Ka and Kb:

For a conjugate acid-base pair, the ionization constants are inversely related: $K_{a} \times K_{b} = K_{w}$

Where:

* Ka = acid dissociation constant of the acid
* Kb = base dissociation constant of the conjugate base
* Kw = at 25°C (ion-product of water)

iii. Implications:

* Strong acid → very weak conjugate base (large Ka, very small Kb)
* Weak acid → stronger conjugate base (smaller Ka, larger Kb)

iv. pKa and pKb Relationship:

pKa+pKb=14

This helps compare acid and base strength within a conjugate pair.

2. Relationship with Water’s Ionization Constant:

i. Water ionization offers a basic connection between conjugate acid-base pairs:

ii. Key Relationships:

Relationships:

$K_{w} = K_{a} \times K_{b}$

$\text{p}K_w = \text{p}K_a + \text{p}K_b$

Where:

$K_w = 1.0 \times 10^{-14}$ at 25°C (autoionization constant of water)
$K_a$ = acid dissociation constant of an acid
= base dissociation constant of its conjugate base
$\text{p}K_w = 14$ at 25°C

iii. What This Means:

* A strong acid has a large Ka → its conjugate base has a small Kb
* A weak acid has a smaller Ka → its conjugate base has a larger Kb

So, acid and base strengths are inversely relate via water:

Stronger acid⇒Weaker conjugate base,and vice versa

$\text{pH} = -\log [H_3O^+]$

AP Chemistry 8.3 Weak Acid and Base Equilibria Study Notes

AP Chemistry 8.3 Weak Acid and Base Equilibria Study Notes - New Syllabus Effective fall 2024