AP Chemistry 8.7 pH and pKa Study Notes - New Syllabus Effective fall 2024

AP Chemistry 8.7 pH and pKa Study Notes- New syllabus

AP Chemistry 8.7 pH and pKa Study Notes – AP Chemistry – per latest AP Chemistry Syllabus.

LEARNING OBJECTIVE

Explain the relationship between the predominant form of a weak acid or base in solution at a given pH and the pK_a of the conjugate acid or the pKb of the conjugate base

Key Concepts:

pH & pK_a

AP Chemistry-Concise Summary Notes- All Topics

pH and pKa

Based on the pH of the environment, you can tell the relative ratio of conjugate base to acid
If pH < pKa, then the acid form has the higher concentration
- Weak base & conj acid → conj acid has higher concentration
If pH > pKa, then the conjugate base form has the higher concentration
- Weak base & conj acid → weak base has higher concentration

Acid-Base Indicators

Used in titrations to indicate when we have passed the equivalence point
Are weak acids that change color when they become bases
Endpoint: when the indicator changes color → tell us we have reached the eq point
Indicators have a “useful range” → have kA and pKa values
Useful indicator range =
- Best indicator to choose for a particular titration will be the one whose useful range includes or is closest to the pH at equivalence for that particular titration

8.7.A.1 Protonation State Determined by pH Relative to pKa:

1. Acid–Base Basics:

Definitions of Acids and Bases:

There are a number of definitions of acids and bases, depending on the theory employed:

i. Arrhenius Definition:

* Acid: Raises H⁺ (or H₃O⁺) level in aqueous solution.
Example: HCl → H⁺ + Cl⁻
* Base: Raises OH⁻ level in aqueous solution.
Example: NaOH → Na⁺ + OH⁻

ii. Brønsted–Lowry Definition:

* Base: Proton (H⁺) acceptor
Example: NH₃ + H₂O ⇌ NH₄⁺ + OH⁻
→ NH₃ is the base (accepts H⁺), H₂O is the acid (donates H⁺)

iii. Lewis Definition:

* Base: Electron pair donor
Example: BF₃ + NH₃ → F₃B–NH3

iv. Conjugate Acid–Base Pairs:

When an acid donates a proton, it becomes its conjugate base.
When a base receives a proton, it becomes its conjugate acid.

v. General Reaction:

HA ⇌ H⁺ + A⁻

* HA = Acid
* A⁻ = Conjugate base
* H⁺ = Proton

Example:

HCl ⇌ H⁺ + Cl⁻

* HCl is the acid → Cl⁻ is its conjugate base.

NH₄⁺ ⇌ H⁺ + NH₃

* NH₄⁺ is the acid → NH₃ is the conjugate base.

vi. Conjugate Pairs Summary:

Acid (HA)	Conjugate Base (A⁻)
HCl	Cl⁻
H₂SO₄	HSO₄⁻ or SO₄²⁻
H₂CO₃	HCO₃⁻ or CO₃²⁻
NH₄⁺	NH₃
H₂O	OH⁻

All acid–base reactions will have two conjugate pairs.

2. pH and pKa Concepts:

i. pH and pKa Definitions:

a. The Meaning of pH

pH defines the degree of solution’s acidity which in return depends on concentration of hydrogen ions (H+ or H₃O+) present in the solution.

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

Low pH (0–6.9) = acidic

pH = 7 = neutral (in case of pure water)

High pH (7.1-14) = basic (aka alkaline)

b. The Meaning of pKa:

pKa measures the strength of an acid, or more precisely, the ease at which a proton is lost.

It can be calculated as: $\boxed{\text{pKa} = -\log K_a}$

from dissociation constant of an acid Ka:

Small pKa means strong acid.
Large pKa indicates weak acid.

ii. How pH, pKa, and Strength of Acid Relate:

Henderson–Hasselbalch equation defines the relationship of two values.

$pH = pKa + \log (\frac{[A^{-}]}{[HA]})$

Where:

* HA = is the acid

* A⁻ = conjugate base of the acid.

From this equation, you can also derive:

* At pH = pKa, [HA] = [A⁻], half of the acid is dissociated.

* As for the scenario pH < pKa, there is more HA (the solution is more acidic).

* As for the second case of pH > pKa, there is more A⁻

3. Protonation vs. Deprotonation:

Protonation vs. Deprotonation:

When an acid (HA) is in solution, it can either:

Keep its proton → it stays protonated (HA)
Lose its proton → it becomes deprotonated (A⁻)

The extent to which this happens depends on the pH relative to the pKa of the acid.

Key Rule:

$\boxed{ \begin{cases} \text{If } \text{pH} < \text{pKa} &\Rightarrow \text{Mostly HA (protonated)} \\ \text{If } \text{pH} > \text{pKa} &\Rightarrow \text{Mostly A⁻ (deprotonated)} \end{cases} }$

Why This Happens:

When pH < pKa, the solution has more H⁺ → the acid tends to hold onto its proton → stays protonated (HA).
When pH > pKa, the solution has fewer H⁺ → the acid tends to lose its proton → becomes deprotonated (A⁻).

pH Value	Relative to pKa	Result
3.0	pH < pKa	Mostly CH₃COOH (HA)
4.75	pH = pKa	50% CH₃COOH, 50% CH₃COO⁻
6.0	pH > pKa	Mostly CH₃COO⁻ (A⁻)

8.7.A.2 Acid-Base Indicators Change Properties with pH:

1. Protonation and pH:

i. Protonation and pH

Protonation vs. Deprotonation:

* Protonation is all about gaining a proton (H⁺)
* Deprotonation is about losing a proton (H⁺)

Whether a molecule is protonated or deprotonated depends on the pH of the solution compared to the molecule’s pKa.

Core Rule: $pH < pKa \Rightarrow Mostly Protonated (HA)$

$\boxed{ \text{pH < pKa} \Rightarrow \text{Mostly Protonated (HA)} \\ \text{pH > pKa} \Rightarrow \text{Mostly Deprotonated (A⁻)} }$

ii. How pH Influences Protonation State:

When pH is low (acidic):

* There’s a lot of H⁺ floating around
* Molecules are likely to stay protonated
* For example, a weak acid like acetic acid (CH₃COOH) will remain in its HA form

When pH is high (basic):

* There’s less H⁺ available
* Molecules are more likely to let go of their proton
* This results in the substance becoming deprotonated (A⁻ form)

Condition	[H⁺] Level	Protonation Likely?	Result
pH < pKa	High (acidic)	Yes	Protonated (HA)
pH = pKa	Balanced	50% each	Half HA, half A⁻
pH > pKa	Low (basic)	No	Deprotonated (A⁻)

2. Indicator Color Changes:

* Indicators are weak acids or bases that shift colors based on pH levels.
* They come in two forms:

* HIn (protonated) → Color A
* In⁻ (deprotonated) → Color B

$HIn ⇌ H^{+} + {In}^{-}$

* pH < pKa → predominantly HIn → Color A
* pH > pKa → predominantly In⁻ → Color B
* pH ≈ pKa → a blend of both colors (transition)

Examples:

Indicator	pKa	Color (Low pH)	Color (High pH)
Methyl orange	~3.7	Red	Yellow
Bromothymol blue	~7.0	Yellow	Blue
Phenolphthalein	~9.4	Colorless	Pink

The color change happens because of structural differences between the protonated and deprotonated forms, which influence light absorption.

3. pKa and Transition Range:

* Every indicator has a unique pKa — the pH level where 50% is protonated (HIn) and 50% is deprotonated (In⁻).
* The color change happens within a tight pH range centered around the pKa.

$Transition range \approx pKa \pm 1$

ii. How It Works:

pH Range	Form Dominant	Color Shown
pH < pKa − 1	Mostly HIn	Color A (acid form)
pH ≈ pKa	Mix of HIn and In⁻	Intermediate color
pH > pKa + 1	Mostly In⁻	Color B (base form)

8.7.A.3 Choose Indicators with pKa Near Equivalence Point pH:

1. Equivalence Point in Titration:

In a titration, the equivalence point is the moment when the amount of titrant added perfectly matches the amount of analyte in the sample, meaning that all the acid or base has been neutralized.

a. pH at the Equivalence Point:

The pH at the equivalence point varies based on the type of acid and base used in the titration:

Strong Acid + Strong Base

Here, the equivalence point lands at pH = 7 because the resulting products (water and salt) don’t influence the pH.

Weak Acid + Strong Base

In this case, the equivalence point is at pH > 7. The conjugate base of the weak acid (which forms after neutralization) will hydrolyze, making the solution a bit basic.

Strong Acid + Weak Base

* For this combination, the equivalence point is at pH < 7. The conjugate acid of the weak base will dissociate, resulting in a slightly acidic solution.

2. Indicator pKa and Color Change:

i. pH at Equivalence Point:

* At the equivalence point, the amounts of acid and base are chemically equivalent. The pH here varies based on the specific acid and base involved:

* Strong acid + strong base → pH = 7
* Weak acid + strong base → pH > 7
* Strong acid + weak base → pH < 7

ii. Indicator Color Change:

* An indicator changes color when its protonated and deprotonated forms display different colors. The pKa of the indicator tells us the pH at which this color change occurs.

$HIn ⇌ H^{+} + {In}^{-}$

* If the pKa of the indicator is close to the pH at the equivalence point, the color change will happen right around the equivalence point, making it easy to see when the titration is complete.

iii. Indicator’s pKa and the Transition Range:

* The color change of an indicator takes place over a pH range (usually about ±1 pH unit from its pKa). To make sure the color change aligns with the equivalence point, the indicator’s pKa should be near the pH at that point.

Example:

* Titrating a strong acid with a strong base:

* Equivalence point: pH ≈ 7
* Indicator: Phenolphthalein (pKa ≈ 9.4)

* Phenolphthalein shifts from colorless to pink around pH 8

AP Chemistry 8.7 pH and pKa Study Notes

AP Chemistry 8.7 pH and pKa Study Notes - New Syllabus Effective fall 2024