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\(\text{H}^+\) \(\text{A}^-\)

Acid-Base Concepts
\( \text{p}K_a \) & Conjugates

Master Brønsted-Lowry theory, understand what \( \text{p}K_a \) really measures, and predict the direction of proton-transfer reactions using conjugate pairs.

Organic Chemistry 1

What Is a Brønsted-Lowry Acid?

In organic chemistry, we use the Brønsted-Lowry definition: an acid is a proton (\( \text{H}^+ \)) donor, and a base is a proton acceptor. This is far more useful than the Arrhenius model because it works in any solvent, not just water.

Acid
Donates \( \text{H}^+ \) to another species
Base
Accepts \( \text{H}^+ \) from another species

Understanding Conjugate Pairs

When an acid donates a proton, it becomes its conjugate base. When a base accepts a proton, it becomes its conjugate acid. Every proton-transfer reaction has two conjugate pairs.

\(\text{HA}\) Acid donates \(\text{H}^+\) \(\text{A}^-\) Conjugate Base Conjugate Pair 1 \(\text{B}\) Base accepts \(\text{H}^+\) \(\text{BH}^+\) Conjugate Acid Overall: \(\text{HA} + \text{B}\)
⇌
\(\text{A}^- + \text{BH}^+\)

Why Acid-Base Chemistry Matters in Orgo

Nearly every organic mechanism begins or ends with a proton transfer. Understanding acidity lets you predict which bonds break, which nucleophiles form, and which leaving groups depart.

Reactivity
Stronger acids have weaker conjugate bases: better leaving groups
Mechanisms
Proton transfers are often the first or last step of a mechanism
Selectivity
\( \text{p}K_a \) values determine which proton is removed first

The Acid Dissociation Constant: \( K_a \)

The strength of an acid is quantified by its acid dissociation constant \( K_a \). For the generic reaction in water:

A larger \( K_a \) means the equilibrium lies further to the right: the acid ionizes more completely, so it is a stronger acid.

Defining \( \text{p}K_a \)

Because \( K_a \) values span many orders of magnitude (from \( 10^{10} \) to \( 10^{-50} \)), the logarithmic \( \text{p}K_a \) scale is more convenient. Key relationships:

Lower \( \text{p}K_a \)
Stronger acid. More willing to donate \( \text{H}^+ \).
Higher \( \text{p}K_a \)
Weaker acid. Less willing to donate \( \text{H}^+ \).

The \( \text{p}K_a \) Scale

-10 0 10 25 40 50 STRONGER ACID Weaker conj. base WEAKER ACID Stronger conj. base \(\text{HCl}\) (-7) \(\text{RCOOH}\) (5) \(\text{ROH}\) (16) \(\text{RNH}_2\) (38) \(\text{RH}\) (50) \(\text{p}K_a\) increases →

Predicting Reaction Direction

In a proton-transfer reaction, equilibrium always favors formation of the weaker acid and weaker base: the side with the higher \( \text{p}K_a \).

\(\text{HA}\) \(\text{p}K_a = 5\) + \(\text{B}^-\) favored \(\text{A}^-\) + \(\text{BH}\) \(\text{p}K_a = 16\) Equilibrium favors the side with the higher \(\text{p}K_a\) → Products are favored (\(\text{p}K_a\) 16 > \(\text{p}K_a\) 5)

Brønsted-Lowry vs. Lewis

Brønsted-Lowry Lewis
Acid is... \( \text{H}^+ \) donor Electron-pair acceptor
Base is... \( \text{H}^+ \) acceptor Electron-pair donor
Requires proton? Yes No
Examples of acids \(\text{HCl}\), \(\text{RCOOH}\) \(\text{BF}_3\), \(\text{AlCl}_3\)
Used for \( \text{p}K_a \)? Yes No

Four Factors That Affect Acidity

To predict relative \( \text{p}K_a \) values, evaluate the stability of the conjugate base. A more stable conjugate base means a stronger acid (lower \( \text{p}K_a \)).

1. Element
Across a period, electronegativity matters (e.g., \( \text{H}_2\text{O} \) more acidic than \( \text{NH}_3 \)). Down a group, size dominates: \(\text{HI} > \text{HBr} > \text{HCl} > \text{HF}\)
2. Resonance
Delocalization stabilizes the conjugate base: carboxylate > alkoxide
3. Induction
Electron-withdrawing groups pull density away, stabilizing the anion
4. Hybridization
\( sp > sp^2 > sp^3 \): more s-character holds electrons closer

How to Compare Acidities: Step by Step

1
Identify the proton being lost from each acid.
2
Draw the conjugate base that results from removing that proton.
3
Evaluate stability of each conjugate base using the four factors (element, resonance, induction, hybridization).
4
The more stable conjugate base came from the stronger acid (lower \( \text{p}K_a \)).

Example 1: Ethanol vs. Acetic Acid

Which is more acidic: ethanol (\( \text{CH}_3\text{CH}_2\text{OH} \)) or acetic acid (\( \text{CH}_3\text{COOH} \))?

Ethanol Conjugate base: \(\text{CH}_3\text{CH}_2\text{O}^-\) Charge on ONE oxygen \(\text{p}K_a \approx 16\) Acetic Acid Conjugate base: \(\text{CH}_3\text{COO}^-\) Charge delocalized over TWO oxygens \(\text{p}K_a \approx 5\) Resonance stabilization makes acetate far more stable ∴ Acetic acid is the stronger acid (lower \(\text{p}K_a\))

Example 2: Inductive Effects on Acidity

Rank in order of decreasing acidity: \( \text{CH}_3\text{COOH} \), \( \text{ClCH}_2\text{COOH} \), \( \text{Cl}_2\text{CHCOOH} \)

\(\text{Cl}_2\text{CHCOOH}\) \(\text{p}K_a \approx 1.3\) \(\text{ClCH}_2\text{COOH}\) \(\text{p}K_a \approx 2.9\) \(\text{CH}_3\text{COOH}\) \(\text{p}K_a \approx 4.8\) Most acidic → Least acidic More Cl atoms = more electron withdrawal = lower \(\text{p}K_a\) Inductive effect: electronegative atoms stabilize the conjugate base

Example 3: Hybridization and \(\text{C-H}\) Acidity

Which \(\text{C-H}\) bond is most acidic? Ethane, ethylene, or acetylene?

1
Ethane (\( sp^3 \) carbon): \( \text{p}K_a \approx 50 \). 25% s-character. Least acidic.
2
Ethylene (\( sp^2 \) carbon): \( \text{p}K_a \approx 44 \). 33% s-character. More acidic.
3
Acetylene (\( sp \) carbon): \( \text{p}K_a \approx 25 \). 50% s-character. Most acidic!

Common Mistakes to Avoid

✕ Confusing \( \text{p}K_a \) Direction
Lower \( \text{p}K_a \) = stronger acid. Students often reverse this because "bigger number seems stronger."
✕ Ignoring Conjugate Base
Always evaluate the stability of the conjugate base, not the acid itself. The base's stability drives acidity.
✕ Mixing Up Definitions
Brønsted acids donate \( \text{H}^+ \); Lewis acids accept electron pairs. They are not interchangeable in \( \text{p}K_a \) problems.

Key \( \text{p}K_a \) Reference Values

Functional Group Example \( \text{p}K_a \) Conjugate Base
Strong mineral acid \(\text{HCl}\) -7 \( \text{Cl}^- \)
Carboxylic acid \( \text{CH}_3\text{COOH} \) 4.8 \( \text{CH}_3\text{COO}^- \)
Ammonium ion \( \text{RNH}_3^+ \) 10 \( \text{RNH}_2 \)
Water / Alcohol \(\text{ROH}\) 16 \( \text{RO}^- \)
Terminal alkyne \( \text{RC}{\equiv}\text{CH} \) 25 \( \text{RC}{\equiv}\text{C}^- \)
Amine \( \text{RNH}_2 \) 38 \( \text{RNH}^- \)
Alkane \( \text{CH}_4 \) 50 \( \text{CH}_3^- \)

Question 1 of 5

An acid has a \( \text{p}K_a \) of 3 and another has a \( \text{p}K_a \) of 8. Which statement is correct?

Question 2 of 5

What is the conjugate base of \( \text{H}_2\text{O} \)?

Question 3 of 5

Acetic acid (\( \text{p}K_a \approx 5 \)) reacts with sodium ethoxide (\( \text{CH}_3\text{CH}_2\text{O}^- \), conjugate acid \( \text{p}K_a \approx 16 \)). Is this reaction favorable?

Question 4 of 5

Which factor best explains why \( \text{CH}_3\text{COOH} \) (\( \text{p}K_a \approx 5 \)) is a much stronger acid than \( \text{CH}_3\text{CH}_2\text{OH} \) (\( \text{p}K_a \approx 16 \))?

Question 5 of 5

Rank these \(\text{C-H}\) bonds in order of increasing acidity: \( sp^3 \) \(\text{C-H}\), \( sp^2 \) \(\text{C-H}\), \( sp \) \(\text{C-H}\).