Unit 8 Notes Topic 7 AP CHEMISTRY

📊 Deep Dive: pH & pKa

Unit 8 | Topic 7 – How Acidity and Equilibrium Connect

🔍 What is pH?

pH is a numerical scale used to specify the acidity or basicity (alkalinity) of an aqueous solution. The term stands for "power of hydrogen" and reflects the concentration of hydrogen ions (H⁺) or hydronium ions (H₃O⁺) in the solution.

pH is calculated as:

pH = –log[H₃O⁺]

• If [H₃O⁺] is high → pH is low → solution is acidic
• If [H₃O⁺] is low → pH is high → solution is basic

In AP Chemistry, it's okay to use [H⁺] instead of [H₃O⁺] — they’re functionally interchangeable in calculations.

To go from pH to [H₃O⁺], you reverse the formula:

[H₃O⁺] = 10⁻ᵖᴴ

🧪 What is pKa?

pKa is the negative base-10 logarithm of the acid dissociation constant (Ka). It gives you a sense of how weak or strong an acid is. The smaller the pKa value, the stronger the acid, because it means the acid dissociates more in water to release H⁺ ions.

pKa = –log(Ka)

Ka = 10⁻ᵖᴷᵃ

• Low pKa (e.g. 0–1) = Strong acid, dissociates easily
• High pKa (e.g. 9–14) = Weak acid, barely dissociates

⚖️ pH vs pKa – What's the Connection?

The Henderson-Hasselbalch equation shows how pH relates to pKa and the ratio of conjugate base [A⁻] to acid [HA] in a buffer solution.

pH = pKa + log([A⁻]/[HA])

• [A⁻] = concentration of the conjugate base (what’s left after acid donates H⁺)
• [HA] = concentration of the acid

This formula is especially useful for buffer calculations and understanding how pH shifts depending on acid/base ratios.

🧪 Titration, pH Curves & pKa

During a titration between a weak acid and strong base (or vice versa), the pH changes gradually until it hits a sharp rise or drop — this is the equivalence point.

Half-Equivalence Point: This is the point in the titration where exactly half of the acid has been neutralized by the base. At this moment:

• [HA] = [A⁻]
• So:
  pH = pKa

This is a key method to find the pKa of a weak acid — just measure the pH at the half-equivalence point!

💡 What's the Real Difference?

pH	pKa
Measures how acidic/basic a solution is	Measures the strength of the acid itself
Changes depending on concentration	Constant for a given acid at a fixed temperature
Used to describe solutions	Used to compare acids

📘 Worked Example: Finding pKa

Q: A 0.020 M solution of a weak acid has a pH of 4.80. What is its pKa?

Step 1: Find [H₃O⁺]

[H₃O⁺] = 10⁻⁴.⁸ = 1.58 × 10⁻⁵

Step 2: Build ICE table for HA ⇌ H₃O⁺ + A⁻

	HA	A⁻	H₃O⁺
Initial	0.020	0.00	0.00
Change	–1.58×10⁻⁵	+1.58×10⁻⁵	+1.58×10⁻⁵
Equilibrium	0.01998	1.58×10⁻⁵	1.58×10⁻⁵

Step 3: Calculate Ka

Ka = [H₃O⁺][A⁻] / [HA] = (1.58×10⁻⁵)² / 0.01998 = 1.25 × 10⁻⁸

Step 4: Find pKa

pKa = –log(1.25×10⁻⁸) = 7.90

✅ Final Answer: pKa = 7.90

💡 Exam Tip: If you’re working with weak acids or buffers, pKa helps you estimate how the solution resists pH changes. Know the Henderson-Hasselbalch equation by heart!