Unit 8 Notes Topic 2 AP CHEMISTRY

💧 The Ionic Product of Water

Unit 8 | Acids, Bases, and Water Equilibrium

🌊 Autoionization of Water

The pH, pOH, [H₃O⁺], and [OH⁻] are all interconnected through the self-ionization of water:

2H₂O (l) ⇌ H₃O⁺ (aq) + OH⁻ (aq)

OR: H₂O (l) ⇌ H⁺ (aq) + OH⁻ (aq)

The equilibrium expression becomes:

K_w = [H₃O⁺][OH⁻] = 1.00 × 10⁻¹⁴ (at 25 °C)

• In a neutral solution, [H₃O⁺] = [OH⁻]
• [H₃O⁺] = √K_w

📉 Temperature and K_w

The ionization of water is an endothermic process:

2H₂O (l) ⇌ H₃O⁺ (aq) + OH⁻ (aq)

According to Le Châtelier’s Principle:

• ⬆️ Temp → favors forward reaction → ⬆️ [H₃O⁺], ⬆️ [OH⁻], ⬆️ K_w
• ⬇️ pH (solution becomes more acidic)
• ⬇️ Temp → ⬇️ K_w, ⬆️ pH (more basic)

Graph Insight: As temperature ↑, K_w ↑ and pH ↓

🔁 Relationship Between pH, pOH, [H₃O⁺], and [OH⁻]

All values are mathematically related. Key formulas:

pOH = –log[OH⁻]

pH = –log[H₃O⁺]

pH + pOH = 14

[H₃O⁺] = 10⁻ᵖᴴ | [OH⁻] = 10⁻ᵖᴼᴴ

✅ Worked Example

Convert between pH, pOH, [H₃O⁺], and [OH⁻]. Round to 2 decimal places.

[H₃O⁺]	[OH⁻]	pH	pOH
2.40 × 10⁻⁴	4.17 × 10⁻¹¹	3.62	10.38
2.17 × 10⁻¹⁰	4.60 × 10⁻⁵	9.66	4.34
4.37 × 10⁻¹¹	2.29 × 10⁻⁴	10.36	3.64
6.17 × 10⁻⁴	1.62 × 10⁻¹¹	3.21	10.79

💡 Quick Tip: If you have any one of the four values (pH, pOH, [H₃O⁺], or [OH⁻]), you can find the other three using just these formulas. Keep practicing conversions for AP mastery!