Unit 8 Notes Topic 8 AP CHEMISTRY Titration Curves & Equivalence Points

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📉 Titration Curves & Equivalence Points

Unit 8 | Topic 8 – Visualizing Acid-Base Neutralization

📊 What is a Titration Curve?

A titration curve is a graph that shows how the pH of a solution changes when you slowly add one solution (the titrant) to another (the analyte). Usually, the x-axis is the volume of titrant added, and the y-axis is the pH of the mixture.

These curves help us visualize acid-base reactions and identify the equivalence point, where neutralization occurs.

🧪 4 Regions on Every Titration Curve

• Start: Where the solution contains only acid or only base.
• Buffering Region: pH starts changing more slowly. There's a mix of acid and conjugate base or base and conjugate acid. This forms a buffer.
• Equivalence Point: Number of moles of acid = moles of base. Neutralization is complete!
• Post-Equivalence: Excess titrant dominates and pH spikes up or down.

⚖️ What is the Equivalence Point?

This is the **exact point** where the amount of acid added is exactly enough to neutralize the base — or vice versa. It’s usually right in the middle of the steep vertical rise in the titration curve.

Equivalence Point → moles of titrant = moles of analyte

Important: The pH at the equivalence point depends on the strength of acid/base involved:

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

🎯 How to Read a pH Curve

• Starting pH = pH of acid/base alone
• Buffer zone = where pH rises slowly → use Henderson-Hasselbalch here
• Half-Equivalence Point = [HA] = [A⁻] → pH = pKa
• Equivalence point = where neutralization is complete

📘 Worked Example: Molar Mass from Titration

Q: A 0.675 g sample of HA was made into 100 mL solution. 25.0 mL was titrated with 0.100 M NaOH. It took 12.1 mL to reach the equivalence point. What is the molar mass of HA?

Step 1: Write balanced equation

HA + NaOH → NaA + H₂O

Step 2: Moles of NaOH

n(NaOH) = 0.0121 L × 0.100 mol/L = 1.21 × 10⁻³ mol

Step 3: Moles of HA = moles of NaOH (1:1 ratio)

Step 4: Scale up to full solution

1.21 × 10⁻³ mol × (100 / 25) = 4.84 × 10⁻³ mol

Step 5: Calculate molar mass

M = mass / moles = 0.675 g / 4.84 × 10⁻³ mol = 139.5 g/mol

✅ Final Answer: 139.5 g/mol

🚨 Common Student Mistakes (And How to Fix Them)

• Wrong indicator? Use one that changes color at the correct pH.
• Adding titrant too fast? Near the endpoint, go drop-by-drop!
• Not swirling the flask? Uneven mixing = pH errors
• Reading burette wrong? Always view from eye-level and read from the bottom of the meniscus.
• Units confusion? You can use mL or L in C₁V₁ = C₂V₂, as long as they’re the same!

💡 Quick Formula: C₁V₁ = C₂V₂ Use this when titrating strong acids and bases (monoprotic only). - C₁ = concentration of acid, V₁ = volume of acid - C₂ = concentration of base, V₂ = volume of base ➕ You don’t need to convert to dm³ if both volumes are in the same unit!