Stoichiometry of Weak Acid-Strong Base Titrations: A Detailed Explanation

📚 Stoichiometry of Weak Acid-Strong Base Titrations: A Detailed Explanation

Weak acid-strong base titrations involve the reaction of a weak acid with a strong base. The pH changes during the titration can be determined using stoichiometry and equilibrium calculations. This guide explains the process step-by-step, focusing on key points in the titration curve.

🎯 Objectives

• 🔬 Understand the reaction between a weak acid and a strong base.
• 📊 Calculate the pH at different stages of the titration (initial, before equivalence point, at equivalence point, after equivalence point).
• 🧪 Interpret titration curves for weak acid-strong base titrations.

🧰 Materials

• 🧪 A weak acid solution (e.g., acetic acid, $CH_3COOH$).
• 💧 A strong base solution (e.g., sodium hydroxide, $NaOH$).
• ⚗️ Burette, beakers, and volumetric flasks.
• 🌡️ pH meter or indicator.

🔥 Warm-up (5 mins)

• ❓ Review the concepts of weak acids and strong bases.
• 🤔 Briefly discuss equilibrium constants ($K_a$) for weak acids.
• ➕ Remind students of the definition of pH and its calculation.

🧪 Main Instruction

The titration of a weak acid with a strong base involves several key stages. Let's use acetic acid ($CH_3COOH$) titrated with sodium hydroxide ($NaOH$) as an example.

• 📝 Initial pH:

  Before any base is added, the pH is determined by the dissociation of the weak acid. Use an ICE table to calculate the $[H^+]$ concentration and then the pH.

  Example: For 0.1 M $CH_3COOH$ ($K_a = 1.8 \times 10^{-5}$):

  $CH_3COOH(aq) \rightleftharpoons H^+(aq) + CH_3COO^-(aq)$

  ICE Table:

  	$CH_3COOH$	$H^+$	$CH_3COO^-$
  Initial	0.1	0	0
  Change	-x	+x	+x
  Equilibrium	0.1-x	x	x

  $K_a = \frac{[H^+][CH_3COO^-]}{[CH_3COOH]} = \frac{x^2}{0.1-x} = 1.8 \times 10^{-5}$

  Assuming x is small, $x = \sqrt{1.8 \times 10^{-6}} = 0.00134$

  $pH = -log(0.00134) = 2.87$
• ➕ Before the Equivalence Point:

  The solution contains a mixture of the weak acid and its conjugate base. Use the Henderson-Hasselbalch equation to calculate the pH.

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

  Where $pK_a = -log(K_a)$, $[A^-]$ is the concentration of the conjugate base ($CH_3COO^-$), and $[HA]$ is the concentration of the weak acid ($CH_3COOH$).

  Example: After adding 10 mL of 0.1 M $NaOH$ to 100 mL of 0.1 M $CH_3COOH$, calculate the new moles of $CH_3COOH$ and $CH_3COO^-$ and then use the Henderson-Hasselbalch equation.

• ⚖️ At the Equivalence Point:

  The weak acid has been completely neutralized, and the solution contains only the conjugate base. The pH is determined by the hydrolysis of the conjugate base.

  $CH_3COO^-(aq) + H_2O(l) \rightleftharpoons CH_3COOH(aq) + OH^-(aq)$

  Calculate the concentration of $CH_3COO^-$ and use an ICE table with $K_b$ to find $[OH^-]$ and then calculate pOH and pH.

  $K_b = \frac{K_w}{K_a}$

• ✅ After the Equivalence Point:

  The solution contains the conjugate base and excess strong base. The pH is determined primarily by the excess strong base.

  Calculate the concentration of the excess $OH^-$ and then calculate pOH and pH.

📝 Assessment

Solve the following problems to assess your understanding:

• ❓ What is the pH of a 0.2 M solution of formic acid ($HCOOH$), $K_a = 1.8 \times 10^{-4}$?
• 🧪 25 mL of 0.1 M $NaOH$ is added to 50 mL of 0.1 M $CH_3COOH$. What is the pH of the solution?
• 📊 What is the pH at the equivalence point when 50 mL of 0.1 M $CH_3COOH$ is titrated with 0.1 M $NaOH$?
• ➕ What is the pH after adding 60 mL of 0.1 M $NaOH$ to 50 mL of 0.1 M $CH_3COOH$?
• 🤔 Sketch the titration curve for a weak acid-strong base titration, labeling the buffer region and equivalence point.
• ✅ Explain why the pH at the equivalence point of a weak acid-strong base titration is greater than 7.
• 💡 How does the $K_a$ of a weak acid affect the shape of the titration curve?