8.5: Acid-Base Titrations

Introduction

Titration is a common lab technique used to determine the concentration of an unknown acid or base solution by neutralizing it with a solution of known concentration. This process involves the gradual addition of a titrant (the solution of known concentration) to an analyte (the solution of unknown concentration) until the reaction between them is complete, which is the equivalence point.

Titration Curve

A titration curve is a graph that plots the pH of the solution as a function of the volume of titrant added. The shape of the curve can provide valuable information about the strength of the acid and base involved.

Strong Acid - Strong Base Titrations

• Initial pH: Determined by the concentration of the strong acid.

• Equivalence Point: pH = 7 (neutral) because the salt formed does not undergo hydrolysis.

• Sharp pH change near the equivalence point.

• Example: Titrating $ HCl $ with $ NaOH $ .

  $$ HCl(aq) + NaOH(aq) \rightarrow NaCl(aq) + H_2O(l) $$

Weak Acid - Strong Base Titrations

• Initial pH: Determined by the concentration and $ K_a $ of the weak acid. Requires an ICE Tables calculation.

• Equivalence Point: pH > 7 (basic) because the conjugate base of the weak acid hydrolyzes water, producing $ OH^- $ .

• Less sharp pH change near the equivalence point compared to strong acid-strong base titrations.

• Half-Equivalence Point: pH = pKa, where [HA] = [A-]. This is because at the half equivalence point, half of the weak acid has been neutralized, resulting in equal concentrations of the weak acid and its conjugate base. This is useful for determining the $ K_a $ of the weak acid.

  $$ HA(aq) + OH^-(aq) \rightarrow A^-(aq) + H_2O(l) $$ $ A^- $ undergoes Salt Hydrolysis.

Strong Acid - Weak Base Titrations

• Initial pH: Determined by the concentration and $ K_b $ of the weak base.

• Equivalence Point: pH < 7 (acidic) because the conjugate acid of the weak base hydrolyzes water, producing $ H_3O^+ $ .

• Less sharp pH change near the equivalence point compared to strong acid-strong base titrations.

• Half-Equivalence Point: pOH = pKb, where [B] = [BH+].

  $$ B(aq) + H_3O^+(aq) \rightarrow BH^+(aq) + H_2O(l) $$ $ BH^+ $ undergoes Salt Hydrolysis.

Weak Acid - Weak Base Titrations

• Titration curves for weak acid-weak base titrations are complex.
• The pH at the equivalence point depends on the relative strengths of the acid and base. The pH will be acidic if $ K_a > K_b $ , basic if $ K_b > K_a $ , and neutral if $ K_a = K_b $ .
• The pH change near the equivalence point is typically very gradual, making it difficult to accurately determine the equivalence point. Therefore, these titrations are rarely performed.

Equivalence Point

The equivalence point is the point in the titration where the moles of acid are stoichiometrically equal to the moles of base. This is the ideal point for the completion of the titration. It is not always at pH 7, as that is only true for strong acid-strong base titrations.

Endpoint

The endpoint is the point in the titration where the Acid-Base Indicators changes color. Ideally, the endpoint should be as close as possible to the equivalence point. The selection of the appropriate indicator is crucial for accurate results.

Calculations

Determining Concentration

The key to titration calculations is understanding the stoichiometry of the reaction. At the equivalence point:

$$ moles\ of\ acid = moles\ of\ base $$
$$ M_A V_A = M_B V_B $$ where:

• $ M_A $ = Molarity of the acid
• $ V_A $ = Volume of the acid
• $ M_B $ = Molarity of the base
• $ V_B $ = Volume of the base

This equation only works for monoprotic acids and monobasic bases (one mole of $ H^+ $ reacts with one mole of $ OH^- $ ). For polyprotic acids and polybasic bases, the stoichiometry must be taken into account. For example, if titrating $ H_2SO_4 $ with $ NaOH $ ,

$$ 2 * M_A V_A = M_B V_B $$

pH Calculations During Titration

• Before the equivalence point:
  • Strong Acid/Base: Calculate the remaining $ [H^+] $ or $ [OH^-] $ directly.
  • Weak Acid/Base: Use an ICE Tables to determine the $ [H^+] $ or $ [OH^-] $ , considering the formation of the conjugate base or acid. The Buffer Solutions region occurs before the equivalence point.
• At the equivalence point:
  • Strong Acid/Base: pH = 7.
  • Weak Acid/Strong Base: Consider hydrolysis of the conjugate base formed. Calculate the $ [OH^-] $ from the hydrolysis using an ICE Tables and $ K_b $ .
  • Strong Acid/Weak Base: Consider hydrolysis of the conjugate acid formed. Calculate the $ [H^+] $ from the hydrolysis using an ICE Tables and $ K_a $ .
• After the equivalence point:
  • Calculate the excess $ [OH^-] $ or $ [H^+] $ from the titrant added beyond the equivalence point.

Polyprotic Acid Titrations

Polyprotic Acids have multiple ionizable protons. Their titration curves show multiple equivalence points, one for each proton. The pH at the half-equivalence point for each proton corresponds to the $ pK_a $ for that proton.