pH Calculation Examples in Acid-Base Titration

Explore practical examples of calculating pH in weak acid and strong base titrations.
By Jamie

Introduction to pH Calculation in Acid-Base Titration

In chemistry, titration is a technique used to determine the concentration of an unknown solution. When a weak acid is titrated with a strong base, the pH of the solution changes significantly as the titration progresses. Understanding how to calculate the pH at various points during the titration can aid in predicting the endpoint and understanding the behavior of acid-base reactions. Below are three practical examples that illustrate how to calculate pH in this context.

Example 1: Titrating Acetic Acid with Sodium Hydroxide

In this example, we will titrate a 0.1 M solution of acetic acid (CH₃COOH) with a 0.1 M solution of sodium hydroxide (NaOH). Acetic acid is a weak acid, while sodium hydroxide is a strong base.

At the start of the titration, we need to calculate the initial pH of the acetic acid solution before any base is added. The dissociation constant (Kₐ) for acetic acid is approximately 1.8 x 10⁻⁵.

Using the formula for pH:

  1. Calculate the concentration of H⁺ ions:

    [H⁺] = sqrt(Kₐ × [HA]) = sqrt(1.8 x 10⁻⁵ × 0.1)

    = 0.00134 M

  2. Calculate pH:

    pH = -log[H⁺] = -log(0.00134)

    = 2.87

At the equivalence point (where moles of acid equal moles of base), the pH will be above 7 due to the hydrolysis of the acetate ion (CH₃COO⁻). The calculation at this point involves finding the concentration of acetate ion and then using its Kb value to find the pH.

Relevant Notes

  • The initial pH of a weak acid is typically less than 7.
  • At the equivalence point, the solution is slightly basic due to the conjugate base.

Example 2: Titration of Phthalic Acid with Potassium Hydroxide

In this case, we will titrate a 0.05 M solution of phthalic acid (C₈H₆O₄), a diprotic weak acid, with a 0.1 M solution of potassium hydroxide (KOH).

To find the pH after the addition of 25 mL of KOH, we first determine how much phthalic acid is present:

  • Initial volume of phthalic acid solution = 50 mL
  • Moles of phthalic acid = 0.05 M × 0.050 L = 0.0025 moles

When 25 mL of KOH is added:

  • Moles of KOH = 0.1 M × 0.025 L = 0.0025 moles
  • At this point, the acid is fully neutralized, producing the phthalate ion (C₈H₄O₄²⁻) which will hydrolyze. We can determine the pH using the Kb of the phthalate ion, which is approximately 5.6 x 10⁻¹⁰.

  1. Calculate the concentration of phthalate ion:

    [C₈H₄O₄²⁻] = 0.0025 moles / 0.075 L = 0.0333 M

  2. Calculate [OH⁻] using Kb:

    Kb = Kw / Kₐ = (1 x 10⁻¹⁴) / (1.3 x 10⁻⁴)

    = 7.69 x 10⁻¹¹

  3. Set up the equilibrium expression and solve for [OH⁻]:

    Kb = [OH⁻]² / [C₈H₄O₄²⁻ - x]

    = (7.69 x 10⁻¹¹) o [OH⁻] ≈ 1.06 x 10⁻⁵ M

  4. Calculate pOH and then pH:

    pOH = -log(1.06 x 10⁻⁵) = 4.98
    pH = 14 - pOH = 14 - 4.98 = 9.02

Relevant Notes

  • The pH at the equivalence point of a diprotic acid will require consideration of both dissociation stages.
  • The resulting solution will be basic due to the presence of the phthalate ion.

Example 3: Titration of Citric Acid with Sodium Hydroxide

In this example, we will titrate a 0.1 M solution of citric acid (C₆H₈O₇) with a 0.1 M solution of sodium hydroxide. Citric acid is a triprotic weak acid, meaning it has three dissociable protons.

To calculate the pH after the addition of 10 mL of NaOH to 50 mL of citric acid:

  1. Determine the moles of citric acid initially present:

    Moles of citric acid = 0.1 M × 0.050 L = 0.005 moles

  2. Determine the moles of NaOH added:

    Moles of NaOH = 0.1 M × 0.010 L = 0.001 moles

  3. Since citric acid has three dissociable protons, we can calculate the pH after 10 mL of NaOH is added:

    • The first dissociation constant (Kₐ1) for citric acid is approximately 7.4 x 10⁻⁴. We calculate the pH using the Henderson-Hasselbalch equation:

    pH = pKₐ1 + log([A⁻]/[HA])

    = -log(7.4 x 10⁻⁴) + log((0.005 - 0.001)/(0.001))

    = 3.13 + log(4) o pH ≈ 3.13 + 0.60 = 3.73

Relevant Notes

  • The pH will change gradually as more base is added due to the buffering capacity of the weak acid.
  • As more NaOH is added, the pH will shift significantly at the equivalence points associated with each proton dissociation.

These examples illustrate the practical applications of calculating pH during the titration of weak acids with strong bases. Understanding these calculations can enhance your grasp of acid-base chemistry and its implications in various scientific fields.