16.7
Titration Calculations: Weak Acid - Strong Base
Calculating pH for Titration Solutions: Weak Acid/Strong Base
For the titration of 25.00 mL of 0.100 M CH3CO2H with 0.100 M NaOH, the reaction can be…
The pH at different stages of a weak acid or base titration is calculated using different methods during various points of the titration.
If a weak acid or base is the main determinant of the pH, the Ka or Kb and an ICE table, or the Henderson-Hasselbalch equation are used. If strong acid or base is present after the neutralization reaction, the concentration of the remaining hydronium or hydroxide ions is used to calculate the pH.
The initial pH of 50 mL of a 0.10 M acetic acid solution is 2.87 and is calculated using the Ka and an ICE table, as acetic acid is the main contributor.
If this solution containing 0.0050 moles of acetate is titrated with 0.10 M sodium hydroxide, the hydroxide ions react with acetic acid to produce acetate, resulting in a buffer.
Therefore, when 10 mL of the sodium hydroxide containing 0.0010 moles of hydroxide ions is added, 0.0010 moles of acetate are formed, and 0.0040 moles of acetic acid remain. The pH of the buffer can be calculated by substituting these values into the Henderson-Hasselbalch equation and equals 4.14.
When 25 mL of the sodium hydroxide is added, half of the initial moles of acetic acid are converted into acetate. At this point, the pH equals the pKa, as the amount of acetic acid and acetate ion are equal.
The further addition of sodium hydroxide up to 50 mL converts all of the acetic acid molecules into acetate, and the equivalence point is reached. As acetate ions are basic, the equivalence point lies in the basic region.
The concentration of the acetate ion is calculated by dividing the number of moles by the total volume of the solution.
The pH is determined using the Kb for acetate ions and an ICE table, as the acetate ion is the main contributor to the pH at the equivalence point.
The Kb for acetate is calculated using the formula, Kw = Ka × Kb, and equals 5.6 × 10−10.
Substituting equilibrium concentrations in the expression for Kb gives the hydroxide concentration, 5.3 × 10−6 M. The pOH and pH of the solution are 5.28 and 8.72, respectively.
Further addition of sodium hydroxide in the solution results in a mixture of acetate ions and sodium hydroxide. However, the final concentration of sodium hydroxide determines the pH of the solution, as it is a stronger base than acetate.
Therefore, if 70 mL of sodium hydroxide is added into the solution, the final concentration of the hydroxide ions can be calculated by subtracting the total moles of acetic acid, 0.0050 moles, from the total moles of hydroxide ions added, 0.0070 moles, and dividing it by the total volume of the solution, 120 mL or 0.12 L.
As the hydroxide ion concentration is 0.017 M, the pOH and pH of the solution are calculated to be 1.78 and 12.22, respectively.
View the full transcript and gain access to JoVE Core videos
Q1: How do you calculate the initial pH of a weak acid before titration begins?
The initial pH is calculated using the Ka (acid dissociation constant) and an ICE table, since the weak acid is the main pH contributor. For example, a 0.10 M acetic acid solution has an initial pH of 2.87. This method applies whenever a weak acid or base dominates the pH before any titrant is added.
Q2: What happens to the pH when you add sodium hydroxide to a weak acid solution?
When sodium hydroxide is added to a weak acid, hydroxide ions react with the acid to form its conjugate base, creating a buffer solution. The pH can be calculated using the henderson hasselbalch equation calculating buffers. As more base is added, the buffer resists pH change until the equivalence point is reached.
Q3: Why does the pH equal the pKa at the half-equivalence point?
At the half-equivalence point, exactly half of the weak acid has been neutralized to form its conjugate base. Since the concentrations of weak acid and conjugate base are equal, the Henderson-Hasselbalch equation simplifies to pH = pKa. For acetic acid titration, this occurs at 12.50 mL of added sodium hydroxide.
Q4: What is the pH at the equivalence point for a weak acid-strong base titration?
At the equivalence point, all weak acid has been converted to its conjugate base, which is basic. The pH is calculated using the Kb of the conjugate base and an ICE table. For acetic acid titrated with sodium hydroxide, the equivalence point pH is 8.72, significantly higher than 7 due to the basic nature of acetate ions.
Q5: How do you find the Kb of a conjugate base from the Ka of the weak acid?
The relationship between Ka and Kb is given by Kw = Ka × Kb, where Kw is the water ionization constant (1.0 × 10⁻¹⁴). Rearranging gives Kb = Kw / Ka. For acetate ion, Kb = 1.0 × 10⁻¹⁴ / 1.8 × 10⁻⁵ = 5.6 × 10⁻¹⁰.
Q6: What determines the pH after the equivalence point in a weak acid-strong base titration?
After the equivalence point, excess strong base (sodium hydroxide) is present in solution. The strong base is a much stronger contributor to pH than the conjugate base, so the final pH is determined by the concentration of excess hydroxide ions. For example, adding 70 mL of 0.10 M NaOH results in a pH of 12.22.
Q7: How does the titration curve for a weak acid-strong base differ from a strong acid-strong base titration?
In weak acid-strong base titrations, the equivalence point occurs in the basic region (pH > 7) because the conjugate base is basic. The initial pH is higher, and a buffer region exists before the equivalence point. This contrasts with titration calculations strong acid strong base, where the equivalence point is at pH 7.