8.1.8 Finding Ka

Objective:

The purpose of this practical is to determine the acid dissociation constant, $K_a$, of a weak acid by using titration and measuring the pH at the half-equivalence point. This point in titration provides a direct relationship where the pH equals the $pK_a$, allowing the calculation of the dissociation constant.

Apparatus & Chemicals:

• 0.1 mol dm$⁻³$ ethanoic acid ($CH₃COOH$)
• 0.1 mol dm$⁻³$ sodium hydroxide ($NaOH$)
• Phenolphthalein indicator
• pH meter or calibrated pH probe
• Burette
• Pipette (25 cm³)
• Conical flask
• Distilled water
• Magnetic stirrer or stirring rod (optional)
• Beakers

Theory Overview:

For weak acids, $K_a$ is determined using the relationship between the concentration of the acid and its dissociated ions in equilibrium.

At the half-equivalence point of a titration, the concentration of the acid $[HA]$ is equal to the concentration of its conjugate base $[A^-]$.

At this stage, $K_a$ is numerically equal to the concentration of hydrogen ions $[H^+]$, which is directly related to the pH:

$$K_a = [H^+] = 10^{-\text{pH}}$$

Thus, by measuring the pH at the half-equivalence point, you can calculate the $K_a$ of the weak acid.

Procedure:

1. Calibration of pH Meter:

• Before use, calibrate the pH meter with standard buffer solutions (typically pH 4.00, 7.00, and 10.00) to ensure accuracy in measurements.

2. Initial Titration Setup:

• Use a pipette to transfer 25.0 cm³ of 0.1 mol dm⁻³ ethanoic acid into a conical flask.
• Add 2-3 drops of phenolphthalein indicator to the ethanoic acid solution.
• The indicator will change colour from colourless to pink near the end-point of the titration.

3. Titration with Sodium Hydroxide:

• Fill a burette with 0.1 mol dm⁻³ sodium hydroxide solution and record the initial volume.
• Slowly titrate the sodium hydroxide into the conical flask containing the ethanoic acid while swirling the mixture (use a magnetic stirrer if available for consistent mixing).
• Stop the titration when the solution just turns pink, indicating the equivalence point has been reached. Note the volume of $NaOH$ used.

4. Finding the Half-Equivalence Point:

• After the initial titration, prepare a second conical flask with another 25.0 cm³ of 0.1 mol dm⁻³ ethanoic acid.
• This time, titrate with half the volume of $NaOH$ that was required to reach the equivalence point in the previous titration.
• This volume corresponds to the half-equivalence point.
• At the half-equivalence point, measure the pH of the solution using the calibrated pH meter.

Specimen Results:

• pH at the half-equivalence point: 4.75

Analysis:

1. Understanding the Half-Equivalence Point:

• At the half-equivalence point, the concentration of undissociated acid, $[HA]$, is equal to the concentration of its conjugate base, $[A^-]$. Hence, the acid dissociation constant $K_a$ is equal to the concentration of hydrogen ions, $[H^+]$.

$$K_a = [H^+] = 10^{-\text{pH}}$$

2. Calculation of $K_a$:

• From the measured pH of 4.75 at the half-equivalence point:

$$[H^+] = 10^{-\text{pH}} = 10^{-4.75} = 1.8 \times 10^{-5} \, \text{mol dm}^{-3}$$

Therefore, the dissociation constant:

$$K_a = :highlight[1.8 \times 10^{-5}] \, \text{mol dm}^{-3}$$

3. Interpretation of Results:

• The $K_a$ value obtained is consistent with that expected for weak acids like ethanoic acid, which typically have $K_a$ values around $10^{-5} \, \text{mol dm}^{-3}$.
• This $K_a$ value can now be used to predict the behaviour of the weak acid under different conditions, such as pH changes or in buffer solutions.

Graphical Representation:

A titration curve for the titration of a weak acid with a strong base typically shows a buffer region before the steep rise to the equivalence point.

The half-equivalence point occurs when the titration curve levels off slightly, and at this point, the pH = $pK_a$.

• The equivalence point occurs when equal moles of acid and base have reacted, and the solution contains predominantly the conjugate base.
• The half-equivalence point is at half the volume of base added to reach equivalence. At this point, the concentrations of the acid and its conjugate base are equal.

Conclusion:

By measuring the pH at the half-equivalence point, students can calculate the $K_a$ of a weak acid with precision. This practical reinforces key concepts related to weak acid behaviour, acid-base equilibria, and the relationship between pH and $K_a$. It also provides valuable hands-on experience with titration techniques and pH measurements, both of which are important in the context of A-Level Chemistry practicals and exams.

Practical Tips for Success:

• Calibration of the pH meter is crucial to obtaining accurate results. Ensure that you re-calibrate if needed, especially when switching between acid and basic solutions.
• Swirling the flask consistently during titration helps ensure that the solution is well-mixed and that the indicator accurately reflects the pH change.
• Precision in measurements, such as using the same pipette for adding acid and ensuring no spillage during titration, will lead to more reliable results.