A 25.0mL sample of a 0.100M solution of acetic acid is titrated with a 0.125M solution of NaOH. Calculate the pH of the titration mixture after 10.0, 20.0, and 30.0 mL of base have been added.
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To calculate the pH of the titration mixture, you need to consider the stoichiometry and the acid-base equilibrium of acetic acid and sodium hydroxide.
Acetic acid (CH3COOH) is a weak acid that ionizes partially in water, while sodium hydroxide (NaOH) is a strong base that completely dissociates into its ions (Na+ and OH-) in water.
Let's break down the steps to calculate the pH after each volume addition:
1. Before any NaOH is added:
- The acetic acid solution is a weak acid, so we can assume it is not completely dissociated. It will have both acetic acid (CH3COOH) and the conjugate base (CH3COO-) present in the solution.
- Calculate the initial concentration of acetic acid (CH3COOH) in moles by multiplying the volume (25.0 mL) by the molarity (0.100 M).
- Calculate the initial pH using the Henderson-Hasselbalch equation:
pH = pKa + log([CH3COO-]/[CH3COOH])
where pKa is the acid dissociation constant of acetic acid (4.74), [CH3COO-] is the initial concentration of the conjugate base, and [CH3COOH] is the initial concentration of acetic acid.
2. After 10.0 mL of NaOH is added:
- Determine the number of moles of NaOH added by multiplying the volume (10.0 mL) by the molarity (0.125 M).
- Since NaOH is a strong base, it will react completely with acetic acid to form water and sodium acetate. The reaction equation is:
CH3COOH + NaOH → H2O + CH3COONa
- Calculate the number of moles of acetic acid remaining by subtracting the moles of NaOH added from the initial moles of acetic acid.
- Calculate the concentration of acetic acid and the conjugate base using the new volume and moles of acetic acid remaining.
- Calculate the new pH using the Henderson-Hasselbalch equation.
3. After 20.0 mL of NaOH is added:
- Repeat the same steps as in step 2, but use the new volume (20.0 mL) and adjust the moles and concentrations accordingly.
4. After 30.0 mL of NaOH is added:
- Repeat the same steps as in step 2, but use the new volume (30.0 mL) and adjust the moles and concentrations accordingly.
By following these steps and using the Henderson-Hasselbalch equation, you can calculate the pH of the titration mixture after each volume addition of NaOH.