To calculate the pH at the equivalence point of the titration, we first need to determine the number of moles of acetic acid and sodium hydroxide that react at the equivalence point.
We have 25.0 mL of a 0.100 M acetic acid solution. To find the number of moles, we use the equation:
moles = concentration × volume
moles of acetic acid = 0.100 M × 25.0 mL = 0.100 mol
Since acetic acid is a monoprotic acid, it reacts in a 1:1 ratio with sodium hydroxide. Therefore, at the equivalence point, the number of moles of sodium hydroxide will also be 0.100 mol.
Next, we need to determine the composition of the resulting solution after the reaction has occurred. At the equivalence point, the acetic acid will react completely with the sodium hydroxide to form sodium acetate, NaCH3COO, and water, H2O.
CH3COOH + NaOH → NaCH3COO + H2O
The sodium acetate will dissociate in water to form sodium ions and acetate ions. Since sodium acetate is a salt of a weak acid (acetic acid), its acetate ion will hydrolyze and react with water to form hydroxide ions. This hydrolysis reaction contributes to the basic nature of the solution. The NaOH added during the titration also contributes to the basicity of the solution.
Due to this hydrolysis reaction, we have a basic solution, and the pH is calculated using the equation:
pOH = -log10[OH-]
To determine the pOH, we need to find the concentration of hydroxide ions ([OH-]) in the solution.
In this case, we have added 0.100 mol of NaOH, so the concentration of hydroxide ions will be the same. We now need to find the volume of the solution at the equivalence point.
The volume can be calculated by finding the total volume of the acetic acid solution and the volume of NaOH solution required to reach the equivalence point.
Let's assume we need to add V mL of NaOH solution to reach the equivalence point. The total volume of the solution will then be 25.0 mL + V mL.
At the equivalence point, the moles of hydroxide ions provided by NaOH will be equal to the moles of acetate ions produced from the reaction of acetic acid.
moles of NaOH = moles of acetate ions
0.100 mol = (V mL / 1000 L) × 0.100 M
Solving for V:
V mL = (0.100 mol) × (1000 L / 0.100 M) = 1000 mL
So, at the equivalence point, the volume of the solution will be 25.0 mL + 1000 mL = 1025 mL.
Now, let us calculate the concentration of hydroxide ions ([OH-]) in the solution:
[OH-] = (0.100 mol) / (1025 mL / 1000 L) = 0.0976 M
Finally, we can find the pOH:
pOH = -log10(0.0976) ≈ 1.01
Since pH + pOH = 14 (at 25°C), we can calculate the pH at the equivalence point:
pH = 14 - 1.01 ≈ 12.99
Therefore, the pH at the equivalence point of the titration is approximately 12.99.