To find the pH of the solution, we need to consider the dissociation of acetic acid and the neutralization reaction between acetic acid and sodium hydroxide.

1. Dissociation of acetic acid:
Acetic acid (CH3COOH) is a weak acid that partially dissociates in water. The dissociation equation is as follows:
CH3COOH ⇌ CH3COO- + H+

The equilibrium constant for this dissociation is given by the expression Ka = [CH3COO-][H+]/[CH3COOH]

The pKa of acetic acid is given as 4.75, which means that pKa = -log(Ka). Therefore, we can calculate Ka as 10^(-pKa).

2. Calculation of Ka:
Given pKa = 4.75, we can calculate Ka as:
Ka = 10^(-pKa) = 10^(-4.75) = 1.78 x 10^(-5)

3. Calculation of initial concentration of acetic acid:
We are given that 3 g of acetic acid is added to 250 mL of 0.1 M HCl and the solution is made up to 500 mL.
The molar mass of acetic acid is given as 60 g/mol. Therefore, the number of moles of acetic acid added is:
Number of moles = mass/molar mass = 3 g/60 g/mol = 0.05 mol

Since the solution is made up to 500 mL, the initial concentration of acetic acid is:
Concentration = Number of moles/volume = 0.05 mol/0.5 L = 0.1 M

4. Calculation of concentration of acetic acid after dilution:
We are adding 20 mL of the above solution to which a certain volume of 5 M NaOH is added. Since the volume changes negligibly, we can assume that the final volume is still 500 mL.

Since the initial concentration of acetic acid is 0.1 M, the final concentration after dilution is:
Final concentration = (Initial concentration)(Initial volume)/(Final volume)
Final concentration = (0.1 M)(20 mL)/(500 mL) = 0.004 M

5. Calculation of the ratio of acetic acid to acetate ion:
For a weak acid like acetic acid, the ratio of acetic acid to acetate ion can be approximated using the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])

We know that [A-] is the concentration of acetate ion, and [HA] is the concentration of acetic acid. Let's assume [HA] = [A-] = x.

Substituting the values, we get:
5.23 = 4.75 + log(x/x)
0.48 = log(x/x)

Taking the antilog of both sides, we get:
x/x = antilog(0.48) = 3

Therefore, the ratio of acetic acid to acetate ion is 3:1.

6. Calculation of the concentration of acetic acid and acetate ion:
Since the total concentration of acetic acid and acetate ion is 0.004 M and the ratio is 3:1, we can calculate the individual concentrations as follows:

3x +