A solution is prepared by dissolving 15.0 g of pure HC2H3O2 and 15.0 g of NaC2H3O2 in 600 mL of solution (the final volume).

Use the Henderson-Hasselbalch equation.

To determine the pH of the solution, we need to know the concentration of the hydrogen ions (H+) in the solution. This concentration can be calculated using the concentration of the acid (HC2H3O2) and the concentration of its conjugate base (C2H3O2-).

First, let's calculate the concentration of HC2H3O2 and C2H3O2- in the solution.

The molar mass of HC2H3O2 (acetic acid) is approximately 60.05 g/mol. Therefore, the moles of HC2H3O2 can be calculated by dividing the mass of HC2H3O2 by its molar mass:

moles of HC2H3O2 = mass of HC2H3O2 / molar mass of HC2H3O2

moles of HC2H3O2 = 15.0 g / 60.05 g/mol

moles of HC2H3O2 ≈ 0.2499 mol

Similarly, the moles of NaC2H3O2 (sodium acetate) can be calculated using its molar mass, which is approximately 82.03 g/mol:

moles of NaC2H3O2 = mass of NaC2H3O2 / molar mass of NaC2H3O2

moles of NaC2H3O2 = 15.0 g / 82.03 g/mol

moles of NaC2H3O2 ≈ 0.1828 mol

Next, we need to calculate the total moles of both HC2H3O2 and C2H3O2-:

total moles = moles of HC2H3O2 + moles of NaC2H3O2

total moles ≈ 0.2499 mol + 0.1828 mol

total moles ≈ 0.4327 mol

Now, we can calculate the molarity (concentration) of the solution by dividing the total moles by the final volume of the solution in liters:

molarity = total moles / (final volume in L)

molarity ≈ 0.4327 mol / 0.600 L

molarity ≈ 0.7212 mol/L

The molarity indicates the concentration of both HC2H3O2 and C2H3O2- in the solution.

Lastly, let's calculate the pH of the solution. Since we have both an acid (HC2H3O2) and its conjugate base (C2H3O2-), the solution can be considered a buffer solution. The pH of a buffer solution can be calculated using the Henderson-Hasselbalch equation:

pH = pKa + log([A-]/[HA])

Where:
pH = the pH of the solution
pKa = the dissociation constant of the acid (HC2H3O2)
[A-] = the concentration of the conjugate base (C2H3O2-)
[HA] = the concentration of the acid (HC2H3O2)

The pKa for acetic acid (HC2H3O2) is approximately 4.76.

Now, let's substitute the values into the Henderson-Hasselbalch equation:

pH = 4.76 + log([C2H3O2-]/[HC2H3O2])

pH = 4.76 + log(0.7212/0.7212) (since the concentration of C2H3O2- and HC2H3O2 is the same)

pH = 4.76 + log(1)

pH = 4.76 + 0

pH ≈ 4.76

Therefore, the pH of the solution is approximately 4.76.