A solution is prepared by dissolving 25.0 g of pure HC2H3O2 and 25.0 g of NaC2H3O2 in 700 mL of solution (the final volume).
(a) What is the pH of the solution?
(b) What would the pH of the solution be if 65.0 mL of 0.650 M NaOH were added?
(c) What would the pH be if 40.0 mL of 0.30 M HCl were added to the original 700 mL of buffer solution?
To find the pH of the solution, we first need to determine the concentration of acetic acid (HC2H3O2) and its conjugate base (C2H3O2-) in the solution.
(a) pH of the solution:
1. Calculate the moles of HC2H3O2:
moles = mass / molar mass
moles = 25.0 g / 60.052 g/mol (molar mass of HC2H3O2)
2. Calculate the moles of NaC2H3O2:
moles = mass / molar mass
moles = 25.0 g / 82.0343 g/mol (molar mass of NaC2H3O2)
3. Calculate the total moles of the solution:
total moles = moles of HC2H3O2 + moles of NaC2H3O2
4. Calculate the volume of the solution in liters:
volume = 700 mL = 0.7 L
5. Calculate the concentration of HC2H3O2 and C2H3O2-:
concentration = moles / volume
Now, let's calculate the concentration of HC2H3O2 and C2H3O2-:
Concentration of HC2H3O2 = moles of HC2H3O2 / volume
Concentration of C2H3O2- = moles of NaC2H3O2 / volume
(b) pH after adding NaOH:
1. Calculate the moles of NaOH:
moles = volume (in L) * concentration
moles = 65.0 mL * (0.650 mol/L) / 1000 mL/L
2. Determine the limiting reactant:
The limiting reactant is the one that reacts completely, which is the one with fewer moles. It is either HC2H3O2 or NaOH, depending on the stoichiometry.
3. Calculate the moles of the excess reactant:
NaOH moles used = moles HC2H3O2 * (ratio of moles of NaOH / moles of HC2H3O2)
4. Calculate the remaining moles of the limiting reactant:
moles remaining = moles of the limiting reactant - moles of the excess reactant
5. Calculate the new concentration of HC2H3O2 and C2H3O2- using the remaining moles of HC2H3O2 and the original volume:
Concentration of HC2H3O2 = moles remaining / volume
Concentration of C2H3O2- = moles of NaC2H3O2 / volume
(c) pH after adding HCl:
1. Calculate the moles of HCl:
moles = volume (in L) * concentration
moles = 40.0 mL * (0.30 mol/L) / 1000 mL/L
2. Determine the limiting reactant:
The limiting reactant is the one that reacts completely, which is the one with fewer moles. It is either HC2H3O2 or HCl, depending on the stoichiometry.
3. Calculate the moles of the excess reactant:
HCl moles used = moles HC2H3O2 * (ratio of moles of HCl / moles of HC2H3O2)
4. Calculate the remaining moles of the limiting reactant:
moles remaining = moles of the limiting reactant - moles of the excess reactant
5. Calculate the new concentration of HC2H3O2 and C2H3O2- using the remaining moles of HC2H3O2 and the original volume:
Concentration of HC2H3O2 = moles remaining / volume
Concentration of C2H3O2- = moles of NaC2H3O2 / volume
To calculate the pH, we need to use the Henderson-Hasselbalch equation, which relates the pH to the concentrations of the acid and its conjugate base:
pH = pKa + log([C2H3O2-] / [HC2H3O2])
The pKa for acetic acid (HC2H3O2) is 4.74.
Now, we have all the information needed to calculate the pH in each scenario.