Answer:
The balanced chemical equation for the reaction between H3AsO4 and NaOH is:
H3AsO4 + 3NaOH -> Na3AsO4 + 3H2O
The stoichiometry of the reaction shows that one mole of H3AsO4 reacts with three moles of NaOH. Therefore, to determine the volume of NaOH required to reach the half-equivalence and equivalence points, we need to calculate the number of moles of H3AsO4 in the solution.
Assuming a 1 L solution of H3AsO4, the number of moles of H3AsO4 is given by:
n(H3AsO4) = mass(H3AsO4) / molar mass(H3AsO4)
where the mass of H3AsO4 is not provided, so we cannot calculate it directly. However, we can use the information about the pKa values of H3AsO4 to estimate the number of moles of H3AsO4 at the half-equivalence and equivalence points.
At the half-equivalence point, [H3AsO4] = [H2AsO4-]. Therefore, we can assume that half of the H3AsO4 has been converted to H2AsO4-. At this point, the pKa1 of H3AsO4 is used up, and the pKa2 becomes relevant. The pKa2 of H3AsO4 is 6, which means that the pH of the solution will be close to 6. At this pH, approximately half of the H2AsO4- will be deprotonated to form HAsO42-. Therefore, we can assume that the number of moles of H3AsO4 at the half-equivalence point is equal to the number of moles of H2AsO4-.
At the equivalence point, all the H3AsO4 has been neutralized by NaOH, and the solution contains only Na3AsO4 and water.
To calculate the volume of NaOH required to reach each point, we need to use the molarity of the NaOH solution. The molarity of the 12 M NaOH solution is:
M(NaOH) = moles(NaOH) / volume(NaOH in liters)
where the moles of NaOH are equal to the moles of H3AsO4 at the half-equivalence or equivalence point, and the volume of NaOH is what we need to calculate.
At the half-equivalence point:
Moles of H3AsO4 = Moles of H2AsO4-
Moles of H2AsO4- = Moles of H3AsO4 / 2
Moles of NaOH = 3 x Moles of H3AsO4
Molarity of NaOH = 12 M
Volume of NaOH = Moles of NaOH / Molarity of NaOH
Substituting the values, we get:
Moles of H3AsO4 = 0.5 x mass(H3AsO4) / molar mass(H3AsO4)
Moles of H2AsO4- = 0.25 x mass(H3AsO4) / molar mass(H3AsO4)
Moles of NaOH = 1.5 x mass(H3AsO4) / molar mass(H3AsO4)
Molarity of NaOH = 12 M
Volume of NaOH = 1.5 x mass(H3AsO4) / (12 M x molar mass(H3AsO4))
Similarly, at the equivalence point, all the H3AsO4 has been neutralized, so the number of moles of NaOH is equal to the number of moles of H3AsO4 in the solution. Thus, we can use the same formula as for the half-equivalence point, but with the moles of NaOH equal to the moles of H3AsO4 at the equivalence point.
In summary, to calculate the volume of NaOH required to reach the half-equivalence and equivalence points, we can use the following formulas:
Volume of NaOH at the half-equivalence point = 1.5 x mass(H3AsO4) / (12 M x molar mass(H3AsO4))
Volume of NaOH at the equivalence point = mass(H3AsO4) / (12 M x molar mass(H3AsO4))
These formulas will give the volume of NaOH in milliliters (mL) required to reach each point. Note that the mass of H3AsO4 is not provided, so we cannot calculate the actual volume required, but we can use these formulas to estimate the relative volumes at each point.