Final answer:
To reach the second equivalence point in the titration of 77.0 mL of 0.500 M malonic acid with 0.255 M NaOH, approximately 0.077 moles (or 302 mL) of NaOH are needed since two moles of NaOH are required for each mole of the diprotic acid.
Step-by-step explanation:
The student's question involves determining the amount of sodium hydroxide (NaOH) required to reach the second equivalence point in a titration with a diprotic acid (malonic acid, H2C3H2O4). The second equivalence point occurs when both protons of the diprotic acid have been neutralized by the base. First, we need to find the total moles of malonic acid in the original solution:
Moles of H2C3H2O4 = Volume (L) × Concentration (M)
= 0.077 L × 0.500 M
= 0.0385 mol
Since malonic acid is diprotic, two moles of NaOH are required to neutralize one mole of H2C3H2O4, thus we multiply the moles of malonic acid by 2 to find the moles of NaOH required to reach the second equivalence point:
Moles of NaOH = 0.0385 mol × 2
= 0.077 mol
Considering the concentration of NaOH is 0.255 M, the volume of NaOH needed can be calculated using the formula:
Volume of NaOH (L) = Moles of NaOH / Concentration of NaOH (M)
= 0.077 mol × 1/0.255 M
≈ 0.302 L or 302 mL
Therefore, to reach the second equivalence point in the titration, approximately 0.077 moles (or 302 mL) of 0.255 M NaOH are required.