An analytical chemist is titrating 102.5mL of a 0.2000M solution of formic acid H2CO2 with a 0.9800M solution of KOH. The pKa of formic acid is 3.74. Calculate the pH of the acid solution after the chemist has added 15.87mL of the KOH solution to it.Note for advanced students: you may assume the final volume equals the initial volume of the solution plus the volume of KOH solution added.Round your answer to 2 decimal places.

To solve this problem, we need to follow these steps:

1. Calculate the moles of formic acid (H2CO2) and KOH initially present.

   Moles of H2CO2 = Volume (L) x Molarity (M) = 0.1025 L x 0.2000 mol/L = 0.0205 mol

   Moles of KOH = Volume (L) x Molarity (M) = 0.01587 L x 0.9800 mol/L = 0.01555 mol

2. Determine the limiting reactant. In this case, KOH is the limiting reactant because there are fewer moles of KOH than H2CO2. The reaction between H2CO2 and KOH will consume all of the KOH and some of the H2CO2, leaving some H2CO2 unreacted.

3. Calculate the moles of H2CO2 remaining after the reaction with KOH.

   Moles of H2CO2 remaining = Initial moles of H2CO2 - moles of KOH = 0.0205 mol - 0.01555 mol = 0.00495 mol

4. Calculate the total volume of the solution after the addition of KOH.

   Total volume = Initial volume of H2CO2 solution + volume of KOH solution = 102.5 mL + 15.87 mL = 118.37 mL = 0.11837 L

5. Calculate the concentration of H2CO2 after the reaction.

   Concentration of H2CO2 = Moles of H2CO2 / Total volume (L) = 0.00495 mol / 0.11837 L = 0.0418 M

6. Use the Henderson-Hasselbalch equation to calculate the pH of the solution.

   pH = pKa + log([A-]/[HA]) Since the reaction between H2CO2 and KOH produces water and a formate ion (HCO2-), the concentration of HCO2- is equal to the initial moles of KOH divided by the total volume.

   Concentration of HCO2- = Moles of KOH / Total volume (L) = 0.01555 mol / 0.11837 L = 0.1313 M

   Substituting these values into the Henderson-Hasselbalch equation gives:

   pH = 3.74 + log(0.1313/0.0418) = 4.74

So, the pH of the acid solution after the chemist has added 15.87mL of the KOH solution to it is 4.74 (rounded to two decimal places).