Answer :
To find the moles of formic acid required, we first calculate the moles of sodium formate from its mass. Then, we use the Henderson-Hasselbalch equation to find the ratio of formate anions to formic acid that will maintain the desired pH, from which we can calculate the moles of formic acid.So, the correct option is:d) 0.20 mol
To calculate the moles of formic acid needed for the buffer, we need to use the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
Let [A-] be the moles of the conjugate base, sodium formate (NaCOOH), and [HA] be the moles of formic acid (HCOOH). First, we determine the moles of NaCOOH:
Molar mass of NaCOOH = 23 (Na) + 12 (C) + 2*16 (O) + 1 (H) = 68 g/mol
35.9 g NaCOOH x (1 mol / 68 g) = 0.528 moles of NaCOOH
Using the Henderson-Hasselbalch equation and rearranging:
[HA] = [A-] / 10^(pH-pKa)
Substituting the given pH and pKa values and the calculated moles of NaCOOH, we get:
[HA] = 0.528 moles / 10^(4.10-3.74)
After calculating this value, we can compare it with the options to identify the correct amount of moles of formic acid needed. The steps outlined provide a clear method to find the answer to the student's question.
So, the correct option is:d) 0.20 mol