Answer :
To prepare a buffer with a pH of 4.10, the Henderson-Hasselbalch equation is used to calculate the required concentration of formic acid based on the given amount of sodium formate. The moles of formic acid needed are then obtained by converting the calculated concentration to moles, considering the total volume of the buffer.
To create a buffer with a pH of 4.10 using formic acid (HCHO2, pKa = 3.74) and sodium formate (NaCHO2), one can utilize the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA]), where [A-] is the concentration of the conjugate base (formate ion) and [HA] is the concentration of the weak acid (formic acid). First, we need to find how many moles of sodium formate we have: 35.9 grams NaCHO2 (molar mass = 68.007 g/mol) gives us 0.528 moles NaCHO2.
Assuming that sodium formate dissociates completely in solution, this represents the concentration of the formate ion ([A-]). To make 250.0 mL (0.250 L) of buffer at this pH, we can rearrange the Henderson-Hasselbalch equation to solve for the [HA] (formic acid concentration) needed and then calculate the moles of formic acid required.
Next, we calculate the mole ratio using the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
Solve for [HA]:
[HA] = [A-] / 10^(pH - pKa)
After solving for [HA], we convert this concentration into moles, considering the buffer's total volume (0.250 L).
