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Given a 250 mL buffer with a pH of 4.10 and a pKa of 3.74 containing 35.9 g of NaCOOH, how many moles of formic acid are needed?

A. 0.35 mol
B. 0.25 mol
C. 0.30 mol
D. 0.20 mol

Answer :

To solve this problem, we'll use the Henderson-Hasselbalch equation, which relates the pH of a buffer solution to the pKa of the acid and the ratio of the concentrations of the conjugate base to the weak acid.

The Henderson-Hasselbalch equation is:

pH = pKa + log ([base][acid])

Given that the pH of the buffer solution is 4.10 and the pKa of the acid is 3.74, we can rearrange the Henderson-Hasselbalch equation to solve for the ratio of base to acid:

pH = pKa + log ([base][acid])

10pH-pKa = [base][acid]

[base] = [acid] x 10pH-pKa

Since we know the concentration of the base (NaCOOH) and the acid (formic acid) are equal in a buffer solution, we can find the concentration of the acid using the given concentration of the base.

First, let's find the concentration of NaCOOH in the buffer solution:

Molarity of NaCOOH = moles of NaCOOH

Volume of solution (L)

Given that the volume of the buffer solution is 250 mL (0.250 L), and the molar mass of NaCOOH is 68.01 g/mol, we can find the moles of NaCOOH:

moles of NaCOOH = mass \ molar mass

moles of NaCOOH = 35.9g \ 68.01g\mol

moles of NaCOOH = 0.527 mol

Now, using the Henderson-Hasselbalch equation, we can find the concentration of formic acid (HCOOH) in the buffer solution:

[base] = [acid] x 10^pH-pKa

0.527 = [acid] x 10^4.10- 3.74

0.527 = [acid] x 10^0.39

[acid] = 0.527 \ 10^0.36

[acid] = 0.335 mol

Therefore, the moles of formic acid needed are approximately 0.335 mol, which is closest to option:

c) 0.30 mol

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