A solution of formic acid (0.15 M, 15.00 mL), a monoprotic acid, was titrated with 18.50 mL of 0.10 M sodium hydroxide (K_a of formic acid = 1.80 $\times$ 10^-4). What is the final pH of this solution?

Question

Quizplus · Accepted Answer

First, we need to write the balanced chemical equation for the reaction:

HCOOH + NaOH → NaCOOH + H2O

From the balanced equation, we can see that the stoichiometry is 1:1 between formic acid and sodium hydroxide. This means that all the formic acid will react with the sodium hydroxide, and the remaining sodium hydroxide will determine the pH of the solution.

To calculate the amount of sodium hydroxide used, we can use the formula:

n(NaOH) = M(NaOH) x V(NaOH)

n(NaOH) = 0.10 mol/L x 0.01850 L

n(NaOH) = 0.00185 mol

Since the stoichiometry is 1:1, this means that there were also 0.00185 mol of formic acid in the solution at the start of the titration.

To calculate the concentration of formic acid after the titration, we can use the formula:

C(F) = n(F) / V(F)

C(F) = 0.00185 mol / (15.00 mL / 1000)

C(F) = 0.1233 mol/L

Now we need to calculate the pKa of formic acid. This is given by the equation:

pKa = -log(Ka)

where Ka is the acid dissociation constant for formic acid. The pKa for formic acid is 3.75.

To calculate the pH of the solution after the titration, we need to use the Henderson-Hasselbalch equation:

pH = pKa + log([A-] / [HA])

where [A-] is the concentration of the formate ion (from the dissociation of formic acid), and [HA] is the concentration of undissociated formic acid.

At the equivalence point, all the formic acid has been converted to the formate ion, so [A-] = 0.00185 mol / (15.00 mL / 1000) = 0.1233 mol/L.

The concentration of undissociated formic acid can be calculated using the relationship:

[F-] + [HA] = [F]0

where [F]0 is the initial concentration of formic acid, which is 0.15 mol/L.

[F-] is equal to [A-] since the stoichiometry is 1:1, so:

[HA] = [F]0 - [A-] = 0.15 mol/L - 0.1233 mol/L = 0.0267 mol/L

Now we can plug these values into the Henderson-Hasselbalch equation:

pH = 3.75 + log(0.1233 mol/L / 0.0267 mol/L)

pH = 4.41

Therefore, the final pH of the solution is 4.41, which corresponds to answer choice B.

A Solution of Formic Acid (0 ×\times× 10-4)

A Solution of Formic Acid (0 $\times$ 10^-4)