Step-by-step explanation:
Formic acid (HCOOH) reacts with sodium hydroxide (NaOH) to form sodium formate (HCOONa) and water. The balanced chemical equation is:
HCOOH + NaOH → HCOONa + H2O
The reaction is a strong acid-strong base titration. We can use the following equation to calculate the concentration of formate ion (HCOO^-) in the resulting solution:
[HCOO^-] = [OH^-] - [HCOOH]
where [OH^-] is the concentration of hydroxide ion and [HCOOH] is the concentration of formic acid before the reaction.
Before the reaction, the solution contains 0.25 mol/L of formic acid in 55.0 mL, or 0.25 mol/L × 0.055 L = 0.01375 mol of formic acid. The solution also contains 0.12 mol/L of sodium hydroxide in 75.0 mL, or 0.12 mol/L × 0.075 L = 0.009 mol of sodium hydroxide.
Since the reaction between formic acid and sodium hydroxide is a 1:1 reaction, all the 0.009 mol of sodium hydroxide will react with 0.009 mol of formic acid, leaving 0.00475 mol of formic acid unreacted.
[HCOO^-] = [OH^-] - [HCOOH]
[OH^-] = [NaOH] = 0.12 mol/L × 0.075 L / 0.13 L = 0.0692 mol/L
[HCOO^-] = 0.0692 mol/L - 0.00475 mol/L = 0.0645 mol/L
Now we can calculate the pH of the resulting solution using the Ka expression for formic acid:
Ka = [HCOO^-][H3O^+]/[HCOOH]
[H3O^+] = Ka × [HCOOH] / [HCOO^-]
[H3O^+] = 1.77 × 10^-4 × 0.00475 mol/L / 0.0645 mol/L
[H3O^+] = 1.29 × 10^-5 mol/L
pH = -log[H3O^+]
pH = -log(1.29 × 10^-5)
pH = 4.89
Therefore, the resulting pH is 4.89.