What is the pH when 3.46 mL of 2.37 M KOH is added to 26.9 mL of a 1.78 M solution of formic acid (HCOOH)?
3.46 mL x 2.37 M KOH = 8.20 mmoles.
26.9 mL x 1.78 M HCOOH = 47.88 mmoles.
............HCOOH + KOH ==> HCOOK + H2O
initial......8.20...47.88......0.......0
change.....-8.2....-8.2.....8.2.....8.20
final.......0.......40.68....8.20....8.20
You should recognize this as a buffered solution; i.e., it is a weak acid (HCOOH) with its salt (HCOOK). Use the Henderson-Hasselbalch equation to solve for pH.
To find the pH of the solution, we need to first calculate the concentration of the formic acid (HCOOH) after the reaction with KOH.
Let's start by writing the balanced chemical equation for the reaction between formic acid (HCOOH) and potassium hydroxide (KOH):
HCOOH + KOH --> HCOOK + H2O
From the balanced equation, we can see that the reaction produces potassium formate (HCOOK) and water (H2O).
Next, we can calculate the moles of HCOOH and KOH using the given volumes and concentrations:
moles of HCOOH = volume (in L) x concentration
= 26.9 mL x (1 L / 1000 mL) x 1.78 M
= 0.0479142 mol
moles of KOH = volume (in L) x concentration
= 3.46 mL x (1 L / 1000 mL) x 2.37 M
= 0.0081802 mol
Since the reaction between HCOOH and KOH occurs in a 1:1 ratio, the moles of HCOOH consumed and HCOOK produced are equal to the moles of KOH used. Therefore, the concentration of HCOOH after the reaction is:
moles of HCOOH = initial moles - moles of KOH
= 0.0479142 mol - 0.0081802 mol
= 0.039734 mol
The final volume of the solution is the sum of the initial volumes of HCOOH and KOH:
final volume = volume of HCOOH + volume of KOH
= 26.9 mL + 3.46 mL
= 30.36 mL
To find the final concentration of HCOOH, we divide the moles of HCOOH by the final volume:
final concentration of HCOOH = moles of HCOOH / final volume
= 0.039734 mol / (30.36 mL x (1 L / 1000 mL))
= 1.309 M
Now, the pH can be calculated using the equation:
pH = -log[H+]
Since formic acid (HCOOH) is a weak acid, it will partially ionize in water to produce H+ ions. Therefore, we will assume that the concentration of H+ ions from HCOOH after the reaction is equal to the final concentration of HCOOH.
Taking the negative logarithm of the H+ concentration:
pH = -log(1.309)
= 0.882
So, the pH of the solution, after adding 3.46 mL of 2.37 M KOH to 26.9 mL of a 1.78 M solution of formic acid (HCOOH), is approximately 0.882.