Calculate the pH of solution made by combining 75.0 mL of 0.10 M formic acid with 30.0 mL of 0.25 M KOH. (Ka for formic acid, HCOOH, is 1.8 X 10^-4)
Write the equation. Convert to moles KOH and moles formic acid, determine which reagent is in excess, calculate the amount of the excess reagent plus the amount of salt formed, then use the Henderson-Hasselbalch equation.
HCOOH + OH- --> COOH- + H20
Kb = [OH-][HCOOH]/[COOH-] = x^2/(0.0714-x)
= 5.55 x 10^-11
x=1.99 x 10^-6
pOH = 5.70
pH = 14 - 5.70 = 8.30
^ Will that also work?
Yes it will work and what I wrote for you will not work BECAUSE I didn't work the problem and I just assumed that the acid would be in excess and that would give you a formate/formic acid buffer. Actually, it gives you an EXACT neutralization where neither KOH NOR formic acid are in excess and you have only the salt present (and no buffer so the H-H equation won't work). Therefore, it must be done by the hydrolysis of the salt and you have approached it correctly. I see one small correct; in this step you wrote,
Kb = [OH-][HCOOH]/[COOH-] = x^2/(0.0714-x) . The denominator should be(COOK) [or (COO^-)] which is the concn of the salt. You substituted the correct value for it in your solution.
To calculate the pH of the solution, we need to determine the concentration of the H+ ions present in the solution. In this case, we are mixing formic acid (HCOOH) with KOH (potassium hydroxide), which is a strong base.
First, let's calculate the moles of formic acid and KOH used.
Moles of formic acid:
Moles = concentration (M) x volume (L)
Moles = 0.10 M x (75.0 mL / 1000 mL/L)
Moles of KOH:
Moles = concentration (M) x volume (L)
Moles = 0.25 M x (30.0 mL / 1000 mL/L)
Next, we need to determine the reaction between formic acid and KOH, which will produce water (H2O) and the formate ion. The balanced chemical equation is:
HCOOH + KOH β H2O + HCOOK
Since formic acid is a weak acid and potassium hydroxide is a strong base, we can assume that the reaction goes to completion. Therefore, all the formic acid will react with KOH, and there will be no formic acid left in the final solution.
Now, let's determine the moles of H+ ions produced by the reaction. Based on the balanced equation, we see that one mole of HCOOH produces one mole of H+ ions.
Moles of H+ ions = moles of formic acid
Now, let's calculate the total volume of the solution after mixing the two solutions.
Total volume = volume of formic acid + volume of KOH
Total volume = 75.0 mL + 30.0 mL
Total volume = 105.0 mL or 0.105 L (Note: We convert mL to L for consistency in units.)
To find the concentration of H+ ions, we divide the moles of H+ ions by the total volume of the solution.
Concentration of H+ ions = Moles of H+ ions / Total volume (L)
Finally, we can use the concentration of H+ ions to calculate the pH using the formula:
pH = -log[H+]
Now, let's plug in the values and calculate the pH.
Moles of formic acid = 0.10 M x (75.0 mL / 1000 mL/L) = 0.0075 mol
Moles of KOH = 0.25 M x (30.0 mL / 1000 mL/L) = 0.0075 mol
Moles of H+ ions = 0.0075 mol
Total volume of the solution = 0.105 L
Concentration of H+ ions = 0.0075 mol / 0.105 L = 0.0714 M
pH = -log[H+] = -log(0.0714) = 1.15
Therefore, the pH of the solution is 1.15.