A student titrates 0.100M KOH, potassium hydroxide, into 50.0ml of 0.10M HCOOH, formic acid (Ka=1.8 x 10^-4. What is the pH of the mixture after 25.0ml of the KOH has been added
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To find the pH of the mixture after adding 25.0 mL of 0.100 M KOH to 50.0 mL of 0.10 M HCOOH (formic acid), we need to consider the acid-base reaction that occurs between KOH and HCOOH.
The balanced equation for the reaction between KOH and HCOOH is:
HCOOH + KOH → HCOOK + H2O
In this reaction, formic acid (HCOOH) reacts with potassium hydroxide (KOH) to form potassium formate (HCOOK) and water.
Before the reaction, we have excess formic acid and a small amount of potassium hydroxide. However, since HCOOH is a weak acid and KOH is a strong base, the reaction will go to completion.
To determine the pH of the mixture, we need to calculate the concentration of the resulting potassium formate (HCOOK).
Let's begin by calculating the number of moles of formic acid and KOH present before the reaction:
Moles of HCOOH = Volume (L) × Concentration (mol/L)
Moles of HCOOH = (50.0 mL ÷ 1000 mL/L) × 0.10 mol/L
Moles of HCOOH = 0.0050 mol
Moles of KOH = Volume (L) × Concentration (mol/L)
Moles of KOH = (25.0 mL ÷ 1000 mL/L) × 0.100 mol/L
Moles of KOH = 0.0025 mol
Since the reaction between HCOOH and KOH occurs in a 1:1 ratio, the number of moles of HCOOK formed will also be 0.0025 mol.
Now, let's calculate the total volume of the mixture:
Total volume = Initial volume of HCOOH + Volume of KOH added
Total volume = 50.0 mL + 25.0 mL
Total volume = 75.0 mL
The final concentration of HCOOK can be calculated using the moles of HCOOK and the total volume:
Concentration of HCOOK = Moles of HCOOK / Total volume
Concentration of HCOOK = 0.0025 mol / (75.0 mL ÷ 1000 mL/L)
Concentration of HCOOK = 0.0333 mol/L
To find the pH, we can use the Ka value for HCOOH, which is 1.8 × 10^-4.
First, we'll calculate the concentration of HCOOH remaining in the solution after the reaction:
Concentration of HCOOH remaining = Initial concentration - Concentration of HCOOK formed
Concentration of HCOOH remaining = 0.10 mol/L - 0.0333 mol/L
Concentration of HCOOH remaining = 0.0667 mol/L
Now, we can calculate the concentration of H+ ions (protons) formed by HCOOH:
[H+] = √(Ka × Concentration of HCOOH remaining)
[H+] = √(1.8 × 10^-4 × 0.0667 mol/L)
Finally, we can calculate the pH using the concentration of H+ ions:
pH = -log10[H+]
Now, you can input the calculation in a calculator or use a spreadsheet application to determine the final pH value.