A buffer is prepared by mixing 0.30 mole of formic acid (HCNO2) and 0.20 mole of sodium formate (NaCHO2) in enough water to make 0.50 liter of solution. Ka of formic acid is 1.7 x 10-4. Calculate the pH of the resulting buffer solution.
Use the Henderson-Hasselbalch equation.
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To calculate the pH of the resulting buffer solution, we need to determine the concentrations of the formic acid (HCNO2) and sodium formate (NaCHO2) in the solution.
Step 1: Calculate the molarities of the formic acid and sodium formate.
The molarity (M) is calculated by dividing the moles of solute by the volume of the solution in liters.
Molarity (M) = moles of solute / volume of solution (in liters)
Given:
- Moles of formic acid (HCNO2) = 0.30 mol
- Moles of sodium formate (NaCHO2) = 0.20 mol
- Volume of solution = 0.50 L
Molarity of formic acid (HCNO2) = 0.30 mol / 0.50 L = 0.60 M
Molarity of sodium formate (NaCHO2) = 0.20 mol / 0.50 L = 0.40 M
Step 2: Write the balanced equation for the ionization of formic acid.
Formic acid (HCNO2) ionizes in water to produce hydrogen ions (H+) and formate ions (CHO2-).
The balanced equation is: HCNO2 ⇌ H+ + CHO2-
Step 3: Determine the initial concentrations of the acid (HCNO2) and its conjugate base (CHO2-) in the buffer solution.
The initial concentration of the acid (HCNO2) is equal to its molarity: [HCNO2] = 0.60 M
The initial concentration of the conjugate base (CHO2-) is equal to its molarity: [CHO2-] = 0.40 M
Step 4: Calculate the ratio of the concentrations of the conjugate base to the acid (CHO2-/HCNO2).
Ratio = [CHO2-] / [HCNO2] = 0.40 M / 0.60 M = 2/3
Step 5: Calculate the pH of the buffer solution using the Henderson-Hasselbalch equation.
pH = pKa + log10(Ratio)
Given:
- Ka of formic acid (HCNO2) = 1.7 x 10^-4
pKa = -log10(Ka) = -log10(1.7 x 10^-4) ≈ 3.77
pH = 3.77 + log10(2/3)
pH ≈ 3.77 + (-0.08)
pH ≈ 3.69
Therefore, the pH of the resulting buffer solution is approximately 3.69.