A buffer is made by mixing 100 mL of 0.25 M acetic acid (CH3COOH) and 150 mL of 0.10 M sodium acetate (CH3COONa). Calculate the pH of the solution after 0.5g of solid NaOH is added to the solution (Given Ka (CH3COOH) =1.8 x 10-5)
millimols HAc (CH3COOH) = mL x M = 25
mmols NaAc(CH3COONa) = 15
mmols NaOH = mg/molar mass = 12.5
----------------------------
.......HAc + OH^- ==> Ac^- + H2O
I......25....0.......15........
add.........12.5...................
C...-12.5..-12.5.....12.5.........
E.....12.5...0.......27.5
Substitute the E line into the Henderson-Hasselbalch equation and calculate pH.
19.5
To calculate the pH of the solution after the addition of NaOH, we need to determine the concentration of each species in the solution. Here's how you can calculate it step by step:
Step 1: Calculate the moles of acetic acid (CH3COOH) and sodium acetate (CH3COONa) in the initial solution.
Moles of CH3COOH = volume (L) × concentration (mol/L)
Moles of CH3COOH = 0.100 L × 0.25 mol/L = 0.025 mol
Moles of CH3COONa = volume (L) × concentration (mol/L)
Moles of CH3COONa = 0.150 L × 0.10 mol/L = 0.015 mol
Step 2: Determine the moles of acetic acid (CH3COOH) and sodium acetate (CH3COONa) remaining after the reaction with NaOH.
Since 0.5 g of solid NaOH is added, we need to calculate the moles of NaOH added:
Moles of NaOH = mass (g) ÷ molar mass (g/mol)
Moles of NaOH = 0.5 g ÷ 40.0 g/mol = 0.0125 mol
Note that NaOH reacts with CH3COOH in a 1:1 ratio, so the moles of CH3COOH remaining will equal the moles of NaOH added, and the moles of CH3COONa remaining will be the initial moles minus the moles of NaOH added.
Moles of CH3COOH remaining = Moles of CH3COONa remaining = 0.025 mol – 0.0125 mol = 0.0125 mol
Step 3: Calculate the new volume of the solution.
The volume is the sum of the initial solution (250 mL) and the volume of NaOH added (unknown in this case). Let's convert the initial volume to liters first.
Initial volume = 100 mL + 150 mL = 250 mL = 0.250 L
Now, let's assume the volume of NaOH added is V mL.
New volume = Initial volume + Volume of NaOH added
New volume = 0.250 L + V mL
Step 4: Calculate the concentration of CH3COOH and CH3COONa in the new volume.
Concentration (mol/L) = Moles ÷ Volume (L)
Concentration of CH3COOH = 0.0125 mol ÷ (0.250 L + V mL)
Concentration of CH3COONa = 0.0125 mol ÷ (0.250 L + V mL)
Step 5: Apply the Henderson-Hasselbalch equation to calculate the pH.
pH = pKa + log([CH3COONa] / [CH3COOH])
Since we know that Ka (CH3COOH) = 1.8 × 10^(-5), we can calculate the pKa:
pKa = -log(Ka) = -log(1.8 × 10^(-5))
Now, we can substitute all the values into the Henderson-Hasselbalch equation and calculate the pH.
pH = pKa + log([CH3COONa] / [CH3COOH])