Answer :
The final pH of the buffer system after the addition of HCl is closest to 3.5, calculated using the Henderson-Hasselbalch equation and considering the reaction of HCl with the acetate ion. Hence the correct answer is option b, 3.5 ph.
To solve this problem, we must first understand how a buffer works. A buffer consists of a weak acid and its conjugate base, which can neutralize added acid or base to maintain a relatively stable pH. In this case, we have acetic acid (CH3COOH) and sodium acetate (CH3COONa) serving as our buffer components.
Firstly, let's calculate the initial amounts of acetic acid and acetate in moles before the addition of HCl:
- Acetic acid: 500 mL of 1.5 M implies 0.5 L * 1.5 mol/L = 0.75 moles
- Acetate: 250 mL of 1.0 M implies 0.25 L * 1.0 mol/L = 0.25 moles
After the addition of 100 mL of 1.5 M HCl, we introduce 0.1 L * 1.5 mol/L = 0.15 moles of HCl, which will react with the acetate:
- 0.25 moles acetate - 0.15 moles HCl = 0.10 moles remaining acetate
- 0.75 moles acetic acid + 0.15 moles HCl (as it converts to acetic acid) = 0.90 moles acetic acid after the reaction.
The buffer equation (Henderson-Hasselbalch equation) is pH = pKa + log([A-]/[HA]), where [A-] is the concentration of the acetate ion and [HA] is the concentration of acetic acid. The pKa of acetic acid is approximately 4.76. Using the equilibrium concentrations, we get:
pH = 4.76 + log(0.10/0.90) = 4.76 + log(0.1111) ≈ 4.76 - 0.9542 ≈ 3.8058
Thus, the pH is closest to option b) 3.5.
