Final answer:
The pH of the resulting buffer solution after the addition of perchloric acid (HClO₄) can be calculated using the Henderson-Hasselbalch equation. New concentrations of the buffer components after the acid addition are determined, and then the equation is applied to find the new pH.
Step-by-step explanation:
To calculate the pH of the buffer solution after adding perchloric acid (HClO₄), we use the Henderson-Hasselbalch equation, which describes the pH of a buffer solution as:
pH = pKa + log([A-]/[HA])
Where [A-] is the concentration of the conjugate base (KClO in this case) and [HA] is the concentration of the weak acid (HClO).
Given the concentrations of HClO (0.291 M) and KClO (0.398 M), and knowing the pKa of HClO is 7.53, we can begin our calculation:
pH = 7.53 + log(0.398/0.291)
This gives us the initial pH of the buffer before the addition of HClO₄.
Now, let's consider the addition of HClO₄, which is a strong acid and will react completely with the conjugate base KClO:
KClO + HClO₄ → KClO₄ + H₂O
0.0191 moles of HClO₄ will react with 0.0191 moles of KClO. We calculate the new concentrations as follows:
- [KClO] = (0.398 - 0.0191) M = 0.3789 M
- [HClO] = (0.291 + 0.0191) M = 0.3101 M
Using the updated concentrations in the Henderson-Hasselbalch equation:
pH = 7.53 + log(0.3789/0.3101)
Calculating the pH with the new values, we can determine the pH of the buffered solution after the addition of HClO₄.