Answer:
pH = 8.95
Step-by-step explanation:
A buffer follows H-H equation:
pH = pKa + log [B] / [BH⁺]
Where pH is pH of the buffer: 8.97
pKa is a constant of the buffer (Our incognite)
[B] is molar concentration -or moles- of the base: 0.578M
[BH⁺] is molar concentration -or moles- of conjugate acid: 0.263M
pH = pKa + log [B] / [BH⁺]
8.97 = pKa + log [0.578M] / [0.263M]
8.628 = pKa of the buffer
0.250L contains:
[B] = 0.578M * 0.250L = 0.1445 moles of B
[BH⁺] = 0.263M * 0.250L = 0.06575 moles of BH⁺
When HCl is added, B is consumed and BH⁺ is produced as follows:
HCl + B → BH⁺ + Cl⁻
That means moles of each species after the addition of HCl is:
[B] = 0.1445 moles - 0.0020moles = 0.1425moles
[BH⁺] = 0.06575 moles + 0.0020moles = 0.06775moles
Replacing in H-H equation, pH is:
pH = 8.628 + log [0.1425moles] / [0.06775moles]
pH = 8.95