Chemistry question on ionic equations

Question

A buffer solution of pH of 8.96 contains X mol of a weak base and Z mol of a salt of its conjugate acid. When 144 cm3 of a 0.0212 mol.dm−3 solution of hydrochloric acid was added to this buffer solution the pH changes by 0.250 pH units. If the Kb value for the weak base is 1.66 x 10─5, calculate the values of X and Z.

Answer 1

cm³ = ml

dm³ = L

Let B = weak base

Let BCl = chloride salt of weak base

Henderson Hasselbalch equation: pOH = pKb + log [salt]/[base]

pH = 8.96

pOH = 14 - 8.96

pOH = 5.04

pKb = -log Kb = -log 1.66x10-5

pKb = 4.78

Initial conditions (no HCl added)

5.04 = 4.78 + log (Z/X)

log Z/X = 0.26

Z/X = 1.82 EQUATION 1

After addition of HCl

mols HCl added = 0.144 L x 0.0212 mol/L = 0.00305 mols HCl

Final [B] = X - 0.00305 mo

Final [BCl] = Z + 0.00305 mol

pH = 8.96 - 0.250 = 8.71

pOH = 5.29

5.29 = 4.78 + log (Z+0.00305 / X-0.00305)

5.29 = 4.78 + log [salt]/[base]

5.29 = 4.78 + log (Z+0.00305) / X-0.00305

log (Z+0.00305) / X-0.00305 = 0.51

Z+0.00305 / X-0.00305 = 3.24 EQUATION 2

Use equations 1 and 2 to solve.

Please check math.

X = 0.0091 M

Z = 0.0166 M