initial moles of sodium acetate = acetic acid = 1 m * 1 L = 1 moles
[ acetate ] after adding NaOH = 1 mol+ 0.55 mol = 1.55 M
[acetic acid] after adding NaOH = 1 mol - 0.55 mol = 0.45 M
According to Handerson-Hasselblach equation:
PH = Pka + ㏒ [ acetate]/[acetic acid]
when Pka = 4.74
so, by substitution:
∴PH = 4.74 + ㏒[1.55/0.45]
∴ PH = 5.28