How much will pH change?

A beaker with 145 mL of an acetic acid buffer with a pH of 5.00 is sitting on a benchtop. The total molarity of acid and conjugate base in this buffer is 0.100 M. A student adds 5.30 mL of a 0.250 M HCl solution to the beaker. How much will the pH change? The pKa of acetic acid is 4.760.How much will pH change?
pH = pKa + log [acetate]/ acetic acid]

pH - pKa = [acetate]/ [acetic acid]

5.00 - 4.760= 0.240

10^0.240=1.74 = [acetate]/ [acetic acid]



let x = [acetate] and let y = [acetic acid]



x/y= 1.74

x+y = 0.100



x = 0.100 -y

1.74 = 0.100 - y/ y

1.74 y = 0.100-y

2.74 y=0.100

y=0.036 M

x = 0.100 - 0.036=0.064 M



moles acetate = 0.064 x 0.145 L=0.0093

moles acetic acid = 0.036 x 0.145=0.0052



moles HCl= 0.0053 L x 0.250M=0.00013



moles acetic acid = 0.0052 - 0.00013=0.0051

moles acetate = 0.0093 - 0.00013=0.0092

total volume = 0.1503 L

conc. acetate = 0.0092/ 0.1503=0.0612 M

conc. acetic acid = 0.0051/ 0.1503=0.0339 M



pH = 4.760 + log 0.0612/0.0339=5.02