Adding a strong acid to a buffer?

A beaker with 175 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 0.1 M. A student adds 9.00 mL of a 0.410 \it M \rm HCl solution to the beaker. How much will the pH change? The pKa of acetic acid is 4.76.Adding a strong acid to a buffer?
Let x = [acid]

let y = [salt]

x + y = 0.1



5.00 = 4.76 + log y/x

10^0.24 =1.74 =y/x



x = y / 1.74



y/1.74 + y = 0.1

y + 1.74y = 0.174

y = 0.0635 M

x = 0.0365 M



moles CH3COO- = 0.0635 x 0.175 L =0.0111

moles CH3COOH = 0.0365 x 0.175 = 0.00639



Moles H+ added = 0.009 L x 0.410 =0.00369

CH3COO- + H+ %26gt;%26gt; CH3COOH

moles CH3COOH = 0.00639 + 0.00369 =0.0101

moles CH3COO- = 0.0111 - 0.00369 = 0.00741

total volume = 175 + 9 = 184 mL = 0.184 L

concentration acid = 0.0549 M

concentration salt = 0.0403 M



pH = 4.76 + log 0.0403 / 0.0549 = 4.63