Adding strong acid to buffer. how will it change pH?

A beaker with 105 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 7.50 mL of a 0.410 M HCl solution to the beaker. How much will the pH change? The ka of acetic acid is 4.760.Adding strong acid to buffer. how will it change pH?
let x = concentration acetate

let y = concentration acetic acid



5.00 = 4.76 + log x/y



10^0.24 =1.74 = x/y



x + y = 0.100



y = 0.100-x



1.74 = x/ 0.100-x



0.174 - 1.74 x = x

x = 0.0635 M

y = 0.100 - 0.0635= 0.0365 M



moles acetate = 0.0635 x 0.105 L= 0.00667

molea acid = 0.0365 x 0.105= 0.00383



moles H+ = 0.0075 L x 0.410 M=0.00308



moles acetate = 0.00667- 0.00308=0.00359

moles acid = 0.00383 + 0.00308=0.00691

total volume = 0.1125 L

concentration acetate = 0.00359/ 0.1125=0.0319 M

concentration acid = 0.00691/ 0.1125=0.0614 M



pH = 4.76 + log 0.0319 - 0.0614 =4.48



5.00 - 4.48=0.52 = delta pH