let x = concentration acid

let y = concentration conjugate base

x + y = 0.100

5.00 = 4.760 + log y/x

we must solve this system

5.00 - 4.760 = log y/x

0.24 = log y/x

10^0.24 =1.74 = y/x

1.74 x = y

x + 1.74 x = 0.100

2.74 x = 0.100

x =0.0365 M = concentration acid

0.100 - 0.0365 =0.0635 M= concentration conjugate base

moles acid = 0.150 L x 0.0365 M= 0.00548

moles conjugate base = 0.0635 M x 0.150 L=0.00953

moles HCl = 4.10 x 10^-3 L x 0.480 M=0.00197

A- + H+ = HA

moles conjugate base = 0.00953 - 0.00197=0.00756

moles acid = 0.00548 + 0.00197=0.00745

total volume = 150 + 4.10 = 154.1 mL = 0.1541 L

concentration acid = 0.00745/ 0.1541 =0.0483 M

concentration conjugate base = 0.00756/ 0.1541 =0.0491 M

pH = 4.760 + log 0.0491/ 0.0483=4.77

change pH = 5.00 - 4.77=0.23

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