How much will the pH change?

A beaker with 190mL 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 0.1M . A student adds 8.70mL of a 0.420M HCl solution to the beaker. How much will the pH change? The pKa of acetic acid is 4.76.



Express your answer numerically. Use a minus (-) sign if the pH has decreased.How much will the pH change?
pH = pKa + log [CH3COO-] / [CH3COOH ]

5.00 = 4.76 + log [CH3COO-] / [CH3COOH]

0.24 = log [CH3COO-] / [CH3COOH ]



[CH3COO-] / [CH3COOH ] = 10^0.24 = 1.74

[CH3COO-] + [CH3COOH ] = 0.1

We solve this system and we get

[CH3COOH ] = 0.0365 M

[CH3COO-] = 0.0635 M



Moles CH3COOH = 0.0365 x 0.190 = 0.00694

Moles CH3COO- = 0.0635 x 0.190 = 0.0121



Moles H+ added = 8.70 x 0.420 /1000 = 0.00365

The effect of the added 0.00365 mole of H+ would be to decrease the moles of CH3COO- by 0.00365 and increase the moles of CH3COOH by 0.00365

Moles CH3COOH = 0.0106

moles CH3COO- = 0.00845

Total volume = 198.7 mL = 0.1987 L

concentration CH3COOH = 0.0533 M

concentration CH3COO- = 0.0425

pH = 4.76 + log 0.0425 / 0.0533 = 4.66

(-) from 5.00 to 4.66

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