Question

A beaker with 1.10×102 mL of an acetic acid buffer with a pH of 5.000 is sitting on a benchtop. The total molarity of acid and conjugate base in this buffer is 0.100 M. A student adds 8.00 mL of a 0.370 M HCl solution to the beaker. How much will the pH change? The pKa of acetic acid is 4.740. Express your answer numerically to two decimal places. Use a minus ( − ) sign if the pH has decreased.

Answer 1

we know that

for buffers

pH = pKa + log [salt / acid ]

in this case

pH = pKa + log [ CH3COO- / CH3COOH ]

5 = 4.74 + log [ CH3COO- / CH3COOH ]

[ CH3COO- / CH3COOH ] = 1.82

[CH3COO-] = 1.82 [CH3COOH]

now

given

total molarity = 0.1

so

[CH3COO-] + [CH3COOH] = 0.1

1.82 [CH3COOH] + [CH3COOH] = 0.1

[CH3COOH] = 0.03546

[CH3COO-] = 1.82 x 0.035461 = 0.06454

now

we know that

moles = molarity x volume (L)

so

moles of HCL added = 0.37 x 8 x 10-3 = 2.96 x 10-3

moles of CH3COOH = 0.03546 x 110 x 10-3 = 3.9006 x 10-3

moles of Ch3COO- = 0.06456 x 110 x 10-3 = 7.1016 x 10-3

now

the reaction is

CH3COO- + H+ --> CH3COOH

we can see that

moles of CH3COO- reacted = moles of H+ added = 2.96 x 10-3

moles of CH3COOH formed = moles of H+ added = 2.96 x 10-3

now

finally

moles of CH3COOH = 3.9006 x 10-3 + 2.96 x 10-3 = 6.8606 x 10-3

moles of CH3COO- = 7.1016 x 10-3 - 2.96 x 10-3 = 4.1416 x 10-3

now

pH = pKa + log [ CH3COO- / CH3COOH]

pH = 4.74 + log [ 4.1416 x 10-3 / 6.8606 x 10-3 ]

pH = 4.521

so

the pH of the solution is 4.521

pH change = 4.521 - 5

pH change = - 0.479