Question

The pH of a 1.0 L solution of 0.10 M lactic acid is 4.34. What is the new pH of the solution if 40 mL of 1.0 M HCl is added? The pKa of lactic acid is 3.86.

Answer 1

The pH of a 1.0 L solution of 0.10 M lactic acid is 4.34. What is the new pH of the solution if 40 mL of 1.0 M HCl is added? The pKa of lactic acid is 3.86.

Assume that moles of acid x

Then moles of base = 0.10 –X

the Henderson-AHasselbalch equation is
pH = pKa + log(c_base/c_acid)
the original pH is
4.34 = 3.86 + log(X/0.10-X)
log(X/0.10-X) = 0.48

X/0.10-X= 10^0.48

X/0.10-X=3.02

X = 0.302 -3.02X

4.02 X= 0.302

X= 0.075

Moles of acid =0.075

Moles of base = 0.025

moles H+ added = 40 x 10^-3 L x 1.0M

=0.04

new moles lactic acid = 0.0075 + 0.04

0.0475

Molarity = 0.0475 /1.040

= 0.0456

moles lactate = 0.0025 - 0.04

= -0.0375

Molarity = -0.0375/1.040

= - 0.036

pH = 3.86 + log 0.0456/ (-0.036)

pH = 3.86 + (-0.103)

= 3.757