Calculate the pKa of lactic acid

Question

Calculate the pK_a of lactic acid (CH₃CH(OH)COOH) given the following information.

40.0 mL of 0.2 M KOH are added to 100. mL of a 0.500 M lactic acid solution producing a pH of 3.134.

Answer 1

Let lactic acid be represented by HA

HA + OH- ==> A- + H2O

moles HA = 0.1 L x 0.500 mol / L = 0.0500 mols HA

moles OH- added = 0.040 L x 0.2 mol / L = 0.008 mols OH-

HA + OH- ===> A- + H2O

0.05...0.008.........0...............Initial

-0.008..-0.008....+0.008......Change

0.042----0............0.008.......Equilibrium

Using the Henderson Hasselbalch equation, and solving for pKa, we have...

pH = pKa + log [salt] / [acid]

3.134 = pKa + log (0.008 / 0.042)

3.134 = pKa + (-0.720)

pKa = 3.134 + 0.720

pKa = 3.85

Answer 2

1st determine the concentration of the neutralized acid:

(.1 liter)(.5 mole/liter) - (.04 liter)(.2 mole/liter OH^-) = .3 M Lactic Acid

Henderson Hasselbalch:

pK_A = pH + log([L^-]/[HL])

The [L^-] = [H⁺] and [HL] = .3 - [H⁺] when equilibrium is reached [H⁺] = 10^-3.134= 7.345 x 10^-4 M

pK_A = 3.234 + log(7.345x10^-4/.3) =

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