A buffer contains 0.010 moles of lactic acid (pKa = 3.86) and 0.050 mol of sodium lactate per liter. (a) Calculate the pH of the buffer.
(b) Calculate the change in pH when 5 mL of 0.5 M HCl is added to 1 L of the buffer.
(c) What pH change would you expect if you added the same quantity (5 mL) of HCl to 1 L of pure water?

a. pH = 4.56

b. Change in pH = 0.85

c. Change in pH = 5.4

Explanation:

a. The pKa of lactic buffer is: 3.86.

Using Henderson-Hasselbalch formula for the lactic buffer:

pH = 3.86 + log [Lactate] / [Lactic acid]

Where [] is molarity of each compound but could be taken as moles

Replacing:

pH = 3.86 + log [0.050 moles] / [0.010 moles]

pH = 4.56

b. The HCl added reacts with Lactate producing lactic acid. Moles of HCl are:

5x10⁻³L * (0.5mol /L) = 0.025 moles HCl

Moles of lactate: 0.050moles - 0.025 moles = 0.025 moles

Moles lactic acid: 0.010 moles + 0.025 moles = 0.035 moles

pH = 3.86 + log [0.025 moles] / [0.035 moles]

pH = 3.71

Change in pH = 4.56 - 3.71 = 0.85

c. 1L of pure water has a pH of 7. 0.025 moles of HCl = 0.025 moles H⁺ in 1.005L:

0.025 mol / 1.005L = 0.0249M = [H⁺]

As pH = -log [H⁺]

pH = 1.6

Change in pH = 7.0 - 1.6 = 5.4

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