Exercise on Buffers

The conjugate base (A^-) in a buffer is usually added as the sodium or potassium salt (NaHCO₃ or KHCO₃, for example).

Structures of weak acids:

Guideline for working problems with buffers

I think of the pH scale as a visual line: pH 1                                                                             pH 14. When I'm working with a particular buffer, I place the relevant pK_a on the line and then add the significant pH to the line.

For example, I have two imaginary buffers, X (XH and X^-) and Y (YH⁺ and Y). I chose those as examples of the two most common changes for biochemical acids; that is, either the acid (HA) has no charge and losing H⁺ produces a conjugate base with a negative charge (A^-), or the acid has a positive charge, and losing H⁺ produces a conjugate base with no charge.

XH has a pK_a = 6.7, and YH⁺ has a pK_a = 7.9. If I want to choose a buffer for pH 7, then my visual line would look something like this:

pH 1                                                X (6.7)           7.0              Y (7.9)                                      pH 14

Because both X and Y have pK_a's within the pH + 1, either could be used as a buffer. At pH 6.7, [XH] = [X^-]. Below 6.7, [XH] > [X^-], and above 6.7, [XH] < [X^-]. This means that at pH 7.0, [X^-] > [XH].
Since the pK_a for YH⁺ is above pH 7.0, using Y as a buffer would require having a higher concentration of YH⁺ than of Y.

An alternative method is to write the equation for converting the acid to the conjugate base and to write the pK a above the arrow:

Then I think of the arrow as also representing a pH scale. The reactant side is when the pH is less than 6.7, and the product side is when the pH is greater than 6.7.

Problems

1. Draw the structure of the conjugate base for each acid shown (a-c).

2. A buffer can be made using H₂CO₃ and NaHCO₃.
a. Calculate the concentration of HCO₃^- in the buffer at pH 3.77 if the concentration of H₂CO₃ = 0.75 M.
b. If the buffer pH is adjusted to pH 4.5 by adding NaOH, what is the ratio between [A^-] and [HA]?
c. What is the concentration of H₂CO₃ for this same buffer at pH 4.5?

3. Your lab has bottles of H₃PO₄, NaH₂PO₄, Na₂HPO₄, and Na₃PO₄ that can be used for preparing phosphate buffers.
a. Which two should you use in order to prepare a buffer for pH 2.14?
b. What should their relative concentrations be? That is, what is the ratio between the conjugate base and the acid?
c. What adjustment should you make in order to buffer pH 2.5 instead?
d. Which two should you use in order to prepare a buffer for pH 6.5? The relevant pK_a is 6.86.
e. What is the ratio between the conjugate base and the acid for the buffer in part d?
f. What is the ratio between the conjugate base and the acid for the same buffer if a pK_a of 2.14 is used instead of 6.86?

4. Choose the best acid from Table 1 for making a buffer for each pH listed below. Under "Higher Concentration" write HA if the acid concentration should be higher, A^- if the conjugate base concentration should be higher, and both if their concentrations should be equal.

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