Factors affecting buffer capacity

What are the factors affecting the capacity of a buffer solution?

The effectiveness (or capacity) of a buffer is dependent on a few factors, namely,

1. 1. Absolute concentrations of the conjugate acid and conjugate base
   2. Relative concentrations of the conjugate acid and conjugate base
   3. pK_a (for an acidic buffer) of the weak acid in relation to the pH that the buffer is supposed to maintain
   4. Absolute value of pK_a
   5. Temperature

To rationalise the first factor affecting buffer capacity, we refer to the acidic buffer equilibrium:

As mentioned in the previous article, a base OH^– that is added to the buffer reacts with H₃O⁺ to form water. According to Le Chatelier’s principle, the system counteracts the change by shifting the above equilibrium to the right, with some HA further dissociating to replace H₃O⁺ that is removed. The higher the concentration of the conjugate acid HA is, the larger the amount of HA that can replace the removed H₃O⁺. Similarly, the larger the amount of the conjugate base A^– is, the greater the ability of the buffer to react with acid that is added to it. Hence, buffer capacity is proportional to the combined concentrations of the conjugate acid and conjugate base. Mathematically, the buffer capacity of a weak conjugate acid/conjugate base pair is given by the following equation (see this article for derivation):

where [HA]_T = [HA] + [A^–], i.e. the analytical concentration of HA.

The equation clearly shows that the buffer capacity of an acidic buffer is proportional to the combined concentrations of the conjugate acid and conjugate base.

The second factor states that the relative concentrations of the conjugate acid and conjugate base affects buffer capacity. In fact, the maximum buffer capacity of a solution occurs when the concentration of the conjugate acid equals to the concentration of the conjugate base (see this article for details). Substituting into the Henderson-Hasselbalch equation, we have pH = pK_a. In other words, for an acidic buffer to have maximum buffer capacity, the pK_a of the chosen weak acid must be as close as possible to the pH that the buffer is supposed to maintain. This is how the third factor affects buffer capacity.

It is also important to select an acid with pK_a that is not too high or too low (fourth factor). An acid with pK_a < 3 (K_a > 10^-3) is a relatively strong acid with high degree of dissociation. Likewise, an acid with pK_a > 11 (K_a < 10^-11) is a relatively strong base with high degree of dissociation. As explained in this article, a strong acid (or a strong base) has very low or negligible buffer capacity.

Finally, the buffer capacity of a solution is affected by changes in temperature (fifth factor) since the equilibrium constant is temperature-dependent:

which implies that pK_a is also temperature-dependent.

In short, these five factors are important in preparing a buffer solution, which we will discuss in the next article.

 

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