Question

What is the relationship between the buffer range and the buffer-component concentration ratio?

Short answer

Within a 1 pH value of an acid component, the buffer that can be used is (Ka). As a result, the component concentration ratio should range from 0.1 to 10 .

Step-by-step solution

Buffer range

A buffer range is a pH range across which a buffer will work effectively. When a buffer component ratio is 1 , it has the highest value. As a Buffer Component Ratio deviates from 1, its value steadily declines.

Explanation

In practice, a buffer becomes useless if one component of a buffer ratio is more than 10 times the other. That is, a buffer action will only be effective if the ratio of A to HA is between 0.10 and 10 .

So, we have:

$\text{pH = pKa + log}\frac{\left[{\text{A}}^{\text{-}}\right]}{\text{[HA]}}$

Then, we know that:

$$\begin{gathered} \text{log 10 = 1}\to \\ \text{log 0.1 = - 1} \end{gathered}$$

When [A-] / [HA] is at its maximum— 0.1 or 10 .

$$\begin{gathered} \text{pH = pKa + log}\frac{\text{[A - ]}}{\text{[HA]}} \\ \text{= pKa + log0.1} \\ \text{= pKa - 1.} \end{gathered}$$

Or , it can also be:

$$\begin{gathered} \text{pH = pKa + log}\frac{\text{[A - ]}}{\text{[HA]}} \\ \text{= pKa + log10} \\ \text{= pKa + 1.} \end{gathered}$$

Therefore, a buffer has an useable range of 1 pH value of the acid component (Ka).