Question

The indicator cresol red has${\mathit{K}}_{\mathbf{\text{a}}}\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{5}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{9}}$. Over what approximate pH range does it change color?

Short answer

A cresol red indicator with $K_{\text{a}}=3.5\times {10}^{-9}$ will change its color at an approximate $7.455-9.455$ pH range value.

Step-by-step solution

Definition of pH

pH is a measure of hydrogen ion concentration that indicates whether a solution is acidic or alkaline.

Calculate pKa  value

When it comes to pH indicators, it is important to note that each one changes color based on a specific pH value.

When the pH of an indicator equals the pKa of the indicator, the color changes. The range in which an indicator can change its color is:

pKa (indicator) -1 to pKa (indicator) +1.

$\text{Hln}+{\text{H}}_2\text{O}>>{\text{H}}_3\text{O}+$

In Cresol red $Ka=3.5\times {10}^{-9}.$From the Ka value we can calculate the pKa value:

role="math" localid="1663319871054" $$\begin{gathered} pKa=-\log Ka \\ =-\log \left(3.5\times {10}^9\right) \\ =8.45 \end{gathered}$$

Therefore, the required pKa value is 8.45.

Finding the pH range

As previously stated, the pH range in which an indicator changes colour is approximately from the pKa (indicator) -1 to pKa (indicator) +1 , hence the given cresol red's pH range is:

$$\begin{gathered} 8.455-1=7.455 \\ 8.455+1=9.455 \\ \text{pHrange}:7.455-9.455 \end{gathered}$$

Thus, a cresol red indicator with $K_{\text{a}}=3.5\times {10}^{-9}$ will change its color at an approximate $7.455-9.455$pH range value.