Question

The indicator ethyl red has${\mathit{K}}_{\mathbf{a}}\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{8}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{6}}$. Over what approximatepHrange does it change colour?

Short answer

An ethyl red’s indicator with $K_{\text{a}}=3.8\times {10}^{-6}$ will change its color at an approximate $4.42-6.42$ pH range value.

Step-by-step solution

Definition of pH

A solution'spHvalue, which measures the concentration of hydrogen ions, reveals whether it is acidic or alkaline.

Calculate the pKa value

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

When the pH of an indicator equals the $pKa$of the indicator, the colour changes. An indicator's permissible colour change range is:

$\text{HIn}+{\text{H}}_2\text{O}>>{\text{H}}_3{\text{O}}^{+}+$

In the given instance, ethyl red $Ka=3.8\times {10}^6.$ From the $Ka$value we can calculate the $pKa$ value:

role="math" localid="1663318585069" $$\begin{gathered} pKa=-\log Ka \\ =-\log \left(3.8\times {10}^6\right) \\ =5.42 \end{gathered}$$

Therefore, the required pKa value is 5.42.

Finding the approximate value of pH

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

$$\begin{gathered} 5.42-1=4.42 \\ 5.42+1=6.42 \\ \text{pHrange}:4.42-6.42 \end{gathered}$$

Thus, an ethyl red’s indicator with $K_{\text{a}}=3.8\times {10}^{-6}$ will change its color at an approximate $4.42-6.42$ pH range value.