Q19.49P - Chemistry: Molecular Nature Of Matter And Change

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 approximate  pH range does it change colour?

Step-by-Step Solution

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 1: Definition of pH

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

Step 2: 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:

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

Therefore, the required pKa value is 5.42.

Step 3: 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.