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

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 $Ka=3.5×{10}^{-9}.$From the Ka value we can calculate the pKa value:

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

Therefore, the required pKa value is 8.45.

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 $K_{\text{a}}=3.5×{10}^{-9}$ will change its color at an approximate $7.455-9.455$pH range value.