A few drops of each of the indicators shown in the accompanying table were
placed in separate portions of a \(1.0-M\) solution of a weak acid, HX. The
results are shown in the last column of the table. What is the approximate
\(\mathrm{pH}\) of the solution containing HX? Calculate the approximate value
of \(K_{\mathrm{a}}\) for HX.
$$
\begin{array}{|lcccc|}
\hline \text { Indicator } & \begin{array}{c}
\text { Color } \\
\text { of Hin }
\end{array} & \begin{array}{c}
\text { Color } \\
\text { of In }^{-}
\end{array} & \begin{array}{c}
\mathrm{pK}_{\mathrm{a}} \\
\text { of Hin }
\end{array} & \begin{array}{c}
\text { Color of } \\
1.0 \mathrm{MHX}
\end{array} \\
\text { Bromphenol blue } & \text { Yellow } & \text { Blue } & 4.0 & \text {
Blue } \\
\text { Bromcresol purple } & \text { Yellow } & \text { Purple } & 6.0 &
\text { Yellow } \\
\text { Bromcresol green } & \text { Yellow } & \text { Blue } & 4.8 & \text {
Green } \\
\text { Alizarin } & \text { Yellow } & \text { Red } & 6.5 & \text { Yellow }
\\\
\hline
\end{array}
$$