An acid-base indicator has a $\mathrm{K}_{\mathrm{a}}$ of $3.0 \times 10^{-5} .$ The acid form of the…

An acid-base indicator has a $\mathrm{K}_{\mathrm{a}}$ of $3.0 \times 10^{-5} .$ The acid form of the indicator is red and the basic form is blue. Then:
  1. $\mathrm{pH}$ is $4.05$ when indicator is $75 \%$ red
  2. $\mathrm{pH}$ is $5.00$ when indicator is $75 \%$ red
  3. $\mathrm{pH}$ is $4.05$ when indicator is $75 \%$ blue
  4. none of these

Solution

$\mathrm{HIn} ightleftharpoons \mathrm{In}^{-}+H^{+}$
Red blue
$\mathrm{pH}=\mathrm{pK}_{\mathrm{ln}}+\log \frac{\left[\mathrm{ln}^{-}ight]}{[\mathrm{Hln}]}$
$(5-\log 3)+\log \left(\frac{25}{75}ight)$
$\mathrm{pH}$ is $4.05$ when the indicator is $75 \%$ red.

Asked in: JEE-TOPICTESTS-CHEMISTRY

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