Chemical and Ionic Equilibrium 2 Question 59
59. An acid type indicator, HIn differs in colour from its conjugate base $\left(\mathrm{In}^{-}\right)$. The human eye is sensitive to colour differences only when the ratio $\left[\mathrm{In}^{-}\right] /[\mathrm{HIn}]$ is greater than 10 or smaller than 0.1 . What should be the minimum change in the $\mathrm{pH}$ of the solution to observe a complete colour change? $\left(K_{a}=1.0 \times 10^{-5}\right)$
$(1997,2 \mathrm{M})$
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Solution:
- $\mathrm{pH}=\mathrm{p} K_{\text {In }}+\log 10=\mathrm{p} K_{\text {In }}+1$
$$ \text { When } \frac{\left[\operatorname{In}^{-}\right]}{[\mathrm{HIn}]}=10 $$
$$ =\mathrm{p} K_{\text {In }}+\log (0.1)=\mathrm{p} K_{\text {In }-1} \quad \text { When } \frac{\left[\mathrm{In}^{-}\right]}{[\mathrm{HIn}]}=0.1 $$
$\mathrm{pH}$ range is $\mathrm{p} K_{\text {In }-1}$ to $\mathrm{p} K_{\text {In }+1}$.
