Question

An acid type indicator, $HIn$, differs in colour from its conjugate base ${In}^{-}$. The human eye is sensitive to colour differences only when the ratio $\left[{In}^{-}\right]/\left[HIn\right]$ is greater than $10$ or smaller than $0.1$. What should be the minimum change in pH of solution to observe a complete colour change?
$(K_a={10}^{-5})$

Answer 1

$p_{1}H=p{K}_{In}+\log \frac{\left[I{n}^{-}\right]}{\left[HIn\right]}$

$\Rightarrow p_{1}H=5+\log 10=5+1$

$\Rightarrow p_{2}H=p{K}_{In}+\log \frac{\left[I{n}^{-}\right]}{\left[HIn\right]}$

$\Rightarrow p_{2}H=5+\log 0.1=5-1$

$\therefore pH$ change= $\pm 1$

$\therefore$ The minimum change of $pH$ should be $1$ to observe a complete color change.