Question

An indicator $HIn$ has a standard ionization constant of $9.0\times {10}^{-9}$. The acid colour of the indicator is yellow and the alkaline colour is red. The yellow colour is visible when the ratio of yellow form to red form is $30$ to $1$ and the red colour is predominant when the ratio of red form to yellow form is $2$ to $1$. What is the $pH$ range of the indicator?

• A. < $6.568$
• B. $6.568$ to $8.346$
• C. > $8.346$
• D. None of these

Answer 1

Answer: (B)

$6.568$ to $8.346$

$\underset{Yellow}{HIn}+H_{2}O\rightleftharpoons H_3{O}^{+}+\underset{Red}{I{n}^{-}}$

$K_{In}=\left(\frac{\left[H_3{O}^{+}\right]\left[I{n}^{-}\right]}{HIn}\right)$

Yellow colour is visible when the ratio of acid form to base form is 3 to 1.

$K_{In}=\left(\frac{\left[H_3{O}^{+}\right]\left[1\right]}{30}\right)$

$9\times {10}^{-9}=\left(\frac{\left[H_3{O}^{+}\right]\left[1\right]}{30}\right)$

$\left[H_3{O}^{+}\right]=270\times {10}^{-9}$

$-log\left[H_3{O}^{+}\right]=pH=6.569$

Red colour is predominant when the ratio of base form to acid form is 2 to 1.

$K_{In}=\left(\frac{\left[H_3{O}^{+}\right]\left[2\right]}{1}\right)$

$\left[H_3{O}^{+}\right]=4.5\times {10}^{-9}$

$-log\left[H_3{O}^{+}\right]=pH=8.523$

The pH range of the indicator is 6.569 to 8.523.