Question

An acid-base indicator has a $K_a=3.0\times {10}^{-5}$. The acid form of the indicator is red and the basic form is blue.

Then:

• A. $pH$ is $4.05$ when indicator is $75$% red
• B. $pH$ is $5.00$ when indicator is $75$% blue
• C. Both (A) and (B) are correct
• D. None of these

Answer 1

The correct option is C Both (A) and (B) are correct

For an acid-base indicator

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

So when indicator is 75% red

$\frac{\left[I{n}^{-}\right]}{\left[HIn\right]}=\frac{25}{75}=\frac{1}{3}$

$pH=5-log3+log\frac{1}{3}=4.05$

So when indicator is 75% blue

$\frac{\left[I{n}^{-}\right]}{\left[HIn\right]}=\frac{75}{25}=3$

$pH=5-log3+log3=5$