Question

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

• A. pH is 4.04 when indicator is 75% red
• B. pH is 5.00 when indicator is 75% blue
• C. pH is 5.00 when indicator is 75% red
• D. pH is 4.05 when indicator is 75% blue

Answer 1

Answer: (A), (B)

pH is 4.04 when indicator is 75% red
pH is 5.00 when indicator is 75% blue

For an acid-base indicator

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

So when indicator is 75% red

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

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

So when indicator is 75% blue

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

$pH=5-log3+log3=5$