Question

A certain acid-base indicator has acid form red and blue is basic form $75$% of the indicator is present in the solution in its blue form at $pH=5$. $K_a$ for the indicator is:

• A. $K_a=2\times {10}^{-5}$
• B. $K_a=9\times {10}^{-5}$
• C. $K_a=3\times {10}^{-6}$
• D. $K_a=3\times {10}^{-5}$

Answer 1

The correct option is D $K_a=3\times {10}^{-5}$

$HA\rightleftharpoons H^{+}+A^{-}$

From the equation

$K_a=\frac{\left[H^{+}\right]\left[A^{-}\right]}{\left[HA\right]}$

$\left[H^{+}\right]={10}^{-pH}={10}^{-5}$

Basic form $\left[A^{-}\right]=75$%

Concentration of Solution $\left[HA\right]=25$%

$K_a=\frac{{10}^{-5}\times 75}{25}=3\times {10}^{-5}$.