A certain acid - base indicator is red in acid and blue in basic solution. At pH = 5, 75% of the indicator is present in the solution in its blue form. Calculate dissociation constant (K_a) for the indicator and pH range over which the indicator changes from 90% red- 10% blue to 90% blue-10% red.

A certain acid - base indicator is red in acid and blue in basic solut

1.	A certain acid - base indicator is red in acid and blue in basic solution. At pH = 5, 75% of the indicator is present in the solution in its blue form. Calculate dissociation constant (K_a) for the indicator and pH range over which the indicator changes from 90% red- 10% blue to 90% blue-10% red.
Answer» Solution :Since `K_a` is asked, the indicator must be an acid. Let the acid be represented by HIN. HI n `hArrH^+ + "In"^(-)` In acid solution, the indicator will be predominatly present in the form of HIn (due to common ion effect.) Since in acid solutin the the COLOUR is red, this would be due to HIn. In basic solution, the indicator will be predominatly in the form of `In^–`. Since the indicator is blue in basic solution, so `In^–` must be blue in colour. At PH = 5, the indicator is 75% blue. This also means it is 25% red. `therefore K_a=(10^(-5)xx0.75)/0.25=3xx10^(-5)`pH when it is 90% red & 10% blue `: {H^+ ] =(K_axx[HIn])/([In^-])=(3xx10^(-5)xx0.9)/0.1 = 2.7xx10^(-4)` `therefore` pH=3.56 pH when it is 90% blue and 10% red : `[H^+]=(K_axx[HIn])/([In^-])=(3xx10^(-5) xx0.1)/0.9=3.3xx10^(-6)`