An acid-base indicator has a `K_(a) = 3.0 xx 10^(-5)`. The acid form of the indicator is red and the basic form is blue. Then

Options

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

C

Explanation

`underset(Red)(HIn)overset(K_("Ind"))hArrH^(o+)+underset(Blue)("Ind"^(Theta))`
Use: `pH = pK_("Ind") + "log" (["Ind"^(Theta)])/(["Hin"])`,
`pK_("Ind") =- log (3 xx 10^(-5)) = 4.52`
`75% Red rArr [("Hin"])/(["Ind"^(Theta)]) = (3)/(1)`
`rArr pH = pK_("Ind") + "log" (1)/(3) = 4.05`
`75% Blue rArr (["HIn"])/(["Ind"^(Theta)]) = (1)/(3)`
`rArr pH = pK_("Ind") + "log" (3)/(1) = 5.00`