An acid-base indicator has a `K_(a)` of `3.0 xx 10^(-5)`. The acid form of the indicator is red and the basic form is blue. (a) By how much must the `pH` change in order to change the indicator from `75%` red to `75%` blue?

Explanation

`{:(,"HIn",hArr,H^(oplus)+"Ind"^(Theta)),(,"Acid form",,"Conjugate base or salt"),("i".,75 %"red",,25 % "blue"),("ii".,25 %,,75 % "blue"):}`
When indicator si `75%` red `rArr 25%` blue (basic fomr)
a. `:. pH_(1) = pK_(a) + log (25//75) = pK_(a) + log 1//3 ….(i)`
When acid form of indicator is `75%` blue `rArr 25%` red,
`pH_(2) = pK_(a) + log (75//25) = pK_(a) + log3 ....(ii)`
From equations (i) and (ii)
`pH_(2) - pH_(1) = log3 - log 1//3 = log 9 = log (3)^(2)`
`= 0.4771 xx 2 = 0.9542`
`:.` Change in `pH = 0.9452`