0.1 M solution of `H_(3)A` being a weak triprotic acid having `K _(a _(1)) , K _(a _(2)) and K _(a _(3))` as `10 ^(-5) , 10 ^(-9) and 10 ^(-13)` respectively. If pX represents `- logX and X= ""([ A ^(3-) ])/( [ HA ^(2-)]),` then the value of pX is:

Options

A. 7
B. 8
C. 10
D. 9

Answer

C

Explanation

`[H^(+)]` are obtained in dissociation of `H_(3)` A in all the three steps, but the `[H^(+)]` obtained in II & III steps a too law. Thus `[H^(+)]` can be obtained from 1 step
`[H^(+)] = sqrt(K_(a1) xx c) (1-alpha ~= 1) = sqrt(10^(-5) xx 0.1) = 10^(-3)`
Now, `K_(3) = ([H^(+)][A^(3-)])/([H A^(2-)], [HA^(2-) hArr A^(3-) " II Step"]`
`10^(-13) = (10^(-13)xx [A^(3-)])/([HA^(2-)]) therefore ([A^(3-)])/([HA^(2-)]) = 10^(-10) therefore pX = 10`