i) `H_3PO_(4(aq)) iff H^ _(aq)+ H_2PO_(4(aq))^-`
ii)`H_2PO_(4(aq))^- iff H^ +(aq)+ H_2PO_(4(aq))^(2-)` .
iii) `H_2PO_(4(aq))^(2-) iff H^ +(aq)+ PO_(4(aq))^(3-)` . The equilibrium constantsfor the above reactions at a certain temperature are `K_1, K_2 and K_3` respectively. The equilibrium constant for the reaction. `H_3PO_4(aq) iff 3H^ +(aq)+ PO_(4(aq))^(3-)` in terms `K_1, K_2 and K_3` is

Options

A. `K_(1) +K_(2) +K_(3)`
B. `K_(1)/(K_(2)+K_(3))`
C. `K_(3)/(K_(1)K_(3))`
D. `K_(1) K_(2) K_(3)`

Answer

D

Explanation

Required relation
`H_(3) PO_(4) (aq)hArr 3H^(+) (aq) + PO_(4)^(3-)(aq)`
`:. K_(1)=([H^(+)]_((aq))^(+)[H_(2)PO_(4)^(-)]_((aq)))/(H_(3)PO_(4_((aq))))" ". . . (i)`
`([H^(+)]_((aq))[HPO_(4)^(3-)]_((aq)))/([H_(2)PO_(4)^(-)]_((Aq)))" ". . . (ii)`
`([H^(+)]_((aq))[HPO_(4)^(3-)]_((aq)))/([HPO_(4)^(2-)]_((aq)))" ". . . (iii)`
On multiplying (i), (ii) and (iii)
`K_(1) xx K_(2) xx K_(3)`
` = (3[H^(+)] [H_(2)PO_(4)^(-)]_((aq))[HPO_(4)^(-)]_((aq))[PO_(4)^(3-)]_((aq)))/([H_(3)PO_(4)]_((aq))[H_(2)PO_(4)^(-)]_((aq))[HPO_(4)^(2-)]_((aq)))`
`K_(1) xx K_(2) xx K_(3) = ([H^(+)][PO_(4)^(3-)])/([H_(3)PO_(4)])=K`
Hence, option (d) is the correct answer.