`H_(3)PO_(4)` is a tribasic acid with `pK_(a_(1)), pK_(a_(2))` and `pK_(a_(3)) 1.12, 7.21`, and `12.32`, respectively. It is used in fertiliser productions and its various salts are used in food, detrgent, toothpaste, and in metal treatment.
Small quantities of `H_(3)PO_(4)` are used in inparting the sour or tart taste of soft drinkes, such as Coca Cola, and beers, in which `H_(3)PO_(4)` is prese4nt `0.05%` by weight (density `= 1.0 gmL^(-1))`.
`10^(-3)M H_(3)PO_(4)(pH = 7)` is used in fertilisers as an aqueous soil digesting. Plants can absorb zinc in whater soluble from only. Zinc phosphate is the source of zinc and `PO_(4)^(3-`) ions in the soil. `K_(sp)` of zinc phosphate `= 9.1 xx 10^(-33)`.
`[PO_(4)^(3-)]` ion in the soil with `pH = 7`, is

Options

A. `10^(-3)M`
B. `1.2 xx 10^(-4)m`
C. `2.2 xx 10^(-4)M`
D. `1.1xx10^(-10)M`

Answer

C

Explanation

`K_(a_(1)) xx K_(a_(2)) xx K_(a_(3)) = ([H^(o+)]^(3)[PO_(4)^(3-)])/([H_(3)PO_(4)]) [[[H_(3)PO_(4)]=10^(-3),],[pH=7,]]`
`- log K_(a_(1)) - log K_(a_(2)) - log K_(a_(3)) - log [H_(3)PO_(4)]`
`=- 3 log [H^(o+)] - log [PO_(4)^(3-)]`
`pK_(a_(1)) + pK_(a_(2)) + pK_(a_(3)) = 3pH - log [PO_(4)^(3-)] + log [H_(2)PO_(4)]`
`2.12 + 7.21 + 12.32 = 3 xx 6 - log [PO_(4)^(3-)] -3`
`:. log [PO_(4)^(3-)] =- 3.65`
`[PO_(4)^(3-)] =2.24 xx 10^(-4)M`