`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)`.
`[Zn^(2+)]` ion in the soil is

Options

A. `2.9 xx 10^(-11)M`
B. `4.0 xx 10^(-10)M`
C. `3.0 xx 10^(-6)M`
D. `9.1 xx 10^(-5)M`

Answer

A

Explanation

`Zn_(3) (PO_(4))_(2) hArr 3Zn^(2+) +2PO_(4)^(3-)`
`K_(sp) = [Zn^(2+)]^(3) [PO_(4)^(3-)]^(2)`
`9.1 xx 10^(-33) = (2.2 xx 10^(-4))^(3) [PO_(4)^(3-)]^(2)`
`:. [PO_(4)^(3-)] = 2.9 xx 10^(-11)M`