`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)`.
Calculate the `pH` of a Coca Cola, assuming that the acidity of the cola arises only from `H_(3)PO_(4)` and `K_(a_(2))` and `K_(a_(3))` are no importance.

Options

A. `.18`
B. `2.2`
C. `3.3`
D. `4.4`

Answer

B

Explanation

If `K_(a_(1))` is taken `H_(3)PO_(4)` is a weak acid. `(Mw H_(3)PO_(4) = 98)`
`[H_(3)PO_(4)] = 0.05% = (0.05xx1000)/(100xx98) =5.1 xx 10^(-3)M`
`pH_(W_(A)) = (1)/(2) (pK_(a_(1)) - logC)`
`= (1)/(2) (2.12 - log 5.1 xx 10^(-3))`
`= (1)/(2) (2.12 - 0.7+3) = 2.21`