Calcium lactate is a salt of weak organic acid and strong base represented as `Ca(LaC)_(2).` A saturated solution of `Ca(LaC)_(2)` contains 0.6 mole in 2 litre solution. pOH of solution is 5.60. If `90%` dissociation of the salt takes place then what is `pK_(a)` of lactic acid?

Options

A. `2.8-"log"(0.54)`
B. `2.8+"log"(0.54)`
C. `2.8+"log"(0.27)`
D. `2.8-"log"(0.27)`

Answer

A

Explanation

`Ca(La)_(2) rarr Ca^(2+) + 2LaC^(-)`
Initial concentration `0.6//2 = 0.3 M`
After association
`[LaC^(-)] = 2 xx 0.3 xx 0.9 = 0.54 M`
`pH = 1/2[pK_(w) + pK_(a) + "log"(Lac^(-))]`
`14-5.6 = 1/2[14 + pK_(a) + "log" (0.54)]`
`pK_(a) = 2.8 - "log" (0.54)`