The sodium salt of a carboxylic acid `(A)` was produced by passing a gas `(B)` into an aqueous solution of caustic alkali at an envolved temperature and pressure `(A)` on heating in the presence of sodium hydroxide followed by the treatment with sulphuric acid gave a dibasic acid `(C)`. A sample of `0.4 gm` of acid `(C)` on combustion gave `0.08 gm` of water and weighting `1.0 gm` on ignition yielded `0.71 gm` of silver as residue. Identify `(A), (B),` and (C)`.

Explanation

(i) `Gas (B) + NaOH overset (High. P,T)rarr RCOONa`
This is characteristic reaction of `CO_2` with `NaOH` to give sodium formate.
`underset((B)) (CO_2) + NaOH overset(High) underset(P,T)rarr HCOONa overset(H_2O) rarr underset((A)) (HCOOH)`
(ii) `(A)` on heating in the presence of `NaOH` followed with `H_2 SO_4` gives a dibasic acid `( C)`.
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(iii) The data given for `(C )` also confirms that it is oxalic acid.
`|{:("Element","Percentage","Relative no of atoms","Simplest ratio"),(,,=("Percentage")/("at. mass"),),(C,(12)/(44)xx(0.39)/(0.40)xx100=26.59,(26.59)/(12)=2.21,1),(H,(2)/(18)xx(0.08)/(0.40)xx100=2.22,(2.22)/(1)=2.22,1),(O,100-(26.59+2.22)=71.19,(71.19)/(16)=4.44,2):}|`
`:.` Empirical formula of `( C)` is `CHO_2`.
Empirical `wt. 45`
Also, `Mw` of `( C)` is
`(Wt. of Ag)/(Ew of Ag) = ("Wt. of Ag salt")/(E + 108)`
(where `E` is the `Ew` of anion of acid)
`(0.71)/(108) = (1)/(E + 108)`
`:. E = 44` (i.e., `Ew` of anion of acid)
`:. Ew` of acid `= 44 + 1= 45`
`Mw` of acid `= 90`
`:. n = (Mw)/("Empirical formula wt.") = (90)/(45) = 2`
Molecule formula, `= ("Empirical formula")_n`