A mixture of formic acid and oxalic acid is heated with conc. `H_2SO_4` . The gas produced is collected and treated with `KOH` solution where the volume decreases by 1/6th. The molar ratio of two acids (formic acid/oxalic acid) in the original mixuture is:
(a) `4:1`
(b) `1:4`
(c) `2:1`
(d) `1:2`

Explanation

Let x moles of oxalic acid and y moles of formic acid be heated with conc. `H_(2)SO_(4)` according to the following equations
`{:("COOH"),("| "overset(H_(2)SO_(4)//heat)(rarr)CO(g)+CO_(2)(g)+H_(2)O(l)),("COOH"),("x mol x mol x mol"),("HCOOH" overset(H_(2)SO_(4)//heat)(rarr)CO(g)+H_(2)O(l)),("y mol y mol"):}`
Total moles of gaseous mixture = Moles of CO + Moles of `CO_(2)`
`= (x+y)mol + x mol = (2x +y)mol`
Now, KOH absorbs only `CO_(2)` i.e, x moles and the volume of the solution decreases by 1/6th of the its volume. Since equal volumes of gases have equal number of moles according to Avogadro's Law,
`:. ("Moles of "CO_(2))/("Moles of both gases")=(x)/((2x+y))=(1)/(6)or6x=2x+yor 4x=yor (y)/(x)=4`
`:.` Molar ratio of formic acid : Oxylic acid `= 4:1`.