Question

A mixture of formic acid and oxalic acid is heated with conc. ${{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}$ . The gas produced is collected and treated with alkaline solution, whereby the volume decreases by $\dfrac{{\text{1}}}{{\text{6}}}{\text{th}}$ . The molar ratio of the two acids (formic acid/ oxalic acid) is:
(A) 4:1
(B) 1:4
(C) 2:1
(D) 1:2

Answer 1

Hint: Concentrated sulphuric acid is hygroscopic in nature and hence it is used as a dehydrating agent. Carboxylic acids on being treated with concentrated sulphuric acid get dehydrated.
 Dehydration of formic acid will release carbon monoxide gas whereas dehydration of oxalic acid will release two gases, carbon monoxide and carbon dioxide. From the moles of the gases produced, the molar ratio of the two acids can be calculated.

Complete step by step answer:
Given that a mixture of formic acid and oxalic acid is heated with conc. ${{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}$ .
Also given that the gas produced is collected and treated with alkaline solution, whereby the volume decreases by $\dfrac{{\text{1}}}{{\text{6}}}{\text{th}}$ .
We need to find out the molar ratio of the two acids, i.e., the molar ratio of formic acid to oxalic acid.
The dehydration reaction of formic acid with concentrated sulphuric acid is:
${\text{HCOOH + }}{{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}} \to {\text{CO + }}{{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_4}{\text{ + 2}}{{\text{H}}_{\text{2}}}{\text{O}}$
The dehydration reaction of oxalic acid with concentrated sulphuric acid is:
${{\text{H}}_2}{{\text{C}}_2}{{\text{O}}_4}{\text{ + }}{{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}} \to {\text{CO + C}}{{\text{O}}_2}{\text{ + }}{{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_4}{\text{ + }}{{\text{H}}_{\text{2}}}{\text{O}}$
Let the number of moles of formic acid be x and that of oxalic acid be y.
Since the moles of products formed will be equal to the moles of reactants decomposed, therefore, the number of moles of ${\text{CO}}$ formed from formic acid will be x.
And the number of moles of ${\text{CO}}$ and ${\text{C}}{{\text{O}}_2}$ formed from oxalic acid will each be y.
Total moles of gases produced will be ${\text{ = }}\left( {{\text{x + 2y}}} \right)$ .
It is given that after treating gas with alkali solution, the volume decreases by $\dfrac{{\text{1}}}{{\text{6}}}{\text{th}}$ which is because ${\text{C}}{{\text{O}}_2}$ is absorbed. Therefore, it is actually the volume of ${\text{C}}{{\text{O}}_2}$ which is equal to $\dfrac{{\text{1}}}{{\text{6}}}{\text{th}}$ of the total volume of ${\text{CO}}$ and ${\text{C}}{{\text{O}}_2}$ .
Therefore, we will have:

\[
\dfrac{{\text{y}}}{{{\text{x + 2y}}}}{\text{ = }}\dfrac{{\text{1}}}{{\text{6}}} \\
\Rightarrow {\text{x + 2y}} = {\text{6y}} \\
\Rightarrow {\text{x}} = 4{\text{y}} \\
\Rightarrow \dfrac{{\text{x}}}{{\text{y}}} = \dfrac{4}{1} \\
 \]
Therefore, the molar ratio of formic acid to oxalic acid is 4:1.

So, the correct option is A.

Note: When carboxylic acids are heated in presence of a strong dehydrating agent like conc. sulfuric acid, acid anhydrides are formed by the elimination of water from two molecules of the acid. For example, ethanoic anhydride is formed from ethanoic acid.
$2{\text{C}}{{\text{H}}_{\text{3}}}{\text{COOH}}\xrightarrow[{{\text{conc}}{\text{.}}{{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}}]{\Delta }{\left( {{\text{C}}{{\text{H}}_{\text{3}}}{\text{CO}}} \right)_{\text{2}}}{\text{O}}$