Question

A mixture of formic acid and oxalic acid is heated with conc. $H_{2}S{O}_4$. The gas produced is collected and treated with OH solution whereby the volume decreases by $\frac{1}{6}$th. The molar ratio of the two acids (formic acid/oxalic acid) is $x:y$. The value of $(x+y)$ is :

Answer 1

Let $x$ mol of $HCOOH$ and $y$ mol of $(COOH{)}_2$ be present.
$\underset{x}{HCOOH}\stackrel{H_{2}S{O}_4}{\to }{H}_{2}O+\underset{x}{CO}$
$\underset{x}{\left(COO{H}_2\right)}\stackrel{H_{2}S{O}_4}{\to }{H}_{2}O+\underset{x}{CO}+\underset{y}{C{O}_2}$
Total moles of $(CO+C{O}_2)=x+2y$
Total moles of $C{O}_2=y$
According to the question,
$(x+2y)\times \frac{1}{6}=y$
$\therefore \frac{x}{y}=4:1$
Alternatively, mole fraction of $C{O}_2=\frac{y}{x+2y}=\frac{1}{6}$
$\therefore \frac{x}{y}=4:1$
So, $x+y=4+1=5$