Question

A mixture of $HCOOH$ and $H_2{C}_2{O}_4$ is heated with conc. $H_{2}S{O}_4$. The gas produced is collected and on treating with $KOH$ solution, the volume of the gas decreases by $\frac{1}{6}$th. The molar ratio of two acids in the original mixture is $x:y$. The value of $x+y$ is :

Answer 1

(i) $HCOOH\underset{\Delta }{\stackrel{H_{2}S{O}_4}{⟶}}{H}_{2}O+CO$
Initial moles a 0 0
Final moles 0 a a
(ii) $H_2{C}_2{O}_4\underset{\Delta }{\stackrel{H_{2}S{O}_4}{⟶}}{H}_{2}O+CO+C{O}_2$
Intital mole b 0 0 0
Final mole 0 b b b
$\therefore$ Moles of $CO$ formed $=$ a+b
and Moles of $C{O}_2$ formed $=$ b
The gaseous mixture on passing through $KOH(C{O}_2$ is absorbed) reduces its volume by $\frac{1}{6}$, therefore,
Moles of $C{O}_2=\left(\frac{1}{6}\right)\times$ total moles
$b$ $=\left(\frac{1}{6}\right)\times (a+2b)\therefore \frac{a}{b}=\frac{4}{1}$
So, $x+y=4+1=5$.