Question

An organic compound of molar mass greater than $100$ contains only C, H and N. The percentage of C is 6 times that of H while the sum of percentages of C and H is 1.5 times that of N. What is the least molar mass of the compound?

• A. $175g$
• B. $140g$
• C. $105g$
• D. $210g$

Answer 1

The correct option is B $140g$

Let us assume $percentofHasx\%$,
$\therefore percentofCis6x\%$
As per question $\%C+\%H=1.5\left(\%N\right)$
$\therefore percentofNis\frac{14}{3}x\%$
Assuming $100$ g of total compound,
Mass of $H$ is $x$ g $\Rightarrow$ Moles of $H$ is $x$ moles
Mass of $C$ is $6x$ g $\Rightarrow$ Moles of $C$ is $\frac{x}{2}$ moles
Mass of $N$ is $\frac{14x}{3}$ g $\Rightarrow$ Moles of $N$ is $\frac{x}{3}$ moles
Taking simplest mole ratio of all three i.e. $C:H:N$ comes out to be $\frac{x}{2}:x:\frac{x}{3}$.
On simplifying it comes out to be $3:6:2$
$\therefore EmpiricalFormulais{C}_3{H}_6{N}_2$
Empirical Mass = $70g$
It is given in question that molar mass of compound comes out to be greater than 100 hence we need to multiply empirical formula by 2 for getting molecular formula having minimum molar mass greater than 100 .
$\therefore Molecularformulabecomes{C}_6{H}_{12}{N}_4$ whose molar mass is 140 i.e. greater than 100.