Question

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

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

Answer 1

The correct option is B $140$

Let the compound be $C_x{H}_y{N}_z$.
Mass of $C=12x$
Mass of $H=y$
Mass of $N=14z$
Total Mass $=12x+y+14z$
Mass $\%$ of $C=\frac{12x}{(12x+y+14z)}\times 100$

Now given,
(I) Mass $\%$ of $C=6\times$ mass $\%$ of $H$
$⟹12x=6y$
$⟹y=2x$
(II) Mass $\%$ of $C+$ Mass $\%$ of $H=1.5$ (mass $\%$ of $N$)
$⟹12x+y=1.5\times 14z$
$⟹12x+2x=21z$
$⟹x=1.5z$
and $y=3z$.

So, the compound can be expressed as $C_{1.5z}{H}_{3z}{N}_z$ or $C_{3z}{H}_{6z}{N}_{2z}$.
Now choosing, $z=1$, we have $C_3{H}_6{N}_2$.
Molecular weight = $3\times 12+6\times 1+2\times 14=70$ g/mol

Given molecular weight $>100$.
So, when we choose $z=2$, we have $C_6{H}_{12}{N}_4$.

Molecular weight = $6\times 12+12\times 1+4\times 14=140$ g/mol which is greater than $100$.