Question

A compound of carbon hydrogen and nitrogen contains these elements in the ratio $9:1:3.5$ If its molecular mass is $108$ what is the molecular formula?
a.) ${{C}_{2}}{{H}_{2}}N$
b.) ${{C}_{3}}{{H}_{4}}N$
c.) ${{C}_{2}}H{{N}_{2}}$
d.) ${{C}_{6}}{{H}_{8}}{{N}_{2}}$

Answer 1

. Using the ratio of the elements present in the given compound which contains carbon hydrogen nitrogen whose molecular mass is 108, try to find out the molecular weight for each element in the compound to find the molecular weight.

Complete step by step answer:
Given that a compound contains carbon hydrogen and nitrogen. These elements in the given compound are present in the ratio of $9:1:3.5$, also given the molecular weight of the compound is $108$using these ratios and the molecular weight of the compound let’s try to find out the molecular weight of each element present in the given compound.
Carbon hydrogen and nitrogen contain in the compound in the ratio $9:1:3.5$
Total molecular weight of an element present in the compound is $=\left( \dfrac{\text{ratio of the element}}{\text{sum of the ratio}} \right)\times \text{molecular weight of the compound}$

The total molecular weight of the carbon present in the compound is $=\left( \dfrac{9}{13.5} \right)\times 108 = 72$
That is $6\times 12\left( \text{molecular weight of the carbon} \right)$. This means there are $6$ carbon atoms present in the given compound.
The total molecular weight of the hydrogen present in the compound is $=\left( \dfrac{1}{13.5} \right)\times 108 = 8$
That is $8\times 1\left( \text{molecular weight of the hydrogen} \right)$. This means there are $8$ hydrogen atoms present in the given compound.
The total molecular weight of the nitrogen present in the compound is $=\left( \dfrac{3.5}{13.5} \right)\times 108 = 28$
That is $2\times 14\left( \text{molecular weight of the nitrogen} \right)$. This means there are $2$ nitrogen atoms present in the given compound.
Therefore there are 6 carbon atoms, 8 hydrogen atoms and 2 nitrogen atoms present in the given compound and hence the molecular formula of the given compound is ${{C}_{6}}{{H}_{8}}{{N}_{2}}$
So, the correct answer is “Option D”.

Note: The molecular weight of the elements present in the given compound is
$carbon-12$
$hydrogen-1$
$nitrogen-14$