Question

An organic compound contains $20\% $ carbon, $6.66\% $ hydrogen, $47.33\% $ nitrogen and the rest was oxygen. Its molar mass is $60g$ the molecular formula of the compound is?
A) $C{H_4}{N_2}O$
B) $C{H_2}N{O_2}$
C) \[{C_2}{H_6}NO\]
D) \[C{H_{18}}NO\]

Answer 1

Hint: A chemical formula is a way of presenting information about the chemical proportions of atoms that constitute a particular chemical compound or molecule. In this question to find the molecular formula of the compound we first calculate the empirical formula of carbon, hydrogen and nitrogen and then divide it by the moles of oxygen.

Complete answer:
With all these empirical formula problems, we assume that there are $100g$ of unknown compounds, and work out the empirical formula appropriately. Now, we calculate the mass and moles of each atom in the compound by using the formula: $Number\,of\,moles = \dfrac{{Mass\,of\,compound}}{{Molecular\,mass}}$.

Moles of carbon$ = \dfrac{{20.0g}}{{12.011gmo{l^{ - 1}}}} = 1.67mol$
Moles of hydrogen $ = \dfrac{{6.66g}}{{1.00794gmo{l^{ - 1}}}} = 6.61mol$

Moles of nitrogen $ = \dfrac{{47.33g}}{{14.01gmo{l^{ - 1}}}} = 3.38mol$
We are also given that the remaining mass belongs to Oxygen. So, we get,

Moles of oxygen $ = \dfrac{{\left( {100 - 20.0 - 6.66 - 47.33} \right)g}}{{15.999gmo{l^{ - 1}}}} = 1.63mol$
And now we divide through by the smallest molar quantity, that of oxygen, to get the empirical formula:
C: $\dfrac{{1.67mol}}{{1.63mol}} \cong 1$
H: $\dfrac{{6.61mol}}{{1.63mol}} \cong 4$
N: $\dfrac{{3.38mol}}{{1.63mol}} \cong 2$
O: $\dfrac{{1.63mol}}{{1.63mol}} \cong 1$

We thus get an empirical formula of $C{H_4}{N_2}O$.
Also, we get the molar mass of the compound as: $12 + 4\left( 1 \right) + 2\left( {14} \right) + 16 = 12 + 4 + 28 + 16$
Opening the brackets and doing the calculations, we get,
$ = 60g$

So, the correct answer is (A) $C{H_4}{N_2}O$

Note: The difference between the molecular and the empirical formula is that an empirical formula represents the simplest whole-number ratio of various atoms present in a compound. The molecular formula shows the exact number of different types of atoms present in a molecule of a compound. The molecular formula can further be obtained if the molar mass is known. Molecular formulas indicate the simple numbers of each type of atom in a molecule of a molecular substance. They are the same as the empirical formula for molecules that only have one atom of a particular type but otherwise may have larger numbers.