Question

A compound of carbon, hydrogen and nitrogen contains these elements in the ratio $9:3:1.5$. Calculate the empirical formula, if its molecular mass is 108, what is the molecular formula.

Answer 1

The simplest positive ratio of atoms presents in the molecule, which forms the empirical formula. Divination of empirical mass and molecular mass by empirical mass to get the factor. Empirical formula multiplies with the factor, we get the molecular formula. Here we know the empirical mass and molecular mass to find the molecular formula.

Complete step by step answer:
Empirical formula is defined by the positive integer ratio of present in the molecule. The given ratio is $9:3:1.5$ which is given for carbon, hydrogen and nitrogen. This ratio is given in mass and we convert it in the moles by dividing it by their respective atomic mass.
The atomic ratio will be given as below,
$\dfrac{9}{{12}}:\dfrac{1}{1}:\dfrac{{3.5}}{{14}} = 0.75:1:0.25$
We have to convert it into a positive integer ratio by dividing the whole ratio by the lowest number which is 0.25.
Now we get the value after dividing whole ratio with 0.25 is given below:
$\dfrac{{0.75}}{{0.25}}:\dfrac{1}{{0.25}}:\dfrac{{0.25}}{{0.25}} = 3:4:1$
Here we put this value in the empirical formula and get the molecular formula is ${C_3}{H_4}N$.
Now we calculate with the help of molecular mass which is 108. Empirical formula is formed by using molecular mass of the compound which is shown as below:
$12 \times 3 + 1 \times 4 + 14 = 54g$
Now we divide 108 by 54 and get the value. hence the actual ratio is $6:8:2$ so the empirical formula is ${C_6}{H_8}{N_2}$. Hence $x = 6,y = 8,z = 2$.

Note: It is used to get the molecular formula of unknown molecules in the way shown above. It provides the lowest whole number ratio of atoms. We have calculated in the preceding section to express the simplest atomic ratio between the elements in the compound.