Question

A compound of carbon, hydrogen, and nitrogen contains the three elements in the respective ratio of 9:1:3.5. Calculate the empirical formula. If the molecular weight of the compound is 108 and the molecular formula is \[{C_x}{H_y}{N_z}\], then find the value of x, y and z
\[
  A.x = 6,{\text{ }}y = 8,{\text{ }}z = 2 \\
  B.x = 5,{\text{ }}y = 6,{\text{ }}z = 3 \\
  C.x = 6,{\text{ }}y = 10,{\text{ }}z = 2 \\
  D.x = 7,{\text{ }}y = 8,{\text{ }}z = 1 \\
 \]

Answer 1

Hint: We must know that the empirical formula is the simplest positive integer ratio of atoms present in the molecule. Find the empirical mass and divide the molecular mass by empirical mass to get the factor. If we multiply the factor with an empirical formula then we will get the molecular formula.

Complete step by step answer:
Let’s start with discussing a little about the empirical formula. Empirical formula can be defined as the simplest positive integer ratio of atoms present in the molecule.
So, now we know the basics regarding the empirical formula, and the ratio we are given is 9:1:3.5 for carbon, hydrogen and nitrogen. Clearly, the given ratio is in mass and to convert it into moles we will divide it by their respective atomic masses. So, the atomic ratio will be $\dfrac{9}{{12}}:\dfrac{1}{1}:\dfrac{{3.5}}{{14}} = 0.75:1:0.25$.
Now, for converting it into a positive integer ratio we will divide the whole ratio by the lowest number i.e. 0.25. After dividing it by 0.25 we get $\dfrac{{0.75}}{{0.25}}:\dfrac{1}{{0.25}}:\dfrac{{0.25}}{{0.25}}$ which will be equal to $3:4:1$. So the empirical ratio is 3:4:1 and the empirical formula will be \[{C_3}{H_4}N\].
We are provided with the molecular mass which is 108, and the molecular mass of the compound formed using empirical formula is \[12 \times 3{\text{ }} + 1 \times 4 + 14 = 54g\].
Simply dividing 108 by 54 we get 2, which means two times the empirical ratio is the actual molecule ratio, hence the actual molecule ratio is 6:8:2 and the molecular formula \[{C_x}{H_y}{N_z}\] is \[{C_6}{H_8}{N_2}\].
Hence, the correct option is A. x=6, y=8, z=2.

Note:
We must know that the empirical formula provides the lowest possible whole number ratio of atoms possible. It is used to find the molecular formula of unknown molecules in the way shown above. Also unlike the molecular formula, empirical formula does not provide information regarding the absolute number of atoms in a molecule.