Question

A certain compound contains calcium, carbon and nitrogen in the mass ratio $20:6:14$. The empirical formula of the compound is:
(A) $CaCN$
(B) $C{a_2}{C_2}N$
(C) $Ca{(CN)_3}$
(D) $CaC{N_2}$

Answer 1

Hint: If we know the weight ratio of the two or more gases in a compound then we can calculate the molar ratio and then finally we can determine the molecular formula of the compound. Molecular formula will be according to the ratio of the molecular weights of the gases.

Complete step by step solution:
First of all let us read about molecular formulas.
Molecular weight of the substance: It is defined as the sum of the molecular masses of all elements present in the substance.
Number of moles: It is defined as the ratio of mass of the substance to the molecular mass of the substance.
Molecular formula: The molecular composition in the compound is known as molecular formula. For example: the molecule of water is ${H_2}O$ i.e. two atoms of hydrogen with oxygen.
Empirical formula: The molecular composition in the compound in simplest ratio is known as empirical formula. For example: the molecular formula of glucose is ${C_6}{H_{12}}{O_6}$ and its empirical formula is $C{H_2}O$.
Now here in the question we are given with the mass ratio of calcium, carbon and nitrogen as $20:6:14$ And we know that the molecular mass of nitrogen is $14$, molecular mass of carbon is $12$ and molecular mass of calcium is $40$. So the number of moles of nitrogen is $\dfrac{{14}}{{14}}$ , moles of carbon is $\dfrac{6}{{12}}$ and the number of moles of calcium $\dfrac{{20}}{{40}}$ and the ratio of the number of nitrogen and oxygen atom in the compound will be as $\dfrac{{20}}{{40}}:\dfrac{6}{{12}}:\dfrac{{14}}{{14}} = 1:1:2$. So the empirical as well as the molecular formula will be as: $CaC{N_2}$.

Hence, option D is correct.

Note:
Formula mass: It is defined as the sum of the atomic weights of all the atoms present in the compound. And if the compound is covalent in nature then the formula mass is known as molecular mass and if we are calculating mass of one mole of substance then it is known as molar mass.