Question

The molar mass of is $\text{M}{{\text{g}}_{\text{3}}}{{\text{N}}_{\text{2}}}$ is? Given atomic mass of $\left( \text{N}=14,\text{ Mg}=24 \right)$.
(A) 84 g/mol
(B) 98 g/mol
(C) 114 g/mol
(D) 100 g/mol

Answer 1

Hint: The molar mass of a compound is the mass of its one mole. It can be calculated by taking the sum of the standard atomic masses of its constituent elements. Or it can also be found out by dividing the mass of a given compound by its number of moles.

Complete answer:
Magnesium nitride, $\text{M}{{\text{g}}_{\text{3}}}{{\text{N}}_{\text{2}}}$, is an ionic inorganic compound consist of magnesium and nitrogen atoms. Each compound has a particular mass and the mass of a given chemical compound present in one mole of the compound is called molar mass.
The molecular formula of magnesium nitride contains 3 magnesium atoms and 2 nitrogen atoms. This means that one mole of the magnesium nitride will contain 3 moles of magnesium and 2 moles of nitrogen atoms.
Also, the mass of one mole of atoms of an element in grams per mole is known as its atomic mass.
Since the atomic mass of magnesium is 24 g/mol, thus it means that one mole magnesium has a mass of 24 grams. But in $\text{M}{{\text{g}}_{\text{3}}}{{\text{N}}_{\text{2}}}$, there is a total of 3 moles of Mg atoms per mole of compound. So, the mass of magnesium present in 1 mole of $\text{M}{{\text{g}}_{\text{3}}}{{\text{N}}_{\text{2}}}$ will be:
\[\begin{align}
  & \text{Mass of Mg in 1 mole M}{{\text{g}}_{\text{3}}}{{\text{N}}_{\text{2}}}=3\text{ mol}\times 24\text{ g}/\text{mol} \\
 & \therefore {{\text{M}}_{\text{Mg}}}\text{= 72 g} \\
\end{align}\]
Similarly, for nitrogen atom we can write:
\[\begin{align}
  & \text{Mass of N in 1 mole M}{{\text{g}}_{\text{3}}}{{\text{N}}_{\text{2}}}=2\text{ mol}\times 14\text{ g}/\text{mol} \\
 & \therefore {{\text{M}}_{\text{N}}}\text{= 28 g} \\
\end{align}\]
Thus, the total mass of one mole $\text{M}{{\text{g}}_{\text{3}}}{{\text{N}}_{\text{2}}}$ will be:
\[\begin{align}
  & \text{Mass of 1 mole M}{{\text{g}}_{\text{3}}}{{\text{N}}_{\text{2}}}={{\text{M}}_{\text{Mg}}}+{{\text{M}}_{\text{N}}} \\
 & \text{i}\text{.e}\text{. Molar mass of M}{{\text{g}}_{\text{3}}}{{\text{N}}_{\text{2}}}\text{= }\left( \text{72}+\text{28} \right)\text{g/mol}=100\text{ g/mol} \\
\end{align}\]

Hence, the correct answer is (D) 100 g/mol.

Note:
The atomic mass of a pure element is also measured in the unit of atomic mass units (amu). Although mass can be expressed as both amu and g/mol, the latter is the most commonly used system of units in chemistry. Also, 1 amu is equal to $1.662\times {{10}^{-24}}\text{ g}$.