Question

How many moles of ${{\text{N}}_{\text{2}}}{{\text{H}}_{\text{4}}}$ are there in $25.8{\text{ grams}}$?

Answer 1

Hint: We are given the mass of a substance i.e. ${{\text{N}}_{\text{2}}}{{\text{H}}_{\text{4}}}$. To solve this we must know the relationship between mass of a substance and the number of moles of a substance. The number of moles of any substance is the ratio of mass (in grams) to the molar mass (in gram per mol).

Complete step by step solution:
We are given the mass of a substance i.e. ${{\text{N}}_{\text{2}}}{{\text{H}}_{\text{4}}}$. The number of moles of any substance is the ratio of mass (in grams) to the molar mass (in gram per mol).
First we will calculate the molar mass of ${{\text{N}}_{\text{2}}}{{\text{H}}_{\text{4}}}$ as follows:
The sum of the molar mass of each element of the compound is known as the molar mass of the compound. Thus,
Molar mass of ${{\text{N}}_{\text{2}}}{{\text{H}}_{\text{4}}}$ $ = \left( {2 \times {\text{Atomic mass of N}}} \right) + \left( {4 \times {\text{Atomic mass of H}}} \right)$
Substitute $14{\text{ g/mol}}$ for the atomic mass of nitrogen, $1{\text{ g/mol}}$ for the atomic mass of hydrogen. Thus,
Molar mass of ${{\text{N}}_{\text{2}}}{{\text{H}}_{\text{4}}}$ $ = \left( {2 \times 14} \right) + \left( {2 \times {\text{1}}} \right)$
Molar mass of ${{\text{N}}_{\text{2}}}{{\text{H}}_{\text{4}}}$ $ = \left( {28} \right) + \left( 4 \right)$
Molar mass of ${{\text{N}}_{\text{2}}}{{\text{H}}_{\text{4}}}$ $ = 32{\text{ g/mol}}$
Thus, the molar mass of ${{\text{N}}_{\text{2}}}{{\text{H}}_{\text{4}}}$ is $32{\text{ g/mol}}$.
The equation to calculate the number of moles is as follows:
${\text{Number of moles}}\left( {{\text{mol}}} \right) = \dfrac{{{\text{Mass}}\left( {\text{g}} \right)}}{{{\text{Molar mass}}\left( {{\text{g/mol}}} \right)}}$
Substitute $25.8{\text{ grams}}$ for the mass, $32{\text{ g/mol}}$ for the molar mass. Thus,
Number of moles of ${{\text{N}}_{\text{2}}}{{\text{H}}_{\text{4}}}$ $ = \dfrac{{25.8{\text{ grams}}}}{{32{\text{ g/mol}}}}$
Number of moles of ${{\text{N}}_{\text{2}}}{{\text{H}}_{\text{4}}}$ $ = 0.8062{\text{ mol}}$
Thus, moles of ${{\text{N}}_{\text{2}}}{{\text{H}}_{\text{4}}}$ in $25.8{\text{ grams}}$ is $0.806{\text{ mol}}$.

Note: Amount of substance having exactly the same number of atoms as are present in 12 grams of ${{\text{C}}^{{\text{12}}}}$ is known as mole. The number of molecules in one mole of a compound is Avogadro’s number. The number $6.022 \times {10^{23}}$ is known as Avogadro’s number.