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Question: How many moles of \({{\text{N}}_{\text{2}}}{{\text{H}}_{\text{4}}}\) are there in \(25.8{\text{ gram...

How many moles of N2H4{{\text{N}}_{\text{2}}}{{\text{H}}_{\text{4}}} are there in 25.8 grams25.8{\text{ grams}}?

Explanation

Solution

We are given the mass of a substance i.e. N2H4{{\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. N2H4{{\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 N2H4{{\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 N2H4{{\text{N}}_{\text{2}}}{{\text{H}}_{\text{4}}} =(2×Atomic mass of N)+(4×Atomic mass of H) = \left( {2 \times {\text{Atomic mass of N}}} \right) + \left( {4 \times {\text{Atomic mass of H}}} \right)
Substitute 14 g/mol14{\text{ g/mol}} for the atomic mass of nitrogen, 1 g/mol1{\text{ g/mol}} for the atomic mass of hydrogen. Thus,
Molar mass of N2H4{{\text{N}}_{\text{2}}}{{\text{H}}_{\text{4}}} =(2×14)+(2×1) = \left( {2 \times 14} \right) + \left( {2 \times {\text{1}}} \right)
Molar mass of N2H4{{\text{N}}_{\text{2}}}{{\text{H}}_{\text{4}}} =(28)+(4) = \left( {28} \right) + \left( 4 \right)
Molar mass of N2H4{{\text{N}}_{\text{2}}}{{\text{H}}_{\text{4}}} =32 g/mol = 32{\text{ g/mol}}
Thus, the molar mass of N2H4{{\text{N}}_{\text{2}}}{{\text{H}}_{\text{4}}} is 32 g/mol32{\text{ g/mol}}.
The equation to calculate the number of moles is as follows:
Number of moles(mol)=Mass(g)Molar mass(g/mol){\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 grams25.8{\text{ grams}} for the mass, 32 g/mol32{\text{ g/mol}} for the molar mass. Thus,
Number of moles of N2H4{{\text{N}}_{\text{2}}}{{\text{H}}_{\text{4}}} =25.8 grams32 g/mol = \dfrac{{25.8{\text{ grams}}}}{{32{\text{ g/mol}}}}
Number of moles of N2H4{{\text{N}}_{\text{2}}}{{\text{H}}_{\text{4}}} =0.8062 mol = 0.8062{\text{ mol}}
Thus, moles of N2H4{{\text{N}}_{\text{2}}}{{\text{H}}_{\text{4}}} in 25.8 grams25.8{\text{ grams}} is 0.806 mol0.806{\text{ mol}}.

Note: Amount of substance having exactly the same number of atoms as are present in 12 grams of C12{{\text{C}}^{{\text{12}}}} is known as mole. The number of molecules in one mole of a compound is Avogadro’s number. The number 6.022×10236.022 \times {10^{23}} is known as Avogadro’s number.