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Difficulty: MediumThe Mole Concept, Avogadro's Constant, and Molar Mass

Calculate the mass, in grams, of nitrogen contained in a 16.4 g16.4\text{ g} sample of pure calcium trioxonitrate(V), Ca(NO3)2\text{Ca(NO}_3)_2. [Ca=40,N=14,O=16][\text{Ca} = 40, \text{N} = 14, \text{O} = 16]

Answer: 2.8 g

Answer

The mass of nitrogen in the sample is 2.8 g2.8\text{ g}.
The molar mass of Ca(NO3)2\text{Ca(NO}_3)_2 is calculated as 40+2(14+3×16)=164 g/mol40 + 2(14 + 3 \times 16) = 164\text{ g/mol}. A 16.4 g16.4\text{ g} sample corresponds to 16.4164=0.1 mol\frac{16.4}{164} = 0.1\text{ mol} of Ca(NO3)2\text{Ca(NO}_3)_2. Because each formula unit contains 2 nitrogen atoms, 0.1 mol0.1\text{ mol} of compound yields 0.2 mol0.2\text{ mol} of nitrogen. Multiplying 0.2 mol0.2\text{ mol} by the molar mass of atomic nitrogen (14 g/mol14\text{ g/mol}) gives 2.8 g2.8\text{ g}.

Step-by-Step Solution

1
Calculate the molar mass of calcium trioxonitrate(V), Ca(NO3)2\text{Ca(NO}_3)_2
164 g/mol164\text{ g/mol}
Sum the relative atomic masses of all atoms present: 40+2(14+3×16)=164 g/mol40 + 2(14 + 3 \times 16) = 164\text{ g/mol}.
2
Calculate the number of moles of Ca(NO3)2\text{Ca(NO}_3)_2 present in 16.4 g16.4\text{ g}
0.1 mol0.1\text{ mol}
Use the formula moles=massmolar mass=16.4 g164 g/mol=0.1 mol\text{moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{16.4\text{ g}}{164\text{ g/mol}} = 0.1\text{ mol}.
3
Determine the number of moles of nitrogen atoms in 0.1 mol0.1\text{ mol} of Ca(NO3)2\text{Ca(NO}_3)_2
0.2 mol0.2\text{ mol} of N atoms
Each formula unit of Ca(NO3)2\text{Ca(NO}_3)_2 contains 2 nitrogen atoms.
4
Calculate the mass of the nitrogen atoms
2.8 g2.8\text{ g}
Multiply the moles of nitrogen by its atomic mass: 0.2 mol×14 g/mol=2.8 g0.2\text{ mol} \times 14\text{ g/mol} = 2.8\text{ g}.

Key Concept

Mole Concept and Mass Composition of Compounds
Estimated Time:1m 30s
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Topics

The Mole Concept, Avogadro's Constant, and Molar Mass

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