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

A 14.3 g14.3\text{ g} sample of washing soda crystals, hydrated sodium trioxocarbonate(IV) (Na2CO3⋅10H2O\text{Na}_2\text{CO}_3 \cdot 10\text{H}_2\text{O}), is completely dissolved in water. Calculate the total number of moles of oxygen atoms present in this sample. [Relative atomic masses: Na=23\text{Na} = 23, C=12\text{C} = 12, O=16\text{O} = 16, H=1\text{H} = 1]

Answer: 0.65 mol

Answer

The total number of moles of oxygen atoms present in the sample is 0.65 mol.
The molar mass of Na2CO3⋅10H2O\text{Na}_2\text{CO}_3 \cdot 10\text{H}_2\text{O} is 286 g/mol286\text{ g/mol}. A mass of 14.3 g14.3\text{ g} corresponds to 14.3286=0.05 mol\frac{14.3}{286} = 0.05\text{ mol} of the compound. Since each formula unit contains 13 oxygen atoms (3 from the trioxocarbonate anion and 10 from the water of crystallization), the total moles of oxygen atoms present is 0.05×13=0.65 mol0.05 \times 13 = 0.65\text{ mol}.

Step-by-Step Solution

1
Calculate the molar mass of Na2CO3⋅10H2O\text{Na}_2\text{CO}_3 \cdot 10\text{H}_2\text{O}.
Molar mass = 286 g/mol286\text{ g/mol}.
Summing the atomic masses of all constituent atoms, including the 10 water molecules of crystallization: (2×23)+12+(3×16)+10×(18)=286 g/mol(2 \times 23) + 12 + (3 \times 16) + 10 \times (18) = 286\text{ g/mol}.
2
Calculate the number of moles of Na2CO3⋅10H2O\text{Na}_2\text{CO}_3 \cdot 10\text{H}_2\text{O} present in the sample.
Moles of compound = 0.05 mol0.05\text{ mol}.
Dividing the given sample mass by its molar mass: 14.3 g286 g/mol=0.05 mol\frac{14.3\text{ g}}{286\text{ g/mol}} = 0.05\text{ mol}.
3
Determine the stoichiometric ratio of oxygen atoms per mole of hydrated compound.
13 moles of O atoms per 1 mole of Na2CO3⋅10H2O\text{Na}_2\text{CO}_3 \cdot 10\text{H}_2\text{O}.
Each formula unit contains 3 oxygen atoms from the trioxocarbonate group and 10 oxygen atoms from the ten water of crystallization molecules (3+10=133 + 10 = 13).
4
Multiply the moles of compound by the number of oxygen atoms per formula unit.
Total moles of O atoms = 0.65 mol0.65\text{ mol}.
Calculating total oxygen moles: 0.05 mol×13=0.65 mol0.05\text{ mol} \times 13 = 0.65\text{ mol}.

Key Concept

The Mole Concept, Molar Mass, and Stoichiometric Ratios in Hydrated Salts
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Topics

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

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