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Difficulty: MediumOxides of Carbon and Trioxocarbonate(IV) Salts

What mass of anhydrous sodium trioxocarbonate(IV), Na2CO3\text{Na}_2\text{CO}_3, is obtained when 16.8 g16.8\text{ g} of sodium hydrogentrioxocarbonate(IV), \text{NaHCO}_3, is completely decomposed by heating?
[Relative atomic masses: Na=23\text{Na} = 23, H=1\text{H} = 1, C=12\text{C} = 12, O=16\text{O} = 16]

  1. 10.6 g10.6\text{ g}Answer
  2. B
    21.2 g21.2\text{ g}
  3. C
    16.8 g16.8\text{ g}
  4. D
    5.3 g5.3\text{ g}

Answer

10.6 g10.6\text{ g} of sodium trioxocarbonate(IV) is produced.
Thermal decomposition of 2 moles2\text{ moles} (168 g168\text{ g}) of NaHCO3\text{NaHCO}_3 yields 1 mole1\text{ mole} (106 g106\text{ g}) of Na2CO3\text{Na}_2\text{CO}_3, along with gaseous CO2\text{CO}_2 and water vapor. Heating 16.8 g16.8\text{ g} (0.20 mol0.20\text{ mol}) of NaHCO3\text{NaHCO}_3 produces 0.10 mol0.10\text{ mol} of Na2CO3\text{Na}_2\text{CO}_3, which evaluates to exactly 10.6 g10.6\text{ g}.

Step-by-Step Solution

1
Write the balanced chemical equation for the thermal decomposition of sodium hydrogentrioxocarbonate(IV).
2NaHCO3(s)→ΔNa2CO3(s)+H2O(g)+CO2(g)2\text{NaHCO}_3(s) \xrightarrow{\Delta} \text{Na}_2\text{CO}_3(s) + \text{H}_2\text{O}(g) + \text{CO}_2(g)
Establishing the stoichiometric mole ratio between the reactant and solid product.
2
Calculate the molar masses of NaHCO3\text{NaHCO}_3 and Na2CO3\text{Na}_2\text{CO}_3.
Molar mass of NaHCO3=23+1+12+(3×16)=84 g/mol\text{NaHCO}_3 = 23 + 1 + 12 + (3 \times 16) = 84\text{ g/mol}; Molar mass of Na2CO3=(2×23)+12+(3×16)=106 g/mol\text{Na}_2\text{CO}_3 = (2 \times 23) + 12 + (3 \times 16) = 106\text{ g/mol}.
Converting given masses to moles and back.
3
Determine moles of NaHCO3\text{NaHCO}_3 reacted and corresponding moles of Na2CO3\text{Na}_2\text{CO}_3 formed.
Moles of NaHCO3=16.884=0.20 mol\text{NaHCO}_3 = \frac{16.8}{84} = 0.20\text{ mol}. Moles of Na2CO3=0.202=0.10 mol\text{Na}_2\text{CO}_3 = \frac{0.20}{2} = 0.10\text{ mol}.
The balanced equation dictates a 2:12:1 mole ratio between NaHCO3\text{NaHCO}_3 and Na2CO3\text{Na}_2\text{CO}_3.
4
Calculate the mass of Na2CO3\text{Na}_2\text{CO}_3 produced.
Mass =0.10 mol×106 g/mol=10.6 g= 0.10\text{ mol} \times 106\text{ g/mol} = 10.6\text{ g}.
Multiplying the moles of product by its molar mass yields the final mass.

Key Concept

Thermal decomposition of hydrogen trioxocarbonates and stoichiometric mass-mass calculations
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Topics

Oxides of Carbon and Trioxocarbonate(IV) Salts

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