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Difficulty: MediumNitrogen Gas, Nitrogen Cycle, and Oxides of Nitrogen

Ammonium trioxonitrate(V), NH4NO3NH_4NO_3, decomposes on heating to produce dinitrogen(I) oxide and water vapor according to the balanced chemical equation:

NH4NO3(s)→N2O(g)+2H2O(g)NH_4NO_3(s) \rightarrow N_2O(g) + 2H_2O(g)

What volume of dinitrogen(I) oxide gas, measured at STP, is produced from the complete decomposition of 8.0 g8.0\text{ g} of pure ammonium trioxonitrate(V)?
[Molar mass of NH4NO3=80 g mol−1, Molar volume of gas at STP =22.4 dm3 mol−1][\text{Molar mass of } NH_4NO_3 = 80\text{ g mol}^{-1},\text{ Molar volume of gas at STP } = 22.4\text{ dm}^3\text{ mol}^{-1}]

  1. 2.24 dm32.24\text{ dm}^3Answer
  2. B
    2.40 dm32.40\text{ dm}^3
  3. C
    4.48 dm34.48\text{ dm}^3
  4. D
    6.72 dm36.72\text{ dm}^3

Answer

The volume of dinitrogen(I) oxide gas produced at STP is 2.24 dm32.24\text{ dm}^3.
The correct response calculates the mole value of ammonium trioxonitrate(V) as 0.10 mol0.10\text{ mol} (8.0 g/80 g mol−18.0\text{ g} / 80\text{ g mol}^{-1}). Using the 1:11:1 stoichiometric ratio from the balanced decomposition reaction, 0.10 mol0.10\text{ mol} of dinitrogen(I) oxide is produced. At standard temperature and pressure (STP), one mole of any ideal gas occupies 22.4 dm322.4\text{ dm}^3, giving 0.10×22.4=2.24 dm30.10 \times 22.4 = 2.24\text{ dm}^3.

Step-by-Step Solution

1
Calculate the number of moles of NH4NO3NH_4NO_3 reacted
Moles of NH4NO3=MassMolar Mass=8.0 g80 g mol−1=0.10 mol\text{Moles of } NH_4NO_3 = \frac{\text{Mass}}{\text{Molar Mass}} = \frac{8.0\text{ g}}{80\text{ g mol}^{-1}} = 0.10\text{ mol}
Converting given mass into moles is necessary to apply stoichiometric relationships.
2
Determine the mole ratio between NH4NO3NH_4NO_3 and N2ON_2O
From the balanced equation, 1 mol of NH4NO31\text{ mol of } NH_4NO_3 produces 1 mol of N2O1\text{ mol of } N_2O. Thus, 0.10 mol of NH4NO30.10\text{ mol of } NH_4NO_3 yields 0.10 mol of N2O0.10\text{ mol of } N_2O.
Stoichiometry dictates the theoretical mole yield of the target product.
3
Calculate the volume of N2ON_2O gas at STP
Volume at STP=0.10 mol×22.4 dm3 mol−1=2.24 dm3\text{Volume at STP} = 0.10\text{ mol} \times 22.4\text{ dm}^3\text{ mol}^{-1} = 2.24\text{ dm}^3
Multiplying the mole amount of gas by the molar volume at STP (22.4 dm3 mol−122.4\text{ dm}^3\text{ mol}^{-1}) gives the volume.

Key Concept

Stoichiometric gas volume calculation at standard temperature and pressure (STP) for thermal decomposition reactions of nitrogen compounds.
Estimated Time:1m 30s
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Topics

Nitrogen Gas, Nitrogen Cycle, and Oxides of Nitrogen

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