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Difficulty: MediumGay-Lussac's Law of Combining Volumes and Avogadro's Law

Fill in the blanks with the correct numerical values based on volume stoichiometry at constant temperature and pressure.

Answer:When 40 cm340\text{ cm}^3 of nitrogen(II) oxide gas (NONO) is reacted with 30 cm330\text{ cm}^3 of oxygen gas (O2O_2) according to the equation 2NO(g)+O2(g)→2NO2(g)2NO_{(g)} + O_{2(g)} \rightarrow 2NO_{2(g)}, the volume of unreacted oxygen gas remaining is 【10】 cm3\text{cm}^3 and the total volume of the resulting gaseous mixture is 【50】 cm3\text{cm}^3.

Answer

The volume of unreacted oxygen gas remaining is 10 cm310\text{ cm}^3 and the total volume of the resulting gaseous mixture is 50 cm350\text{ cm}^3.
According to Gay-Lussac's Law of Combining Volumes, 2 volumes2\text{ volumes} of NONO react with 1 volume1\text{ volume} of O2O_2 to yield 2 volumes2\text{ volumes} of NO2NO_2. Therefore, 40 cm340\text{ cm}^3 of NONO reacts with 20 cm320\text{ cm}^3 of O2O_2, leaving 10 cm310\text{ cm}^3 of unreacted O2O_2 (30 cm3−20 cm330\text{ cm}^3 - 20\text{ cm}^3). The reaction produces 40 cm340\text{ cm}^3 of NO2NO_2 gas. Summing the product volume (40 cm340\text{ cm}^3) and unreacted excess gas (10 cm310\text{ cm}^3) gives a total residual gas volume of 50 cm350\text{ cm}^3.

Step-by-Step Solution

1
Determine combining volume ratios from the balanced chemical equation.
The mole/volume ratio is 2 vol NO:1 vol O2:2 vol NO22\text{ vol } NO : 1\text{ vol } O_2 : 2\text{ vol } NO_2.
By Gay-Lussac's Law of Combining Volumes, gases at the same temperature and pressure react in volumes that bear simple whole-number ratios to one another and to gaseous products.
2
Identify the limiting reactant and calculate volumes consumed and produced.
40 cm340\text{ cm}^3 of NONO requires 12×40=20 cm3\frac{1}{2} \times 40 = 20\text{ cm}^3 of O2O_2, producing 40 cm340\text{ cm}^3 of NO2NO_2. NONO is completely used up.
40 cm340\text{ cm}^3 of NONO is the limiting reactant because 30 cm330\text{ cm}^3 of O2O_2 is available, which is more than the required 20 cm320\text{ cm}^3.
3
Calculate remaining unreacted oxygen and total residual gas volume.
Excess O2=30 cm3−20 cm3=10 cm3O_2 = 30\text{ cm}^3 - 20\text{ cm}^3 = 10\text{ cm}^3. Total residual volume = 40 cm3 (NO2)+10 cm3 (O2)=50 cm340\text{ cm}^3\,(NO_2) + 10\text{ cm}^3\,(O_2) = 50\text{ cm}^3.
The total final volume equals the volume of gaseous product formed plus any unreacted excess gas.

Key Concept

Gay-Lussac's Law of Combining Volumes and Avogadro's Law
Estimated Time:1m 30s
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Gay-Lussac's Law of Combining Volumes and Avogadro's Law

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