Answer:
The composition of the resulting gas;
A. 5 cm³ of CO₂, 10 cm³ of O₂, 80 cm³ of N₂, and 10 cm³
Explanation:
The given parameters are;
The volume of CH₄ in the mixture of air and methane = 5 cm³
The volume of air in the mixture of air and methane = 100 cm³
The percentage by volume of nitrogen, N₂ in the air = 80%
The percentage by volume of oxygen, O₂ in the air = 20%
The equation for the reaction of the chemical reaction between the methane and the air in the mixture is given as follows;
CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l)
Therefore, we have;
1 mole of CH₄ reacts with 2 moles of O₂ to produce 1 mole of CO₂ and 2 moles of H₂O
By Avogadro's law, we have that equal volumes of all gases at the same temperature and pressure contains equal number of molecules
Therefore, we have;
1 cm₃ of CH₄ reacts with 2 cm³ of O₂ to produce 1 cm³ of CO₂ and 2 cm³ of H₂O
From which we have;
5 cm₃ of CH₄ reacts with 10 cm³ of O₂ to produce 5 cm³ of CO₂ and 10 cm³ of H₂O (steam)
The volume of the oxygen used in the reaction = 10 cm³
The volume of oxygen present in the air = 20% × 100 cm³ = 20 cm³
The volume of nitrogen present in the air = 80% × 100 cm³ = 80 cm³
Therefore, the composition of the resulting gas is given as follows;
1) 80 cm³ Nitrogen
2) 10 cm³ Oxygen
3) 5 cm³ CO₂
4) 10 cm³ H₂O
The final composition of all the gases in the mixture has been [tex]\rm 80\;cm^3[/tex] Nitrogen, [tex]\rm 10\;cm^3[/tex] oxygen, [tex]\rm 5\;cm^3[/tex] carbon dioxide, and [tex]\rm 10\;cm^3[/tex] water (steam). Thus, the correct option is A.
The mixture of air has been composed of 20 % oxygen and 80 % nitrogen. The volume of air has been [tex]\rm 100\;cm^3[/tex]. Thus, the volume of oxygen and nitrogen in the air has been:
The volume of oxygen, [tex]V_O_2=20\;\rm cm^3[/tex]
The volume of nitrogen, [tex]V_N_2=80\;\rm cm^3[/tex]
Since the reaction, the nitrogen has been remained unused, thus the final composition of nitrogen has been [tex]\rm 80 \;cm^3[/tex].
The balanced equation for the reaction of methane with oxygen has been:
[tex]\rm CH_4\;+\;2\;O_2\;\rightarrow\;CO_2\;+\;2\;H_2O[/tex]
According to Avogadro's law, the presence of gases at the same temperature has volume proportional to the moles of the gases.
Thus, from the balanced chemical equation:
[tex]\rm 1\;cm^3\;CH_4=2\;cm^3\;O_2[/tex]
Thus,
[tex]\rm 5\;cm^3\;CH_4=10\;cm^3\;O_2[/tex]
Since the available oxygen has been [tex]\rm 20\;cm^3[/tex], the remaining oxygen after the reaction has been [tex]\rm 10\;cm^3[/tex].
Thus, the final composition of oxygen has been [tex]\rm 10\;cm^3[/tex].
Methane has been the limiting reactant. Thus, the concentration of carbon dioxide and water formed has been:
[tex]\rm 1\;cm^3\;CH_4=1\;cm^3\;CO_2\\5\;cm^3\;CH_4=5\;cm^3\;CO_2[/tex]
The final composition of carbon dioxide has been [tex]\rm 5\;cm^3[/tex].
[tex]\rm 1\;cm^3\;CH_4=2\;cm^3\;H_2O\\5\;cm^3\;CH_4=10\;cm^3\;H_2O[/tex]
The final composition of water (steam) has been [tex]\rm 10\;cm^3[/tex].
The final composition of all the gases in the mixture has been [tex]\rm 80\;cm^3[/tex] Nitrogen, [tex]\rm 10\;cm^3[/tex] oxygen, [tex]\rm 5\;cm^3[/tex] carbon dioxide, and [tex]\rm 10\;cm^3[/tex] water (steam). Thus, the correct option is A.
For more information about the composition of gas, refer to the link:
https://brainly.com/question/4391235
