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Answer: 84.2 mol hydrogen gas (H₂) woiuld be needed to react with excess carbon dioxide to produce 42.1 moles of water vapor.

Explanation:

1) Word equation:

  • hydrogen (g) + carbon dioxide (g) → water (g) + methane (g)

2) Molecular equation:

  • H₂(g) + CO₂(g)→ H₂O(g) + CH₄(g)

3) Balanced molecular equation:

  • 4H₂(g) + CO₂(g)→ 2H₂O(g) + CH₄ (g)

4) Stoichiometric mole ratios:

  • 4 mol H₂ : 1 mol CO₂ : 2 mol H₂O(g) : 1 mol CH₄

5) Set a proportion with the stoichiometric mole ratios, the moles of water vapor produced and the unknown:

  • 4 mol H₂ / 2 mol H₂O = x / 42.1 mol H₂O  

     ⇒ x = 42.1 mol H₂O × 4 mol H₂ / 2 mol H₂O = 84.2 mol H₂ ← answer

Answer:

84.2 moles of hydrogen gas will be needed to produce 42.1 moles of water vapors.

Explanation:

[tex]4H_2+CO_2\rightarrow 2H_2O+CH_4[/tex]

According to reaction 4 moles of hydrogen gas gives 2 moles of water vapor.

Then, 42.1 moles of water vapor will be produced by:

[tex]\frac{4}{2}\times 42.1=84.2 moles [/tex] hydrogen gas

84.2 moles of hydrogen gas will be needed to produce 42.1 moles of water vapors.

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