Question

under certain circumstances, carbon dioxide, co₂(g), can be made to react with hydrogen gas, h₂(g), to produce methane, ch₄(g), and water vapor, h₂o(g). co₂(g) + 4h₂(g)→ch₄(g) + 2h₂o(g) part a part b how many moles of hydrogen gas would be needed to react with excess carbon dioxide to produce 53.6 moles of water vapor? express your answer with the appropriate units. view available hint(s) 107 mol previous answers correct

Explanation:

Step1: Analyze the stoichiometric ratio

From the balanced chemical equation \(CO_2(g)+4H_2(g)\to CH_4(g) + 2H_2O(g)\), the ratio of \(H_2\) to \(H_2O\) is \(4:2 = 2:1\).

Step2: Calculate the moles of \(H_2\)

Let \(n_{H_2}\) be the moles of \(H_2\) and \(n_{H_2O}=53.6\space mol\). Using the ratio \(\frac{n_{H_2}}{n_{H_2O}}=\frac{2}{1}\), we have \(n_{H_2}=2\times n_{H_2O}\).
Substitute \(n_{H_2O} = 53.6\space mol\) into the equation: \(n_{H_2}=2\times53.6\space mol\)
\(n_{H_2}=107.2\space mol\approx107\space mol\) (rounded to three significant figures)

Answer:

\(107\space mol\)