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Answer :
To determine how many moles of hydrogen gas are needed to react with excess carbon dioxide to produce 99.1 moles of water vapor, we can use stoichiometry based on the balanced chemical reaction.
The balanced chemical equation for the reaction between hydrogen gas ([tex]\( H_2 \)[/tex]) and carbon dioxide ([tex]\( CO_2 \)[/tex]) to produce water vapor ([tex]\( H_2O \)[/tex]) and carbon monoxide ([tex]\( CO \)[/tex]) is:
[tex]\[ 2 \, H_2 + CO_2 \rightarrow 2 \, H_2O + CO \][/tex]
From this equation, we can see that 2 moles of hydrogen gas ([tex]\( H_2 \)[/tex]) produce 2 moles of water vapor ([tex]\( H_2O \)[/tex]). This is a 1:1 ratio. Therefore, the number of moles of hydrogen gas needed is equal to the number of moles of water vapor produced.
Since the problem states that 99.1 moles of water vapor are produced, we need 99.1 moles of hydrogen gas to react.
Thus, the answer is:
99.1 mol
The balanced chemical equation for the reaction between hydrogen gas ([tex]\( H_2 \)[/tex]) and carbon dioxide ([tex]\( CO_2 \)[/tex]) to produce water vapor ([tex]\( H_2O \)[/tex]) and carbon monoxide ([tex]\( CO \)[/tex]) is:
[tex]\[ 2 \, H_2 + CO_2 \rightarrow 2 \, H_2O + CO \][/tex]
From this equation, we can see that 2 moles of hydrogen gas ([tex]\( H_2 \)[/tex]) produce 2 moles of water vapor ([tex]\( H_2O \)[/tex]). This is a 1:1 ratio. Therefore, the number of moles of hydrogen gas needed is equal to the number of moles of water vapor produced.
Since the problem states that 99.1 moles of water vapor are produced, we need 99.1 moles of hydrogen gas to react.
Thus, the answer is:
99.1 mol
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