Final answer:
To produce 1.00 kg of methanol, approximately 126.17 grams of hydrogen gas (H₂) is required based on stoichiometric calculations using the molar masses of the compounds.
Step-by-step explanation:
To calculate the amount of hydrogen gas (H₂) required to produce 1.00 kg of methanol (CH₃OH) through the reaction CO + 2 H₂ → CH₃OH, we need to know the molar mass of the compounds involved and apply stoichiometry. Methanol has a molar mass of 32.04 g/mol, therefore 1.00 kg of methanol is equivalent to 31.23 moles. According to the reaction, 2 moles of H₂ are needed to produce 1 mole of CH₃OH, hence we need 62.46 moles of hydrogen gas.
The molar mass of H₂ is approximately 2.02 g/mol, so the mass of hydrogen needed is 62.46 moles × 2.02 g/mol, which equals 126.17 grams.