Question

Hydrogen gas is a very useful reagent with many uses in the petroleum, food, and chemical industries. Most hydrogen exists in covalently bonded molecules, and atmospheric air contains less than 1 ppm of diatomic hydrogen. Therefore, hydrogen gas is produced on a large scale for these uses, where steam reforming with methane and electrolysis of water are two of the primary methods. The more economic reaction of steam reforming is the reverse of the reaction depicted in Carbon Monoxide and Hydrogen - Sample 1 in the Simulation. Hydrogen has also been considered as an alternative fuel for vehicles designed to combust hydrogen and oxygen, which produces water as a product. However, concerns were raised because methane is typically used on a large scale to produce hydrogen gas. Assume that a gallon of gasoline contains 2400 g of carbon. If a gasoline engine achieves 30 miles per gallon, each mile consumes 80 g of carbon (about 107 g of methane contains 80 g of carbon). Alternatively, a hydrogen engine can achieve 80 miles per kilogram of hydrogen gas. What is the mass of methane (CH4) needed to produce enough hydrogen gas (H2) to drive one mile using the theoretical hydrogen engine? Express the mass in grams to two significant digits.

Answer 1

Mass of Hydrogen gas required to run the Hydrogen engine for 80 miles = 1 Kg

Mass of Hydrogen gas required to run the Hydrogen engine for one mile = 1 mole x (1 Kg H₂/ 80 mile) = 0.0125 Kg H₂

Moles of Hydrogen gas required to run the Hydrogen engine for one mile = 0.0125 Kg H₂ x (1 K mol H₂/2Kg H₂) = 0.00625 kmol H₂

We have the steam reforming reaction to produce H₂ gas

CH₄ + H₂O   CO + 3H₂

One mol of CH₄ reacts with one mole of H₂O to produce 3 moles of H₂

Therefore,

Moles of CH₄ required for the formation of 0.00625 kmol H₂ = (0.00625 kmol H₂) x (1 mol CH₄/3 mol H₂) = 0.00208 kmol CH₄

Mass of CH₄ required for the formation of 0.00625 kmol H₂ = 0.00208 kmol CH₄ x (16 Kg CH₄/1 Kmol CH₄) = 0.033 Kg CH₄

Mass of methane gas required to run the theoretical Hydrogen gas = 0.033 Kg