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?

Answer 1

it is said that you need 1 kilograms to run 80 miles so:

= 0.0125 Kg of H₂

in order to work with stoichiometry we need to change the values of moles, moles = mass / molar mass

kilomoles = kg / molar mass; 0.0125 / 2 = 0.00625 kilomoles of H2 required or 6.25 moles of H₂ required

The steam methane reforming reaction is well known:

CH₄ + H₂O ==== CO + 3H₂

so 1 mole of methane produces 3 moles of Hydrogen; 2 moles of methane will produce 6 moles of H2, we need approximately 2 moles of methane to find this exact value

you have divide by 3 according to stoichiometry: 6.25 / 3 = 2.0833 moles of Methane

the only thing we need to do is to apply the formula

moles = mass / molar mass

mass = moles * molar mass; molar mass of CH4 is 16 g/gmol

mass of methane = 2.0833 * 16 = 33.33 grams of methane

If you want it in kilograms just divide it by 1000

33.33 / 1000 = 0.0333 Kg of methane required

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