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 (since 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

33.33 g of methane

Step-by-step explanation:

This problem is solved by utilizing the stoichiometric quantities in the balanced equation

CH4 + H2O ======== CO + 3 H2

which tell us that 3 mol H2 gas need 1 mol of mehane gas to be produced.

Using the information that 1 Kg H2 has a milleage of 80 we can solve the problem :

1 Kg H2/ 80 miles = 1000g H2/80miles = 12.5 g H2 per mile

12.5 g H2 x 1 mol/ 2 g H2 = 6.25 mol H2

6.25 mol H2 to be produced require 6.25 mol H2 x (1 mol CH4/ 3 mol H2)

= 2.083 mol CH4

2.083 mol CH4 converted to mass is

2.083 mol CH4 x 16 g CH4/ mol = 33.33 g CH4