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CACHE Modules on Energy in the Curriculum
Fuel Cells
Module Title: Application of Heat of Reaction: Hydrogen vs. Gasoline
Module Author: Jason Keith
Author Affiliation: Michigan Technological University
Course: Material and Energy Balances (First chemical engineering course)
Text Reference: Felder and Rousseau, section 4.6
Concepts: Gas law, heat of combustion
Problem Motivation: Fuel cells are a promising alternative energy technology. One type
of fuel cell, a proton exchange membrane fuel cell reacts hydrogen and oxygen together
to produce electricity. Fundamental to the design of fuel cells is an understanding of heat
of reaction of different fuels. In this problem we will use the heat of reaction to determine
the energy contained in a hydrogen cylinder, and determine the equivalent number of
gallons of gasoline.
Consider the schematic of a compressed hydrogen tank feeding a proton exchange
membrane fuel cell, as seen in the figure below. The electricity generated by the fuel cell
is used here to power a laptop computer. We are interested in determining the maximum
amount of time the laptop can be operated from the compressed hydrogen tank.
Computer
(Electric Load)
H2 feed line
Air in
Anode
Gas
Chamber
Cathode
Gas
Chamber
Air / H2O out
H2 out
H2 tank
1st draft
Revision
Fuel Cell
J.M. Keith
J. M. Keith
Page 1
June 5, 2007
July 25, 2007
Problem Information
Home Problem Statement:
A gas cylinder is full of hydrogen gas at room temperature and 2000 psig pressure. This
cylinder has been proposed as a fuel tank for a fuel cell powered vehicle. Note that the
volume of the cylinder is 49.9 L.
a. Determine the energy content in kJ within the cylinder when the hydrogen is
combusted to make liquid water. Use the ideal gas law, PV = nRT.
b. How much gasoline in gallons is this energy equivalent to? Assume liquid
gasoline has a heat of reaction of Hr,gasoline -5370 kJ/mol, an average molecular
weight of 112 g/mol, and a density of 0.69 g/cm3.
c. If the hydrogen in the tank is combusted with oxygen to make water, how much
liquid water is produced?
d. Suppose you have a 100 W fuel cell (which can power a laptop computer). What
is the maximum amount of time you can run the fuel cell (hint: use the total
energy from part a).
Additional information:
Hf H2O = -285.84 kJ/mol (liquid water)
Hf H2O = -241.83 kJ/mol (vapor water)
1st draft
Revision
J.M. Keith
J. M. Keith
Page 2
June 5, 2007
July 25, 2007