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CACHE Modules on Energy in the Curriculum

Fuel Cells

Module Title: Hydrogen Adsorption and Catalyst Surface Coverage

Module Author: Jason Keith

Author Affiliation: Michigan Technological University

Course: Kinetics
and Reaction Engineering

Text Reference:
Fogler (4th edition), Section 10.2.3

Concepts: Given
the mechanism for hydrogen adsorption determine the surface coverage
on a platinum catalyst.

Problem Motivation:

Fuel cells are a promising
alternative energy conversion technology. One type of fuel cell, a proton
exchange membrane fuel cell (PEMFC) reacts hydrogen with oxygen to produce
electricity (Figure 1). Fundamental to the design of fuel cells is an
understanding of the effect of kinetics on the fuel cell performance.�

Consider the schematic
of a compressed hydrogen tank (2000 psi, regulated to 10 psi) feeding
a proton exchange membrane fuel cell, as seen in Figure 2 below. We
will now focus on the voltage / current relationship of the fuel cell.

Figure 1. Reactions in
the PEMFC

H2

O2

H+

Anode

Electrolyte

Cathode

O2

H2O

O2

H+

H2

H2O

��

H2 tank

Fuel Cell

Computer

(Electric Load)

H2 out

Air in

Air / H2O out

Figure 2. Diagram for fueling a laptop.

Pressure regulator

H2 feed line

FLOW
CHANNELS�

The PEMFC reactions are:�Anode:��H2 ��
2H+ + 2e-

Cathode:��
O2 + 2H+ + 2e- H2O

Overall:�H2
+ � O2 ��
H2O

For each mole of
hydrogen consumed, two moles of electrons are passed through the electric
load. To convert electron flow (moles of electrons/s) to electrical
current (coulombs/s or amps), one would use Faradays constant:coulombs
/ mole of electrons. The primary objective of a fuel cell is to deliver
energy to the electric load. To calculate the energy delivery rate (also
know as power) one would multiply the current times the cell voltage: Power = Current
� Voltage. (Recall the unit conversions: and).

Background

Figure 3 shows a
polarization plot which is the relationship between current density i (fuel cell current per unit area of the electrode, in units
of milliamps per square centimeter) and cell voltage Vc (in units of volts). There
are several things to note here:

Theoretical
voltage of 1.2 V

Overvoltage

Rapid drop

(kinetic losses)

Linear drop

(ohmic losses)

Rapid drop at higher currents

(mass transfer

losses)

�

The theoretical maximum
voltage of this fuel cell is 1.2 V. This is called the theoretical, or open circuit voltage .
The hydrogen
reaction rate (in moles per second, for example) is directly proportional to the current (in coulombs per second, or amperes), since for each hydrogen molecule that reacts, two electrons are
formed.
Any drop from
this maximum value is termed overvoltage. It is desired to minimize the overvoltage so that the fuel cell can operate as efficiently as possible.
There is a
critical current density called the exchange
current density with
symbol io. For current densities i < io, the cell voltage is equal to the theoretical value. For current
densities i > io, there is a rapid fall in cell voltage, due to a slow
reaction rate constant (kinetics). It is desired to
have as high a value of io as possible, and as rapid kinetics as possible.
At current
densities between 100 mA/cm2 and about 1000 mA/cm2, there
is a linear fall in voltage as the current density increases. This effect
is due to the fact that there is a resistance to current and ion flow within the fuel cell. As the current increases, the voltage drop will
increase. In physics and electrical e<span class="

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