This document summarizes a student lab report on characterizing proton exchange membrane fuel cells. The students tested a hydrogen fuel cell and a 3% methanol fuel cell. Their results showed the hydrogen fuel cell generated a greater electric potential, consistent with published data. The report provides background on fuel cells and PEM fuel cells. It describes the chemical reactions in hydrogen and methanol fuel cells. Equations are given for calculating cell potential and Faraday efficiency. Graphs and losses in fuel cell performance are also discussed.

1. CENG 176, WI/SP 2017
Drews et al.
Section A01 (M/W), Team 9, Lab 1:
Characterization of Proton Exchange
Membrane Fuel Cell
Part I: Keirith Atwal
Part II: Sarah Woodward
Part III: Zichen Zhang
Part IV: Giahan Nguyen
Abstract
The demand for energy that is more environmentally friendly and economically advantageous
is a driving motivator for innovators to explore alternative fuel sources for better sustainability in
the future. The heavy carbon footprint on Earth due to burning fossil fuels is spurring research to
find a cleaner, more efficient energy source. This report focuses on identifying the electric potential
of a simple hydrogen fuel cell and a 3% methanol in water fuel cell, and determining Faraday
efficiency for hydrogen fuel cell. Upon analysis, the electric potential for the hydrogen fuel cell is
greater than its methanol counter-part. A hydrogen fuel cell will generate more electronic potential
than an aqueous methanol fuel cell, but considerations must be taken into account in using H2 as
a fuel source, due to its difficulty in storing, being expensive to produce and its relatively limited
efficiency.

2. 1 Introduction
The Proton Exchange Membrane Fuel Cell (PEMFC) has a wide application background ranging
in providing electrical power to: equipment on spacecraft, residential households, commercialized
electronics and even micro-sized electronics in hand-held devices, as the global dependency on
fossil fuels needs to be reduced.1 The major focus of PEMFCs appears to be in the mass trans-
portation field, as fuel cell vehicles; powered by hydrogen emitting water as waste, are being de-
veloped by various automobile companies to design energy efficient buses, cars and motorbikes.2
Fuel Cell technology appears to still be in a developing stage, as major issues regarding affordabil-
ity and environmental regulations are preventing this technology from being readily available for
commercial usage, especially in the automobile industry.3 Fossil fuel combustion is employed in
most industry practice and is considered the norm fuel source, though its weaknesses have been
documented in carbon emission, efficiency and non-renewability.4 PEMFCs could serve as a more
efficient, environmentally friendly and renewable energy source alternative to fossil fuels, but at
this point is still not developed nor economically viable to replace fossil fuels as the primary source
of energy in industry. This report narrows the focus on providing a fundamental understanding of
a basic PEMFC fueled by hydrogen and then 3% methanol in water, by comparing characteristic
curves and determining each cells electric potential.5 Though this report will solely focus on hy-
drogen and methanol fuel sources to power PEMFCs, there are many other fuel cells such as: Solid
Oxide Fuel Cells (SOFCs), Alkaline Fuel Cells (AFCs), Phosphoric acid Fuel Cells (PAFCs) and
Molten Carbonate Fuel Cells (MCFCs), which use various sources as proton conductors, and have
different strengths and weaknesses compared to their PEMFC counter part.6
1Sopian, K.; Daud, W. R. W. Renewable Energy 2006, 31, 719–727.
2Wang, Y. et al. Applied Energy 2011, 88, 981–1007.
3Thomas, C. et al. International Journal of Hydrogen Energy 1998, 23, 507–516.
4Turner, J. A. Science 1999, 285, 687–689.
5Drews, A. UCSD CENG 176 wikia., www.ucsd-ceng-176.wikia.com.
6Wang et al., “A review of polymer electrolyte membrane fuel cells: technology, applications, and needs on funda-
mental research”.
1

3. 2 Background
Proton exchange membranes utilize the reaction between hydrogen and oxygen on the membrane
as a source of electrical current. Instead of heat loss, a byproduct of the combustion of hydrogen,
a fuel cell converts the heat into current to be utilized as an alternative source for energy.7 The
current problems facing hydrogen fuel cells as a viable alternative include the slow reaction of
hydrogen in PEM fuel cells at moderate temperatures thus reducing efficiency and resulting in lim-
ited applicability as a source for energy in equipment not operating at high temperatures.8 Another
problem facing hydrogen fuel cells is the difficulty and cost of using pure hydrogen gas as well as
the cost of manufacturing hydrogen PEM fuel cells. While costs have decreased in recent years,
the cost of PEM fuel cells is still nearly double the targeted cost for the department of energy.9
Thus the PEM fuel cell technology must continue to be researched in order for it to have any prac-
tical usability in commercial processes. Hydrogen PEM fuel cells are an appealing alternative for
energy sources due to their relative high efficiencies compared to internal combustion engines due
to hydrogen PEM fuel cells not following the limit of Carnot efficiency, however the cost for the
efficiency produced is still high.10 However, hydrogen fuel cells still provide challenges including
cost, operating limits, and the efficiency could be improved if the heat lost by the system could
be converted to additional electrical current. Most applications of the hydrogen PEM fuel cell are
attempting to correct these problems, such as recycling the heat produced back into the fuel cell
thus improving the efficiency.
Here, we used a hydrogen proton exchange membrane fuel cell and a 3% direct methanol fuel
cell to explore the efficiency and overall practicality of fuel cells as an energy alternative. Our
results within this experiment in regards to efficiency of fuel cells, are in agreement with published
data on efficiency for non recycled heat loss. Our results concerning the comparison of hydrogen
7Larmaine, J.; Dicks, A., A Fuel Cell System Explained, 2nd ed.; John Wiley and Sons: West Sussex, 2003, pp 1.1–
1.14.
8Kreuer, K. J Membrane Sci 2001, 185, 29–39.
9Wang et al., “A review of polymer electrolyte membrane fuel cells: technology, applications, and needs on funda-
mental research”.
10Barbir, F; Gomez, T Int J Hydrogen Energ 1997, 22, 1027–1037.
2

4. to methanol as a hydrogen source for fuel cells remained consistent with known data, in that the
hydrogen cell had a higher efficiency than methanol. Thus our work supported current literature
on the feasibility of methanol as a source for hydrogen and also was within the range of efficiency
currently expected for hydrogen fuel cells.
3 Theory
3.1 Chemicals and Reactions
In this experiment there are two separate fuel cells: the Proton Exchange Membrane (PEM)
and Direct Methanol (DMFC) that result in a transfer of electrons thus resulting in a measur-
able current density. The proton exchange membrane fuel cell operates under the equation
of
H2 +
1
2
O2 −−→ H2O, (1)
where hydrogen enters the PEM Fuel Cell on the anode and oxygen is supplied on the cath-
ode reacting on the electroltye membrane containing free flowing protons.11 Current density
within the system is observed through the flow of electrons occuring within the PEM fuel
cell. The electrons in the fuel cell flow in both directions thus resulting in a reversible reac-
tion,12
O2 +4e−
+4H+ −−−− 2H2O. (2)
The direct methanol fuel cell operates based off the overall reaction of methanol and oxygen,
CH3OH+1
1
2
O2 −−→ 2H2O+CO2, (3)
11Larmaine, J.; Dicks, A., A Fuel Cell System Explained, 2nd ed.; John Wiley and Sons: West Sussex, 2003, pp 1.1–
1.3.
12Larmaine, J.; Dicks, A., A Fuel Cell System Explained, 2nd ed.; John Wiley and Sons: West Sussex, 2003, p 3.50.
3

5. however to understand the reaction and the need for water throughout the reaction it is nec-
essary to observe the half reactions that take place on the anode. The overall anode reaction
for DMFCs is
CH3OH+H2O −−→ 6H+
+6e−
+CO2, (4)
where the H2O necessary for the anode reaction is produced in the reaction at the cathode
1
1
2
O2 +6H+
+6e−
−−→ 3H2O. (5)
The reaction at the anode takes place in three steps, where the first step is the formation of
methanol
CH3OH −−→ CH2O+2H+
+2e−
, (6)
which then forms methanoic acid in a second step,
CH2O+H2O −−→ HCOOH+2H+
+2e−
. (7)
In the third step, carbon dioxide is formed
HCOOH −−→ CO2 +2H+
+2e−
(8)
thus the summation of these partial equations equal Eq. (4). There are alternative products
that could be formed that would still result in the same products, however this pathway is the
only one that provides stable products at all steps.13
13Larmaine, J.; Dicks, A., A Fuel Cell System Explained, 2nd ed.; John Wiley and Sons: West Sussex, 2003,
pp 6.143–6.146.
4

6. Figure 1: Characteristic Curve for PEM Fuel Cell. Current den-
sity data over the range of 0 to 100 mA/cm2 demonstrate activation
losses. The linear section over the range of 100 to 500 mA/cm2
demonstrate ohmic losses. Data over the range of 500 to 800
mA/cm2 demonstrate the mass transport losses.
3.2 Mathematics
Losses may occur through the fuel cell due to activation losses, ohmic losses, and mass trans-
fer losses. Activation losses are due to overvoltage during the initial drive of a reaction and
the slow speed of the reactions. Ohmic losses occur as there is small resistances throughout
the equipment that hinder the flow of current. Mass transport losses are attributed to changes
in pressure due to concentration fluctuations resulting in a voltage drop.14
E = E0,R −blog j −Rj −menj
, (9)
where E0,R is a fitted parameter for the reversible cell potential, b is the oxygen reduction fit-
ted parameter, R is the linear resistance fitted parameter, and m and n represent the parameter
for mass transfer limitations. The characteristic curve (see Fig. 115) produced by the charac-
teristic equation models the behavior of the PEM fuel cell.16 Faraday’s efficiency is defined
as the amount of electrical charge or current that can be transfered during the reaction within
14Larmaine, J.; Dicks, A., A Fuel Cell System Explained, 2nd ed.; John Wiley and Sons: West Sussex, 2003,
pp 3.48–3.60.
15Kim, J. et al. J. Electrochem. Soc. 1995, 142, 2671.
16Kim, J. et al. J. Electrochem. Soc. 1995, 142, 2670–2674.
5

7. the fuel cell.
ηFaraday =
Vth
H2
Vc
H2
, (10)
where Vc
H2
is the consumed volume at a time, t, and Vth
H2
is the necessary theoretical volume
to produce the desired current in m3 found through the assumption that the gas is operating
under ideal gas law conditions PV = nRT and that the total amount of charge is equivalent
to the product of current and time, Q = nzF = tI. Thus the volume is found through an
arrangement of these equations,
Vth
H2
=
R·I ·T ·t
F · p·z
, (11)
where R is the universal gas constant, I is current in Amperes, T is the temperature in Kelvin,
t is the time in seconds, F is Faraday’s constant, 96485 C, p is the ambient pressure in Pa,
and z is the required number of electrons to release one molecule.
4 Methods
A basic fuel cell is comprised of a positive anode, a negative cathode and an electrolyte. The fuel
cell was connected to the resistance source then to the ammeter device all in series, so the current
flowed in a clock-wise flow. Lastly the voltage source was connected in parallel to the fuel cell to
complete the fuel cell circuit diagram. Refer to Figure 1 for wiring schematic.17
Figure 2: Wiring schematic for fuel cell
17Drews, UCSD CENG 176 wikia.
6

8. The desired experimental hydrogen fuel cell was obtained. The fuel cell was inspected to find
the membrane. The membrane area was measured to determine current density. The fuel cell was
then reassembled and placed in circuit with the correct tubing. The hydrogen cell was purged
a couple of times, being filled up then drained, which removed excess air from the system. As
the fuel cell operated, the time was noted, and data regarding the cell voltage output and the cell
current density were recorded by computer program for a set amount of Hydrogen consumed. The
resistance was manipulated by a known amount each time to determine a characteristic curve for
the hydrogen fuel cell. The circuit was then opened to allow for an open-cell voltage reading
to be determined. In determining Faraday’s constant, a resistance that best optimized the power
consumption was selected and a fixed amount of hydrogen was produced then consumed by a
smaller amount in a stepwise fashion, where the current density and voltage were recorded.
Next the desired methanol fuel cell was obtained, and filled with 3 percent methanol in water. A
similar procedure to the hydrogen fuel cell was performed to determine the characteristic equation,
where the resistance was manipulated by a known amount to determine readings for the voltage
output and current density. The fuel cell was then purged of all remaining methanol by water and
allowed to drain.
5 Results
The following curve in Fig. 3 is the characteristic curve of a hydrogen fuel cell. In this curve,
the cell potential decreases from 1050 mV to 750 mV. At the same time, current density increases
from 0 mA/cm2 to 18 mA/cm2 while resistance decreases from 1000 Ohm to 10 Ohm in 50 Ohm
decrements.
The following curve in Fig. 4 is the characteristic curve of a 3% methanol fuel cell. In the
figure, the cell potential decreases from 500 mV to 200 mV while current density is increasing
from 0 mA/cm2 to 3 mA/cm2. The resistance changing is also decreased by 50 from 1000 ohm to
10 ohm.
7

9. Figure 3: Hydrogen fuel cell calibration curve of Current density j
vs Cell potential E. The horizontal error bar is calculated by cur-
rent reading error due to machine and length error due to reading.
Vertical error bar is determined by the machine itself. The red line
is non-linear fitting by eliminate variable n from equation (x elimi-
nation equation). 95% prediction interval is presenting in blue dash
line.
Figure 4: 3% methanol fuel cell calibration curve of Current density
j vs Cell potential E. The horizontal error bar is calculated by cur-
rent reading error due to machine and length error due to reading.
Vertical error bar is determined by the machine itself. The red line
is non-linear fitting by eliminate variable n from equation (x elimi-
nation equation). 95% prediction interval is presenting in blue dash
line.
Using MATLAB to fit the the data to Eq. (9) we obtained the following data for the fitted
parameters
8

10. H2 Methanol
E0 (mV) 78.85 (-7.767e+07, 7.767e+07) 89.39 (-6.374e+08, 6.374e+08)
B(mV) 38.04 (35.76, 40.32) 88.93 (54.94, 122.9)
R(MOhm cm2) 0.735 (fixed at bound) 0.735 (-41.78, 43.25)
m(cm2/mA) -804.4 (-7.767e+07, 7.767e+07) -280.8 (-6.374e+08, 6.374e+08)
Table 1: Matlab fitting data, reported with 95% confidence interval
6 Discussion
The error for the current density of the characteristic curve was calculated using Section 7 . We
used a 12-inch ruler to measure the dimension of the fuel cell membrane. The error of the current
and voltage measurements are 0.05mA and 0.05mV, respectively. These uncertainties can be found
in the user manual of the NI myDAQ32. To get the error for Faraday efficiency of the hydrogen
fuel cell Eq. (10) is followed. The error of Vc
H2
is due to the precision of cylinder and the error of
Vth
H2
is calculated by Eq. (11)
As shown in the table in Section 5 and the characteristic curves Fig. 3 and Fig. 4, the hydrogen
PEMFC has a higher relative cell potential than that of DMFC with the same resistance value. This
means as a fuel, pure hydrogen gas has a better ability than aqueous methanol for transferring the
electrons. Another explanation for the hydrogen PEMFC’s higher cell potential than its methanol
counterpart is the fact the the hydrogen fuel was more concentrated than the 3% methanol fuel cell
which was diluted in water. Due to the hydrogen fuel cell having a larger cell potential, the current
density is also larger than that of the methanol fuel cell. In fitting both characteristic curves to
Eq. (9) , we eliminated variable n in the mass transport loss. Our first reason for the elimination
is nitrogen, from air, is treated as a contaminant in the hydrogen fuel cell and is the main reason
for mass transport loss.18 However, we used pure hydrogen and oxygen gas and aqueous methanol
which contains very little,if any, contaminants. Secondly, from the original fit, the 95% confidence
interval for n included zero and according to regression analysis,19 it should be omitted.
The Faraday efficiency of the hydrogen fuel cell was calculated to be 0.36 ± 0.03 using equa-
18Experiment:Fuel Cell.
19Drews, UCSD CENG 176 wikia.
9

11. tion Eq. (10) and Eq. (11). The reason why this efficiency is relatively low is because during the
experiment, there is a leakage of hydrogen gas from the connection tube between the hydrogen
tank and the fuel cell. This causes a larger reading in Vc
H2
than the actual amount of H2 consumed
by the cell. In addition, the limited precision of the graduated cylinder containing the hydrogen
gas resulted in imprecision in the volumetric reading. A more precise cylinder should be used to
decrease the observation error. When we calculate the efficiency, we found the first two data points
are very low compared to the average efficiency. This is because the whole system needed time to
begin the reaction. To eliminate this, more data points should be collected.
7 Conclusions
The experimentation and subsequent analysis provided two characteristic curves, that display how
current density varied with cell potential for a hydrogen fuel cell, and a 3% methanol by water fuel
cell. In studying the two curves produced, it can be concluded that the hydrogen fuel cell offered
a high cell potential over equivalent resistance than the 3% methanol by water fuel cell. Thus the
hydrogen fuel cell can facilitate electron movement better and is the more optimal fuel source then
methanol in water. This is due to the hydrogen being more concentrated than the diluted methanol
as the reaction proceeds. It was observed that pure H2 would generate more electric potential than
an aqueous methanol solution, thus H2 should be favored when looking to build fuel cells based on
electric potential created. Upon analysing the Faraday efficiency of the hydrogen cell was found
to be 0.36 ± 0.03. This value can be attributed to a leakage of H2 from the connecting tube which
caused the volume recorded to be higher than the actual volume of H2 being consumed, resulting
in a decrease in the overall Faraday efficiency of the fuel cell.
10

12. Appendix
e2
Y =
N
∑
i=1
∂Y
∂yi
2
e2
i (12)
e2
j = [(
∂ j
∂I
)2
(e2
i )+(
∂ j
∂A
)2
(e2
A)] (13)
e2
η = [(
∂η
∂Vth
)2
(eV
th
)2
+(
∂η
∂Vc
)2
(eV
c
)2
] (14)
Current density(mA/cm2) time(s) efficiency
19.965 10 2.52E-2
10.797 170.7 0.15
17.824 378.9 0.42
16.192 590.0 0.48
14.531 835.2 0.51
11.94 1090.3 0.47
10.025 1398.7 0.44
7.884 1794.3 0.39
6.110 2231.9 0.34
Table 2: Hydrogen efficiency, Current density (mA/cm2) varies on
time.
A-1