A fuel cell is an electrochemical device in which hydrogen reacts with oxygen
to produce water and DC electricity. A 1-watt proton-exchange membrane fuel
cell (PEMFC) could be used for portable applications such as cellular
telephones, and a \(100-\mathrm{kW}\) PEMFC could be used to power an
automobile. The following reactions occur inside the PEMFC:Anode: \(\quad
\mathrm{H}_{2} \rightarrow 2 \mathrm{H}^{+}+2 \mathrm{e}^{-}\)
Cathode: \(\quad \frac{1}{2} \mathrm{O}_{2}+2 \mathrm{H}^{+}+2 \mathrm{e}^{-}
\rightarrow \mathrm{H}_{2} \mathrm{O}\)
Overall: \(\quad \overline{\mathrm{H}}_{2}+\frac{1}{2} \mathrm{O}_{2}
\rightarrow \mathrm{H}_{2} \mathrm{O}\)
A flowchart of a single cell of a PEMFC is shown below. The complete cell
would consist of a stack of such cells in series, such as the one shown in
Problem 9.19.The cell consists of two gas channels separated by a membrane
sandwiched between two flat carbonpaper electrodes- -the anode and the
cathode- -that contain imbedded platinum particles. Hydrogen flows into the
anode chamber and contacts the anode, where \(\mathrm{H}_{2}\) molecules are
catalyzed by the platinum to dissociate and ionize to form hydrogen ions
(protons) and electrons. The electrons are conducted throughthe carbon fibers
of the anode to an extemal circuit, where they pass to the cathode of the next
cell in the stack. The hydrogen ions permeate from the anode through the
membrane to the cathode.Humid air is fed into the cathode chamber, and at the
cathode \(\mathrm{O}_{2}\) molecules are catalytically split to form oxygen
atoms, which combine with the hydrogen ions coming through the membrane and
electrons coming from the external circuit to form water. The water desorbs
into the cathode gas and is carried out of the cell. The membrane material is
a hydrophilic polymer that absorbs water molecules and facilitates the
transport of the hydrogen ions from the anode to the cathode. Electrons come
from the anode of the cell at one end of the stack and flow through an extemal
circuit to drive the device that the fuel cell is powering, while the
electrons coming from the device flow back to the cathode at the opposite end
of the stack to complete the circuit. is important to keep the water content
of the cathode gas between upper and lower limits. If the content reaches a
value for which the relative humidity would exceed \(100 \%,\) condensation
occurs at the cathode (flooding), and the entering oxygen must diffuse through
a liquid water film before it can react. The rate of this diffusion is much
lower than the rate of diffusion through the gas film normally adjacent to the
cathode, and so the performance of the fuel cell deteriorates. On the other
hand, if there is not enough water in the cathode gas (less than \(85 \%\)
relative humidity), the membrane dries out and cannot transport hydrogen
efficiently, which also leads to reduced performance. 400-sell 300-yolt PEMFS
anerates at stady state witha nonwer outnul of 36 k W, The air fod to It is
important to keep the water content of the cathode gas between upper and lower
limits. If the content reaches a value for which the relative humidity would
exceed \(100 \%,\) condensation occurs at the cathode (flooding), and the
entering oxygen must diffuse through a liquid water film before it can react.
The rate of this diffusion is much lower than the rate of diffusion through
the gas film normally adjacent to the cathode, and so the performance of the
fuel cell deteriorates. On the other hand, if there is not enough water in the
cathode gas (less than \(85 \%\) relative humidity), the membrane dries out and
cannot transport hydrogen efficiently, which also leads to reduced
performance.A 400-cell 300-volt PEMFC operates at steady state with a power
output of 36 kW. The air fed to the cathode side is at \(20.0^{\circ}
\mathrm{C}\) and roughly 1.0 atm (absolute) with a relative humidity of \(70.0
\%\) and a volumetric flow rate of \(4.00 \times 10^{3}\) SLPM (standard liters
per minute). The gas exits at \(60^{\circ} \mathrm{C}\).
(a) Explain in your own words what happens in a single cell of a PEMFC.
(b) The stoichiometric hydrogen requirement for a PEMFC is given by
\(\left(n_{\mathrm{Hz}}\right)_{\text {conanmad }}=I N / 2 F,\) where \(I\) is the
current in amperes (coulomb/s), \(N\) is the number of single cells in the fuel
cell stack, and \(F\) is the Faraday constant, 96,485 coulombs of charge per mol
of electrons. Derive this expression. (Hint: Recall that since the cells are
stacked in series the same current flows through each one, and the same
quantity of hydrogen must be consumed in each single cell to produce that
current at each anode.)
(c) Use the expression of Part (b) to determine the molar rates of oxygen
consumed and water generated in the unit with the given specifications, both
in units of mol/min. (Remember that power = voltage \(\times\) current.) Then
determine the relative humidity of the cathode exit stream, \(h_{\mathrm{r}
\text { rout. }}\)
(d) Determine the minimum cathode inlet flow rate in SLPM to prevent the fuel
cell from flooding ( \(h_{\mathrm{r}, \text { out }}=100 \%\) ) and the maximum
flow rate to prevent it from drying \(\left(h_{\mathrm{r}, \text { out }}=85
\%\right)\) .
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