Department of Physics and Astronomy

University of British Columbia, Vancouver, BC


Physics 409D

The Proton Exchange Membrane Fuel Cell

Shane Luke

    This website is a summary of my UBC Physics 409D project.  The purpose of the project was to explain the basics of proton exchange membrane fuel cells, and to demonstrate how they function using a small working model of a fuel cell powered car.  The demonstration I performed also involved a simple experiment and calculation to determine the power and efficiency of the model.  The intended audience for this demo is grade 11 or 12 high school students.  Despite the somewhat daunting name, the basics of PEM fuel cells can be easily explained to a novice audience.  The detailed physics and engineering is not so easily explained, so we'll steer clear of it. 

What is a PEM fuel cell?

Electrolysis, and the PEM cell in action

Pros & Cons

My demonstration


Let's start by defining the fuel cell:

A fuel cell is a device that converts chemical potential energy (energy stored in molecular bonds) into electrical energy, the fancy jargon for this is an 'electrochemical device'. 

Now we'll take a look at the basic components of the PEM fuel cell:

Anode simply means positive electrode, cathode means negative electrode.  A catalyst is something that promotes or accelerates a reaction; in a PEM cell it is a platinum coated plate.  The membrane itself is a thin polymer film, often Nafion™, which is manufactured by Dupont™.  It serves as a solid electrolyte.

    A PEM cell uses hydrogen gas (H2) and oxygen gas (O2) as fuel.  The products of the reaction in the cell are water, electricity, and heat.  This looks like a big improvement over internal combustion engines, coal burning power plants, and nuclear power plants, all of which produce harmful by-products.  Since O2 is readily available in the atmosphere, we only need to supply the fuel cell with H2.  This can be done by using hydrogen directly, but it is more likely that we will use reformers to extract hydrogen from other sources, such as methanol.  Reformers do emit some greenhouse gases, but it is a fraction of the amount emitted by combustion engines.

To understand how a fuel cell works, let's first take a look at electrolysis: the splitting of water into H2 & O2. 

The chemical equations are as follows:

H2O → H+ + OH-

2H+ + 2e- → H2

4OH- → 2H2O + O2 + 4e-


    So that's electrolysis, but that reaction requires a voltage, it doesn't produce one.  So how is it related to our power-producing PEM cell?  If you have been paying attention you can probably guess: we can simply run the reaction backwards to produce electricity.  Oxidizing hydrogen to form water is the reverse process, and a PEM fuel cell can work either way.  It can 'fuel up' by splitting water into H2 & O2, with an external voltage source, or it can produce a voltage when fuel is supplied to it.  

Here's a schematic view of a PEM cell in action:


The chemical reactions look like this:


2H2 → 4H+ + 4e-


O2 + 4H+ +4e- → 2H2O


2H2 + O2 → 2H2O

    As the name implies, the heart of the cell is the proton exchange membrane.  It allows protons to pass through it virtually unimpeded, while electrons are blocked.  So, when the H2 hits the catalyst and splits into protons and electrons (remember, a proton is the same as an H+ ion) the protons go directly through to the cathode side, while the electrons are forced to travel through an external circuit.  Along the way they perform useful work, like lighting a bulb or driving a motor, before combining with the protons and O2 on the other side to produce water.

    If you are anything like me, you are probably wondering how the PEM manages to transmit protons while blocking electrons.  Well, remember when I said we'd avoid the complicated details...

Okay, so far things look pretty good, so why aren't we all driving fuel cell cars?  Well, there are some down sides. 

Here are some pros and cons of the technology:



    So that's a little theory about PEM fuel cells.  For my project, I used a model from Thames and Kosmos™, which allowed me to demonstrate the cell performing electrolysis and then driving an electric motor by consuming the fuel it produced.  This kit is available from various sources online, and costs about $200.00.  Most of what was needed was contained in the kit, but the same components could easily be purchased individually and then assembled. 

Here is a list of my apparatus:

When assembled, the model car looks like this (the fuel cell is the blue square piece in the middle; the anode side is facing out):

                                                                                                                   Fig. 4 The model car

    The first step in the demonstration is to show electrolysis in action.  This can be done either with the fuel cell directly, or with a simple salt water and electrode set-up (the salt serves as an electrolyte in the absence of the PEM), like the one pictured in Fig. 2 above.  The only advantage of using the salt water set-up is that it is easy to ignite the hydrogen for a simple but effective demonstration of its presence.  I did not do this in class due to time constraints, but it can be done by collecting the bubbles of H2 gas in an inverted test tube, and then turning the tube right side up with a burning splint held over the opening.  When using the cell for electrolysis, the H2 and O2 is stored in the tanks at the rear of the model, and can be observed traveling from the cell to the tanks through the two clear tubes on each side of the fuel cell.  The time to fully fuel the tanks depends on the power and voltage supplied to the cell.  With my photovoltaic panel and 500 watt light source, it takes about 2 minutes.

    Next, we can take a look at the cell in action.  Since we have just finished fueling it, all that remains is to connect the motor and let the car run. 

    Now it's time to do some basic experimental physics.  We are going to design an experiment to measure the power and efficiency of the motor, the fuel cell, and the overall efficiency of the car.  You can probably guess from my apparatus list how the car's power is to be measured: timing its run up a ramp.  In case you have forgotten, power is defined as the rate of work, or the rate of energy consumption, and is measured in units of energy per unit time.  The S.I. unit is the watt, and it is equal to one joule per second.  To determine the power of the car, we can run it up the ramp, and then divide its increase in gravitational potential energy by the time it took to effect that increase.


    Gravitational potential energy can be calculated according to the formula: m×g×h, where m is the mass of the car (0.32 kg with fully fueled tanks), g is the acceleration due to gravity at the surface of the Earth (9.8 m/s^˛), and h is the increase in height of the car (0.23 m with my ramp).  Time is measured, in seconds, with the stopwatch.  When I performed the experiment in class I did three trials, yielding an average power of 0.027 watts.  To get the efficiency of the car, we can now measure, with the multimeter, the operating current and voltage from the fuel cell (these are the values present when the motor is running on power from the cell), and get a power from the formula P = I×V, where P is the power, I is the operating current, and V is the operating voltage.  The efficiency is now just the car's power divided by the electrical power we just calculated.  For the operating efficiency of the cell, all we need is a measurement of the short circuit current and no load voltage.  These are easily measured with the multimeter by simply disconnecting the motor and measuring the needed values.  The operating power over the short circuit power gives the operating efficiency of the cell.  My in-class measurements turned up efficiencies of 52% and 49% respectively.  The car's overall efficiency is the product of these two values: 25%.  Of course, this does not include the loss in energy from the light that was used to fuel the car, but this is of minimal concern if the Sun is the light source.  In case you are wondering, the photovoltaic panel is said by the manufacturer to be about 16% efficient.  This value is not really constant; it actually depends on the spectrum, intensity, and angle of the incident light, but that's one of those complicated matters we are avoiding. 

    As with any experiment, some error analysis is in order.  We'll confine the discussion here to the major sources of possible error, rather than a quantitative analysis, and there are a few.  First, we have not accounted for the loss of energy due to friction.  Second, we have implicitly assumed that the power output of the cell is constant, which is probably not the case.  The power depends, to some extent, on the amount of fuel in the tanks, as well as the force acting against the motor.  Also, we have not made allowance for the difference in kinetic energy the car might have at the beginning and end of its run up the ramp.  This can be managed by adjusting the ramp and the initial velocity of the car so that it starts and finishes its run at about the same speed.  

    So there is my project in a nutshell.  The more I looked at fuel cells, the more I realized they have the potential to revolutionize global power production.  It is clear that some form of change will eventually be required, since fossil fuels are non-renewable, and the fuel cell offers an attractive choice.  Given that many of the world's largest corporations are either oil or car companies, change will likely be slow.  In time, though, we may all trade our dirty gas guzzlers for efficient, reliable, clean fuel cell powered cars.