investigating the faraday constant of the electrolysis and synthesis of water in a reversible...

1Candidate number 003083-007

International Baccalaureate

Chemistry Higher Level Extended Essay

Investigating the Faraday Constant of the Electrolysis andSynthesis of Water in a Reversible Hydrogen Fuel Cell

Name: Kleopas Palate

Candidate number: 003083-007

Date: March 5, 2011

Center number: 003083

Supervisor: Dr. George Georgiadis

School: Pascal English School Larnaca

Word count: 3977


Abstract:

The aim of this essay is to investigate the relationship between the volume of hydrogen gas

converted by a fuel cell and the amount of charge that passes through its circuit.

The research question this essay investigates is: “Does the Faraday constant apply to fuel

cell technology?”

Essentially, the Faraday constant is derived by investigating the forward (electrolysis) and

reverse reaction (synthesis of water) that hydrogen fuel cell technology utilizes.

The experiments only deal with a demonstration Proton Exchange Membrane (PEM)

reversible hydrogen fuel cell, at room temperature and pressure, with a controlled power

supply and load, to limit the scope.

According to the developed hypothesis, the Faraday constant of the reverse redox reaction

for the production of water will be less than the literature value and along with the Faraday

constant for the forward redox reaction (electrolysis of water), it can be used to determine

the Faraday efficiency. Also, the Faraday constant of the forward reaction will equal the

literature value within experimental uncertainties.

A method of measuring the charge passing through the circuit (using an automatic data

logger) while also recording the change in the volume of gas was used.

From the current-time graph produced by the data logger and the change in volume of

hydrogen gas it is possible to calculate the Faraday constant.

The conclusion of the essay is that the hypothesis was correct. Answering the research

question: the Faraday constant was found not to apply to fuel cell technology. More

specifically, it does not apply to PEM hydrogen fuel cells according to this study and within

the experimental uncertainties. The Faraday constants for the forward and reverse reactions

were found to be 94900 ± 2000 C/mol and 77700 ± 3000 C/mol, respectively. The percent

modified Faraday efficiency was found to be 81.9 ± 5%.

Word count: 299


Contents

Research question:.................................................................................................................................. 4

Introduction ............................................................................................................................................4

Background Theory: ................................................................................................................................5

Faraday’s Laws of electrolysis:............................................................................................................5

The Chemistry of the PEM Fuel Cell.................................................................................................... 6

PEM Fuel Cell Redox reactions:....................................................................................................... 7

Reaction Mechanism.......................................................................................................................7

Aim: .........................................................................................................................................................8

Hypothesis: .............................................................................................................................................8

Variables: ................................................................................................................................................8

Apparatus:...............................................................................................................................................9

Procedure:...............................................................................................................................................9

Cylinder ...............................................................................................................................................9

Burette method (used for electrolysis trials only) ..............................................................................9

Digitizing Graph images ....................................................................................................................10

Hoffman apparatus method (both electrolysis and synthesis trials)................................................12

Experiment 1: Investigation of Faraday constant of electrolysis:.........................................................13

Sample Calculations: .........................................................................................................................13

Table 2: Electrolysis trials..................................................................................................................18

Graph 2: Scatter plot of all of the electrolysis trials with best fit, maximum, and minimum ..........19

Experiment 2: Investigation of Faraday constant of water synthesis: .................................................21

Table 4: Water synthesis trials..........................................................................................................22

Graph 4: Scatter plot of all of the synthesis trials with best fit, maximum, and minimum..............23

Result Evaluation ..................................................................................................................................24

Table 5: Experimental Faraday constants with uncertainties and errors.........................................24

Conclusion:............................................................................................................................................26

Evaluation: ............................................................................................................................................26

Bibliography ..........................................................................................................................................28


Research question:

Is the value of the Faraday constant, as derived by the investigation of both the electrolysis

(forward reaction) and the synthesis of water from its elements (reverse reaction) by a

reversible hydrogen fuel cell, the same (within the bounds of the experimental

uncertainties)?

Introduction

The purpose of this extended essay is to investigate the application of the Faraday constant

to the electrolysis and synthesis of water using a reversible hydrogen fuel cell. A reversible

fuel cell can electrolyze distilled water to produce hydrogen and oxygen gases and also can

convert these gases back into water to produce a current.

The electrolysis reaction is expected to have a Faraday constant which equals the literature

value within experimental uncertainties. On the other hand, the same is not expected for

the water synthesis (reverse) reaction. This has to do with the mechanism of the Proton

exchange membrane (PEM) of the fuel cell. Essentially, it is expected that some of the

hydrogen (either in diatomic or monatomic form) will diffuse through the membrane

without first being reduced into ions.

Evidence of this effect can be identified if lower-than-expected amounts of charge are found

for a volume of hydrogen gas consumed. A lower Faraday constant is therefore anticipated

for the water synthesis reaction.

Fuel cells are devices that work on the same principle as a battery with the exception that

the chemicals are continually replenished. The hydrogen fuel cell converts the chemical

energy of the supplied gases (Hydrogen and Oxygen) into electrical energy and water.

The Intergovernmental Panel on Climate Change (IPCC)1 is a scientific intergovernmental

body established in 1988 by the World Meteorological Organization (WMO) and the United

Nations Environment Programme (UNEP)2

The stated aims of the IPCC are to assess scientific information relevant to:

human-induced climate change and its impacts3

options for adaptation and mitigation

Hydrogen and fuel cells have the potential in reducing green house gas - CO2 emissions.4


Hydrogen gas does not occur in nature but in its combined form, water, is the most

abundant element on Earth. It is a clean fuel and can be produced by the electrolysis of

water, using photovoltaics, wind or other renewable energy sources. It is termed an “energy

carrier” since energy is required to produce it in the first place, so it is only useful to do so if

it is produced during times when renewable sources are available, i.e. during daylight, and

used during periods of demand, i.e. evenings.

Recent technology advances have increased attention for the use of hydrogen and fuel cells

as a substitute or complement for oil fuels and internal combustion engines in transport.

“The clear advantage of using hydrogen in fuel cells is that the high efficiency of fuel cells

can be combined with zero CO2 emissions”.

There are a number of obstacles on the path to a hydrogen economy including:

High cost of fuel cells

The absence of an infrastructure for getting hydrogen to consumers

Storage challenges

There are also safety concerns because hydrogen:

has a wide flammability and detonation limit,

a low ignition energy, and

high flame speed.

Background Theory:

Faraday’s Laws of electrolysis:

“…Michael Faraday found that the mass of a substance involved in reaction at the

electrodes is directly proportional to the quantity of electricity passed through the

solution. [Faraday’s 1st law] is independent of temperature, pressure, or the nature of the

solvent, as long as the latter can promote ionization of the solute.” 5

Faraday’s 2nd Law of electrolysis states that:

“The second law states that the number of moles of electrons required to discharge one

mole of an ion at an electrode equals the number of charges on the ion” 6


The value of the Faraday constant is determined by multiplying the charge of an electron

(1.602E-19 Coulomb) by Avogadro’s number (6.022E23), in short it is the total charge

produced by one mole of electrons. The value of which is 96485 C/mol.

The Chemistry of the PEM Fuel Cell

The membrane electrode assembly (MEA) is at the heart of a PEM fuel cell. The electrodes

are coated with 0.1-0.5 milligrams of platinum per square centimetre and finely distributed

and deposited onto specially treated polymer membrane carbon mats. The latter are then

hot-press-bonded with the polymer membrane (Nafion®). The membrane extends into the

porous electrode structures, and the catalyst must have simultaneous contact with the gas,

the proton conductor (polymer membrane) and the electron conductors (electrodes).

Nafion consists of Polytetrafluoroethylene (PTFE) chains, commonly known as Teflon®

forming the backbone of the membrane. Attached to the Teflon chains, are side chains

ending with sulphonic acid (HSO3) groups.

Chemical structure of a PEM fuel cell

membrane. Long chains of PTFE (Teflon®)

with side chain ending with sulphonic acid

(HSO3).

Close-up of a PEM fuel cell membrane shows

long spaghetti-like chain molecules of Teflon

surrounding clusters of hydrated regions

around the sulphonate side chains. An

interesting feature of this material is that

whereas the long chain polymers molecules

are hydrophobic, the sulphonate side chains

are highly hydrophylic.

For the membrane to conduct ions efficiently

the sulphonate side chains must absorb large

quantities of water. Within these hydrated

regions, the hydrogen ions of the sulphonic

acid groups can then move freely, enabling


the membrane to transfer hydrogen ions, in

the form of hydronium ions H3O+ from one

side of the membrane to the other.

The Teflon chains form the backbone of the

membrane. The hydrated regions around the

sulphonate side chains become the

electrolyte. (Source: Larminie & Dicks,

February 2000)

The two half-cell electrochemical reactions in a PEM fuel cell, as with all redox reactions,

take place simultaneously. The oxidation reaction at the anode leads to a loss of electrons

from the hydrogen whilst a reduction reaction at the cathode leads to a gain of electrons by

the oxygen. The resulting product of the reaction is the formation of water from hydrogen

and oxygen gases. In electrolysis the anode and cathode are immersed in an electrolyte

usually a weak solution of sulphuric acid, which allows ions to be transferred from one side

to the other. In a PEM fuel cell the electrolyte is a solid acid supported within the membrane

and this is saturated with water so that the transport of ions can proceed.

PEM Fuel Cell Redox reactions:

Anode reaction: H2 → 2H+ + 2e-

Membrane reaction: 2H+ +2H2O → 2H3O+

Cathode reaction: ½O2 + 2e- + 2H3O+ → 3H2O

Overall reaction: H2 + 1/2 O2 → H2O

Reaction Mechanism

At the anode:

1. Hydrogen molecules diffuse to the catalyst surface.

2. Hydrogen molecules adsorb onto the platinum catalyst forming weak H-Pt bonds.

3. The hydrogen atomizes into single hydrogen atoms.

4. Each hydrogen atom releases its electron, by an ionization process to form a proton

and the electron travels around the external circuit to the cathode (referred to as

electrical current).


5. The hydrogen proton then bonds with a water molecule on the membrane surface,

forming a hydronium ion (H3O+).

6. The hydronium ion diffuses through the membrane to the cathode, leaving the

platinum catalyst site free for the next hydrogen to repeat this process.

Figure 1: Cross section of a membrane electrode assembly (MEA) of a PEM fuel cell7

Note that it is also possible for the hydrogen gas to diffuse through the membrane directly

and then combine with the oxygen directly without the electrons flowing around the

external circuit.

Aim:

The aim of this essay is to investigate the relationship between the volume of hydrogen gas

converted by a fuel cell and the amount of charge that passes through its circuit.

Hypothesis:

If the Faraday constant (96485.34 Coulombs/mole of electrons)8 applies for the electrolysis

of water but a different value is obtained during the recombination of its constituent

molecules, then a basis can be established for the Faraday efficiency (η) to be determined

for a PEM Hydrogen fuel cell.

Variables:

Independent: Volume of hydrogen gas produced

Dependent: Charge (product of current and time)

Control: Temperature, Pressure, same Fuel cell used


Apparatus:

Syringe(s) Gas storage cylinders

Hoffman voltameter

(±0.10 cm3)

Renewable energy monitor (automatic

multimeter)

Burette (±0.10cm3) Leads (wires included in kit)

Deionized water Fuel cell kit chassis with motor

Pinch clamp Reversible fuel cell

Beaker Battery pack

Rubber tubing Stopwatch

Procedure:

Cylinder

Some of the initial trials were conducted using the cylinders from the fuel cell car kit. There

are graduations on the side of the cylinder however the displacement of water due to the

inner cylinders and rubber tubes made accurate volume difficult to obtain using the cylinder

marks alone. The cylinders were calibrated gravimetrically by weighing the mass of water

required to fill a cylinder between two graduated marks to improve the accuracy of the

readings.*

*Upon analysis, the random error of the cylinder trials was deemed too great, and another

measurement procedure was devised.

Burette method (used for electrolysis trials only)

Experimental description:

In this experiment I used the reversible fuel cell to electrolyze distilled water. I collected the

hydrogen gas produced in an inverted burette. I measured initial and final volumes, the

duration of electrolysis, and the current using the datalogger.

Procedure:

1. Fill a beaker and burette with water


2. Cover opening of burette, invert it and submerge into beaker

3. Attach the burette to a lab stand leaving space between the bottom of the beaker

and the opening of the burette

4. Detach bell cap from the tubing on the hydrogen side of the fuel cell

5. Feed the tube into the beaker and up into the burette

6. Pinch off the end of the tube at the hydrogen side with pinch clamp

7. Remove the short tube on the other opening of the hydrogen side and attach a

syringe filled with deionized water, unclamp the other tube, and inject distilled

water to remove air bubbles.

8. Replace clamp, remove syringe, and replace the short tube with end pin

9. If there is too much air already in the burette, then withdraw some from the

opening at the top.

10. Rehydrate the oxygen side of the fuel cell

11. Record the initial volume of gas in the burette (note that number are all upside

down)

12. Connect fuel cell leads to output sockets on automatic multimeter and connect

battery leads to input.

13. Run data logging program and start recording

14. Switch on battery pack and start stopwatch simultaneously

15. Stop the stopwatch, disconnect one of the output leads, and stop the data recording

in the program

16. Record the final volume of gas

17. Take snapshot of graph of current over time

Digitizing Graph images

Process description:

The renewable energy monitor software can record data values at various intervals (e.g. 5

readings per second, 1 reading per second, ect.) One reading per second was the interval

used for all of the trials that follow. Even though the program can record data, there is no

option to export the data collected. All the program can do is to take a snapshot of the

graph on the screen. To extract the data points from the graph snapshots, another program


called Dagra9 was used. Using Dagra, I fit a Bézier curve onto the graph images and exported

the data points into Excel

1. First record data with the Renewable Energy Monitor program10 (from step 13

above)

2. Adjust scale and switch on only the necessary variables to graph (normally only the

current was graphed)

3. Click play and pause as the last sample is plotted.

4. Take a snapshot by clicking the snapshot button in the program

5. Find the JPEG file of the snapshot (labeled with the time and date automatically) and

open the file in an image viewer

6. Run Dagra

7. Choose extract data from snapshot

8. Take a snapshot of the graph image

9. Fit the x and y axis to the image of the graph and enter the correct scales

10. Now fit a Bézier curve onto this image which passed through the datapoints

11. Copy the data points into a spreadsheet application.


Figure 2: Screenshot of Darga taken Feb. 28, 2011 at 8:34 am

Hoffman apparatus method (both electrolysis and synthesis trials)

Experiment description:

The electrolysis data obtained with the burette used only the initial and final volumes. To

show more than just the total change in volume and total coulombs produced, another

experimental set up was required. The burette setup could have worked for this purpose. By

measuring the volume at regular intervals and calculating the total charge at the same

intervals, a wider range of data points can be plotted (not just one point as is the case when

calculating only the total change in volume). The reason the burette setup was only used for

charging trials, was because the rubber tubes were too small to fit on the nozzle of the

burette. The solution to this problem was to use the Hoffman voltameter. This apparatus

was not used for its intended purpose (i.e.to electrolyze water), but instead was used to

measure the volumes of hydrogen gas. The nozzle openings were slightly smaller, and with

the addition of some wider rubber tubing, it was possible to connect the nozzles of the

apparatus to the nozzles of the fuel cell. The other advantage of using the Hoffman

voltameter was that the markings are not upside down as they were with the inverted

burette. The volume was recorded at regular intervals and the coulombs were calculated at

the same intervals.


Experiment 1: Investigation of Faraday constant of electrolysis:

After conducting the electrolysis and water synthesis trials, the data needed to be

manipulated to find the Faraday constant for each trial, and the average Faraday constant of

all the trials. Below are sample calculations showing, step by step, how the Faraday constant

is found for a trial. The example is of an electrolysis trial using the burette, but the same

process is used to calculate the Faraday constant of all of the electrolysis and synthesis

trials.

Sample Calculations:

Raw Data:

Initial volume: 49.4 ± 0.10 ml

Final volume: 16.5 ± 0.10 ml

Time: 4minutes 20 sec = 260 seconds

Figure 3: Snapshot taken of burette trial

Calculating moles produced:

Volume of H2 produced:

Initial Volume: 49.4 ± 0.10 ml


Final Volume: 16.5 ± 0.10 ml

Volume of gas produced= 49.4 – 16.5 = 32.9 ± 0.20 ml

To calculate moles produced, first the volume of gas per mole at the experimental

temperature and pressure must be.

PV=nRT

Rearranging we get V/n=RT/P ( ) × 101 =( ) = × 110 = 23721Moles of H2 produced:

32.9 × 123721 = 1.39 × 10“Theoretical” measured coulombs are found by integration:

= d

Figure 4: Graph showing how data extracted from snapshot is integrated

0

0.2

0.4

0.6

0.8

1

1.2

1.4

10 30 50 70 90 110 130 150 170 190 210 230 250 270

Curr

ent (

Am

ps)

Time (seconds)

I vs. t


The integration was done by multiplying the current at 10 second intervals by 10 (the

product is the charge that has passed through the circuit in that interval. Finding the sum of

these products gives the total amount of charge (Q) that has passed through the circuit.

Q= 257.73 coulombs

Consider that the uncertainty of the current is ±0.05 amps. If 0.05 is added to the values for

current and the new points are integrated, then charge for the maximum current is

obtained. Repeating the process, but instead of adding, this time subtracting 0.05 gives

charge for the minimum current.

Maximum current: 259.08

Minimum current: 256.38

The uncertainty is the difference between the maximum and the minimum divided by two.−2 = 259.08 − 256.382 = 1.35Now the charge should be expressed to 3 significant figures (s.f.) because both current and

time were expressed to3 s.f. on the graph. Uncertainty should be expressed to 1 s.f.

Q= 258 ± 1 coulombs

Finding the Faraday constant:

One Faraday is equivalent to 1 mole of electrons, or 96485.3415 coulombs of charge per

mol.

To derive this constant, simply divide the charge in coulombs (found by integration) by the

moles of electrons in the Hydrogen gas produced (difference of measured volume).

There are 2 moles of electrons per mole of H2.

= 1.39 × 101 × 21 = 2.774 × 10= = 257.72.77 × 10 = 93008 /


Uncertainty:

The Faraday constant is directly proportional to the charge calculated and inversely

proportional to the volume of Hydrogen produced.

Therefore the Faraday constant is largest when calculated using the maximum charge and

minimum volume; it is smallest when using the minimum charge and maximum volume.

(The uncertainty of temperature, which affects the volume, has also been considered. On

the days these experiments took place the temperature was 18 ± 1°C)

The maximum and minimum values for the Faraday constant were calculated, so that the

uncertainty could be found.

Maximum Faraday constant: 94263

Minimum Faraday constant: 91771

= −2 = 94263 − 917702 = 1246.5∴ Faraday constant= 93000 ± 1000 C/mol (3 s.f.)

Calculating the percent error:

= − × 100%= 96485 − 9300096485 × 100% = 3.6 ± 1%

A total of 6 separate electrolysis trials were conducted, and 15 data points were produced.

The data points mostly came from the two Hoffman trials.


Table 1: Burette and Hoffman electrolysis results

Trial Name Change in

volume (cm3)

Uncertainty

of volume

Time (s)

± 1

Charge

(coulombs)

Uncertainty

of Charge

1 Burette 1 32.9 0.2 260 258 1

2 Burette 2 10.0 0.2 100 75.3 0.5

3 Burette 3 10.2 0.2 114 76.2 0.6

4 Burette 4 7.7 0.2 60 53.6 0.3

5 Hoffman 2 9.0 0.2 120 72.1 0.6

6 Hoffman 3 8.4 0.2 121 66.6 0.6

Graph 1: Volume vs. time graph for the burette and Hoffman electrolysis trials

To find the Faraday constant:

There are 15 data points for the electrolysis trials. Most of the data points are instantaneous

measurements taken during the Hoffman trials.

0

10

20

30

40

50

60

0 50 100 150 200 250 300

Vol

ume

H2

(cm

3 ) (±

0.2)

Time (s) (±1)

Volume v. Time

Burette 1

Burette 2

Burette 3

Burette 4

Hoffman 2

Hoffman 3


Each trial produced one or more set of values (depending on whether only the initial and

final volumes were used or not) which were processed to find the Faraday constant for that

trial and its uncertainty. The results can all be found in Table 1.

Table 2: Electrolysis trials

Δ Vol

H2

(cm3)

Uncert.

Vol

Mol H2 Charge

(C)

Uncert.

Charge

Mol

electrons

e-

Faraday

Constant

(C/mol)

Uncert.

Faraday

Constant

%

error

Unc.

%

error

2.2 0.2 9.28E-05 18.9 0.2 1.86E-04 102000 10000 5.7% 6%

2.8 0.2 1.18E-04 20.5 0.2 2.36E-04 86800 7000 10.0% 7%

4.4 0.2 1.86E-04 35.4 0.3 3.71E-04 95400 5000 1.1% 1%

4.9 0.2 2.07E-04 38.6 0.3 4.13E-04 93400 5000 3.2% 3%

6.4 0.2 2.70E-04 50.6 0.5 5.40E-04 93800 4000 2.8% 3%

7.0 0.2 2.95E-04 55.9 0.5 5.90E-04 94700 4000 1.9% 2%

7.7 0.2 3.25E-04 53.6 0.3 6.49E-04 82600 3000 14.4% 3%

8.0 0.3 3.37E-04 73.1 1 6.75E-04 108000 6000 11.9% 6%

8.4 0.2 3.54E-04 65.6 0.6 7.08E-04 92600 3000 4.0% 3%

9.0 0.2 3.79E-04 72.1 0.6 7.59E-04 95000 3000 1.5% 2%

10.0 0.2 4.22E-04 75.3 0.5 8.43E-04 89304 2000 7.4% 2%

10.0 0.3 4.22E-04 89.1 2 8.43E-04 106000 6000 9.9% 6%

10.2 0.2 4.30E-04 76.2 0.6 8.60E-04 88600 2000 8.2% 2%

14.0 0.3 5.90E-04 126 3 1.18E-03 107000 5000 10.9% 5%

32.9 0.2 1.39E-03 258 1 2.77E-03 93000 1000 3.6% 1%

Below all of the points of Table 2 are displayed on a scatter plot of charge versus change in

volume. The gradient is used to calculate the average Faraday constant using the same

techniques as the example from the sample calculations above.


Graph 2: Scatter plot of all of the electrolysis trials with best fit, maximum, and minimum

*uncertainties vary, for actual values see Table 2

To find the average experimental value of the Faraday constant from the electrolysis trials,the gradient of Graph 2 which has units C/cm3 is converted to C/mol

Best Fit:y = 8.0017xR² = 0.989

Faraday Constanty = 8.1351x

Minimum:y = 7.8138xR² = 0.9919

Maximum:y = 8.1924xR² = 0.9846

0

50

100

150

200

250

0 10 20 30

Char

ge (C

oulo

mbs

)

Δ Volume H2 (cm3)

Charge v. Δ Volume

Electrolysis Trials - Best FitFaraday ConstantMinimumMaximum


= ℎ = 8.0017 ⁄The volume of one mole of gas under the experimental conditions was 23721 cm38.0017 × 23721 × 12 = 94903 /

Gradient (C/cm3) Faraday Constant (C/mol e-)Minimum 7.8138 92674Maximum 8.1924 97614

Uncertainty of Faraday constant:

= −2 = 97614 − 926742 = 2470∴ Faraday constant= 94900 ± 2000 C/mol (3 s.f.)


= − × 100%= 96485 − 9490096485 × 100% = 1.6 ± 0.2%


Experiment 2: Investigation of Faraday constant of water synthesis:

The same analysis and calculations were carried out for the 15 discharge data points.

Table 3: Hoffman synthesis results

Trial Name Change involume (cm3)

Uncertaintyof volume

Time (s)± 1

Charge(coulombs)

Uncertaintyof Charge

1 Hoffman 0 3.4 0.2 120 22.6 0.62 Hoffman 1 3.6 0.2 120 22.5 0.63 Hoffman 2 0.8 0.2 30 4.59 0.2

Graph 3: Volume vs. time graph for the Hoffman synthesis trials

25

30

35

40

45

0 20 40 60 80 100 120 140 160

Vol

ume

H2

(cm

3 ) (±

0.2)

Time (s) (±1)

Volume v. Time

Hoffman 0

Hoffman 1

Hoffman 2


Table 4: Water synthesis trials

Δ Vol

H2

(cm3)

Uncert.

Vol

Mol H2 Charge

(C)

Uncert.

Charge

Mol

electrons

e-

Faraday

Constant

(C/mol)

Uncert.

Faraday

Constant

%

error

Unc.

%

error

0.80 0.2 3.37E-05 4.92 0.1 6.75E-05 72900 20000 24.4% 21%

0.80 0.2 3.37E-05 4.59 0.2 6.75E-05 68000 20000 29.5% 21%

1.10 0.2 4.64E-05 6.03 0.2 9.27E-05 65000 10000 32.6% 10%

1.50 0.2 6.32E-05 9.53 0.2 1.26E-04 75400 10000 21.9% 10%

2.00 0.2 8.43E-05 12.0 0.3 1.69E-04 71200 9000 26.2% 9%

2.10 0.2 8.85E-05 14.0 0.4 1.77E-04 79100 10000 18.0% 10%

2.80 0.2 1.18E-04 18.4 0.5 2.36E-04 77900 8000 19.3% 8%

2.80 0.2 1.18E-04 17.8 0.5 2.36E-04 75400 8000 21.9% 8%

3.40 0.2 1.43E-04 22.6 0.6 2.87E-04 78800 7000 18.3% 7%

3.60 0.2 1.52E-04 22.5 0.6 3.04E-04 74100 6000 23.2% 6%

6.30 0.04 2.66E-04 36.4 1 5.31E-04 68500 2000 29.0% 2%

8.28 0.04 3.49E-04 56.5 2 6.98E-04 80900 3000 16.2% 3%

8.29 0.04 3.49E-04 54.4 2 6.99E-04 77900 3000 19.3% 3%

10.8 0.05 4.57E-04 77.5 2 9.14E-04 84800 3000 12.1% 3%

12.0 0.07 5.04E-04 74.3 2 1.01E-03 73700 2000 23.6% 2%


Graph 4: Scatter plot of all of the synthesis trials with best fit, maximum, and minimum

*uncertainties vary, for actual values see Table 4

Best Fit:y = 6.5554xR² = 0.9895

Faraday Constanty = 8.1351x

Minimum:y = 6.2747xR² = 0.9865

Maximum:y = 6.8352xR² = 0.9894

0

10

20

30

40

50

60

70

80

0 2 4 6 8 10 12

Char

ge (C

oulo

mbs

)

Δ Volume H2 (cm3)

Charge v. Δ Volume

Synthesis Trials - Best Fit

Faraday Constant

Minimum

Maximum


To find the average experimental value of the Faraday constant from the water synthesistrials, the gradient of Graph 4 which has units C/cm3 is converted to C/mol

= ℎ = 6.5554 ⁄The volume of one mole of gas under the experimental conditions was 23721 cm36.5554 × 23721 × 12 = 77749 /

Gradient (C/cm3) Faraday Constant (C/mol e-)Minimum 6.2747 74420Maximum 6.8352 81068

Uncertainty of Faraday constant:

= −2 = 81068 − 744202 = 3324∴ Faraday constant= 77700 ± 3000 C/mol (3 s.f.)


= − × 100%= 96485 − 7770096485 × 100% = 19.5 ± 0.3%

Result Evaluation

The Faraday constants found for both experiments are displayed below.

Table 5: Experimental Faraday constants with uncertainties and errors

Faradayconstant(C/mol e-)

Uncertainty Faradayconstant

Percent error UncertaintyPercent error

Electrolysis (forward) 94900 ± 2000 1.6 % ± 0.2%

Synthesis (reverse) 77700 ± 3000 19.5 % ± 0.3%

Faraday efficiency (ηFaraday) is the number of Faradays found experimentally over the

Faraday constant.


Finding the Faraday efficiency of the reverse reaction (ηReverse)11 over the Faraday efficiency

of the forward reaction (ηForward)12 gives the modified Faraday efficiency (η’Faraday)

During this study the Faraday constant found for the forward reaction was (within its

uncertainties) equal to the literature value. The modified Faraday efficiency is a substitute

for the Faraday efficiency of the water synthesis reaction which also takes into

consideration the forward Faraday efficiency and its uncertainties. It provides a comparison

that takes both reactions which occur in a reversible fuel cell into account.

= = ℎ 9648596485 = ℎModified Faraday efficiency calculation:

= ℎ = 77700 ± 3000 /94900 ± 2000 / 0.819 ± 0.05Percent modified Faraday efficiency:% = (0.819 ± 0.05) × 100% = 81.9 ± 5%


Conclusion:

Based on the results found, the answer to the research question: “does the Faraday

constant apply to fuel cell technology?” is that it does not apply within the experimental

uncertainties. The hypothesis was correct, and the modified Faraday efficiency (η’Faraday) was

found to be 0.819 ± 0.05. The Faraday constant for the electrolysis of water was found to be

94900 ± 2000 C/mol, The actual literature value is within this uncertainty, therefore the

Faraday constant is shown to apply to the electrolysis reaction. The Faraday constant for the

synthesis of water was found to be 77700 ± 3000 C/mol, which is outside the uncertainty of

the literature value.

Evaluation:

A percent modified Faraday efficiency of 81.9 ± 5% indicates that synthesis reaction is not as

efficient as the forward reaction. The main losses contributing to a reduction in the

efficiency of a fuel cell include:

1. Activation losses.

As stated in a previous section (Background theory) the reaction taking place requires that

the catalyst use provides an alternative path way of lower activation energy to initiate the

reaction. The fuel cell used in this study utilises a Pt catalyst. Although this is an excellent

catalyst it is still limited by the speed at which the reactions can take place. The reduction of

oxygen at the cathode is about 100 times slower than that of the hydrogen reaction at the

anode, and as a consequence the cathode reaction limits power density.

2. Fuel crossover and internal currents.

Fuel crossover and internal currents are a result of fuel that crosses directly through the

electrolyte, from the anode to the cathode without releasing electrons through the external

circuit, thereby decreasing the efficiency of the fuel cell.

3. Ohmic losses.

Ohmic losses are a result of the combined resistances of the various components of the fuel

cell. This includes the resistance of the electrode materials, the resistance of the electrolyte

membrane and the resistance of the various interconnections.


4. Mass transport or concentration losses.

These losses result from the reduction of the concentration of hydrogen and oxygen gases

at the electrode. For example, following the reaction new gases must be made immediately

available at the catalyst sites. With the build up of water at the cathode, particularly at high

currents, catalyst sites can become clogged, restricting oxygen access.

Random error:

Initially the volume was measured using the cylinders that came with the fuel cell kit. These

cylinders were found to give volume measurements with great random error. The

displacement of water by inner cylinders made the gradations unrepresentative of the true

volumes.

Systematic error:

The Renewable Energy Monitor program posed a challenge for data collection. Other than

the lack of an export feature for the data points, the program also occasionally suffered an

error which caused the recorded points to be lost. Certain trials were lost completely and

some partially.

Limitations:

In order to establish the extent of hydrogen diffusion across the membrane of a PEM cell, it

is necessary to conduct further experiments. The efficiency quoted was evaluated for only

one demonstration PEM reversible hydrogen fuel cell. In order to establish efficiency

applicable to hydrogen PEM cells further experiments are necessary. In future

investigations, other fuel cell technologies (e.g. ethanol) should be considered as well.

Word Count: 3977


Bibliography

1 "The Nobel Peace Prize 2007 - Press Release". Nobelprize.org. 28 Feb 2011http://nobelprize.org/nobel_prizes/peace/laureates/2007/press.html

2 Action confirmed on 6 December 1988 by the United Nations General Assembly throughResolution 43/53.

3 The Royal Society - A guide to facts and fictions about climate change March 2005http://royalsociety.org/uploadedFiles/Royal_Society_Content/News_and_Issues/Science_Issues/Climate_change/climate_facts_and_fictions.pdf

4 Prospects for hydrogen and fuel cells. International Energy Agency, OECD, Paris:

5 Maron, Samuel H., Jerome B. Lando, and Carl F. Prutton. Fundamentals of PhysicalChemistry. New York: Macmillan, 1974. Print, p.491

6 Freemantle, Michael. Chemistry in Action. London: Macmillan, 1995. Print, p.302

7 Cross section of a membrane electrode assembly (MEA) of a PEM fuel cell Source:Heliocentris 1999http://www.aep.com/environmental/education/solar/powerPie/fuelCells/fig3.htm

8 IUPAC Compendium of Chemical Terminology 2nd Edition (1997) CODATA Bull., 1986, 63,1; 1996, 68, 973 http://old.iupac.org/goldbook/F02325.pdf

9 http://www.blueleafsoftware.com/Products/Dagra/

10 http://www.horizonfuelcell.com/store/software.htm

11 Experiments with fuel cells – Experiment #3 –Fuel cell Efficiencies – A REEL Power(TM)experiment http://www.learnonline.com/pdf/Parallax%20Fuel%20Cell%20-%20Fuel%20Cell%20Efficiencies.pdf

12 http://nobel.scas.bcit.ca/chem3310/Fuel%20Cell%20experiment.pdf

investigating the faraday constant of the electrolysis and synthesis of water in a reversible...

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