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INTERNATIONAL JOURNAL OF ENERGY RESEARCHInt. J. Energy Res. 2010; 34:557–567Published online 27 July 2009 in Wiley InterScience(www.interscience.wiley.com). DOI: 10.1002/er.1563
Hydrogen production from sodium borohydride for fuel cellsin presence of electrical field
Omer Sahin1,�,y, Hacer Dolas2, Mustafa Kaya1, Mehmet Sait Izgi1 and Halil Demir1
1Department of Chemical Engineering, Engineering Faculty, Siirt University, Siirt, Turkey2Department of Chemistry, Faculty of Art and Science, Istanbul Technical University, Istanbul, Turkey
SUMMARY
Sodium borohydride (NaBH4) reacts with water to produce 4mol of hydrogen per mol of compound at roomtemperature. Under certain conditions, it was found that 6mol of hydrogen per mol of sodium borohydride was producedin the presence of electrical field created by DC voltages, whereas 4mol of hydrogen was produced in the presence ofcatalyst per mole of sodium borohydride. Electrical field created by alternative current with three different waves (sin,square and triangle type) increases the hydrolysis of sodium borohydride. It was found that hydrogen produced fromsodium borohydride by applying an electrical field can be effectively used for both increasing the electrolysis of water andhydrolysis of sodium borohydride. The hydrolysis reaction was carried out at temperature of 20, 30, 40 and 601C in thepresence of electrical field created by AC voltages square wave. The experimental data were fitted to the kinetic models ofzero-order, first-order and nth-order. The results indicate that the first-order and nth-order model give a reasonabledescription of the hydrogen generation rate at the temperature higher than 301C. Reaction rate constant at differenttemperatures were determined from experimental data, and activation energy was found to be 50.20 and 52.28 kJmol�1
for first-order and nth-order, respectively. Copyright r 2009 John Wiley & Sons, Ltd.
KEY WORDS: sodium borohydride; hydrolysis; hydrogen generation; electrical field; fuel cells; hydrogen storage
1. INTRODUCTION
The world is under threatened environmentalproblems such as acid rain, ozone depletion andclimate changes arise from the presence of CO2, SOx
and NOx in emission gases because of consumptionof fossil fuels containing high amount of carbon/sulphur contents. Most of these problems can bealleviated by using clean and renewable energysources. For this purpose, hydrogen is used as a newenergy source due to concerns about global heating
and the depletion of fossil fuel. Hydrogen fuel cellsare used effectively to produce electrical energy byusing the reaction between hydrogen and oxygen [1].
Proton exchange membrane (PEM) fuel cells areattractive alternative power sources to produce cleanenergy for transportation and personal electronicapplications where low system weight and port-ability are important. For powering these systems,H2 gas is the environmentally desirable anodic fuelsince only water is formed as a reaction product.Pure hydrogen is adopted as the fuel in PEM fuel
*Correspondence to: Omer Sahin, Department of Chemical Engineering, Engineering Faculty, Siirt University, Siirt, Turkey.yE-mail: [email protected], [email protected]
Received 23 December 2008
Revised 7 April 2009
Accepted 14 April 2009Copyright r 2009 John Wiley & Sons, Ltd.
cell (PEMFC). However, currently used hydrogenis mostly produced from natural gas via catalyticreforming [2], which produces a mixture of H2, H2O,N2, CO2 and CO [3]. The performance of PEMFC issensitive to the concentration of carbon monoxide inhydrogen [4–8]. The PEMFC requires hydrogen in apure form due to the presence of carbon monoxidethat poisons the fuel cell catalyst.
As a new fuelling concept, it is accepted thatthe chemical hydrates (NaBH4, KBH4 and NaOH)can be considered as new energy sources supplyinghydrogen at low temperature [9]. In these hydrides,sodium borohydride (NaBH4) is desirable due to itshigh hydrogen content of 10.6wt% and the excellentstability of its alkaline solutions [10]. When sodiumhydroxide is added to aqueous NaBH4 solution athigher pH values (pH410), it can be stored stable atroom temperature monthly. Only when selectedcatalysts are added, it can release hydrogen rapidlyaccording to following equation [11]:
NaBH4 þ 2H2O! NaBO2 þ 4H2
DH ¼ �217kJmol�1
It is an exothermic reaction and can even beinitiated at 01C. The product of sodium metabo-rate (NaBO2) can be removed and it is harmfulto the environment, and it can be recycled asraw material for producing NaBH4. In practice,hydrogen is produced on demand by feedingNaBH4 solution over a supported solid-phasecatalyst in a packed-bed reactor.
A hydrolysis reaction takes place only when analkaline NaBH4 solution is in contact with certaincatalysts. Different catalysts, such as ruthenium (Ru)[1–18], platinum (Pt) [18,19], palladium (Pd) [20],nickel (Ni) [21,22], cobalt (Co) [21,23,24], Co–B[25,26], Ni–B [27], Ni–Co–B [28], carbon nanotubes(CNT) [29], have been extensively studied.
The aim of this study is to investigate the hydro-lytic behavior of sodium borohydride solution inthe presence of electrical field without catalyst andto determine an appropriate kinetic model ofNaBH4 hydrolysis reaction in a batch reactor basedon experiments in the presence of electrical fieldcreated by AC voltages. Therefore, in this studyhydrogen production from sodium borohydridesolution by hydrolysis was investigated under two
main groups both of them having different features.These are the self-hydrolysis of sodium boro-hydride depending on temperature and electricalfield created by DC and AC voltages.
2. EXPERIMENTAL
Sodium borohydride (molecular weight:37.83 gmol�1, assay 98%, Aldrich Chemical Co.)was used for the reaction with water. The solubilityof NaBH4 in water at 251C is 55g/100 g water, butthe solubility of sodium metaborate is 28 g/100 gwater. Sodium borohydride is a white crystallinepowder stable in vacuum up to 4001C and itadsorbs water from air to form hydride thatdecomposes slowly to form hydrogen and sodiummetaborate.
By using a thermostatic circulator, the watertemperature in the bath was kept constant with asensitivity of 70.11C and the solution temperaturewas kept constant with a temperature sensitivityof 70.21C.
In this study, the hydrolysis of sodium boro-hydride was investigated depending on tempera-ture and electrical field created by AC and DCvoltages. An electrolysis cell with two different gasoutlets was used in the experiments as shown inFigure 1.
In the case of electrical field created by applyinga certain amount of voltages (1.5–16 DC V) bet-ween two parallel platinum plates by DC voltages,the anode and cathode gases (O2 and H2) producedby the hydrolysis of sodium borohydride and elec-trolysis of water were collected in different grad-uated cylinders by using line 1 and 2 on Figure 1,separately.
In the condition of electrical field created by ACvoltages and self-hydrolysis of sodium boro-hydride at different temperatures, line 2 on Figure 1was closed and the volume of generated hydrogenwas measured as a function of time by passingit through a condenser by using line 1. The distancebetween two parallel platinum plates used inFigure 1 was 20mm. The hydrolysis of NaBH4 inaqueous solution was studied at the temperatureranges of 30–901C in a water bath with a tempera-ture sensitivity of 0.11C. At different temperature
O. SAHIN ET AL.558
Copyright r 2009 John Wiley & Sons, Ltd. Int. J. Energy Res. 2010; 34:557–567
DOI: 10.1002/er
experiments, humidified hydrogen was cooled downto room temperature through a heat exchanger tocondense water vapor in hydrogen steam. In thecase of electrical field created by AC voltages, awaveform generator (GFG-8016G) was used.
3. RESULTS AND DISCUSSION
3.1. Effect of temperature on the hydrolysisof NaBH4
The self-hydrolysis of sodium borohydride solu-tion depends on the pH and temperature. Toinvestigate the effect of temperature on hydrolysisof NaBH4, four different temperatures wereapplied to 5ml of 30% NaBH4 solution by athermostat and the volume of generated hydrogenwas measured as a function of time using agraduated cylinder. The reactions were carriedout in a batch reactor at temperature of 30, 60, 70,80 and 901C during 150min. The obtained resultsare shown in Figure 2. According to Figure 2, the
accumulative volumetric hydrogen generation ratewith respect to temperature increases exponen-tially with increasing temperature.
3.2. Effect of electrical field created by DC voltage
To examine the production of H2 from NaBH4
aqueous solution, first, an electrical field wascreated by using 7.0 DC voltages between twoparallel platinum plates. Figure 3 shows thevolume of generated H2 and O2 in both anodeand cathode section by hydrolysis and electrolysisas a function of initial NaBH4 percentages. Asseen in Figure 3, the hydrogen generation incathode has lower values than anode. On the otherhand, the oxygen and hydrogen gases produced inboth anode and cathode change with initialNaBH4 concentration linearly. Second, the effectof electrical field created with different DCvoltages on the hydrolysis of NaBH4 solutionwas investigated separately. Figure 4 shows thevolume of generated hydrogen and oxygen gases in
Figure 1. The system used to study the effect of temperature and electrical field created by alternative current (AC) onthe hydrolysis of NaBH4 solution.
HYDROGEN PRODUCTION FROM SODIUM BOROHYDRIDE 559
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DOI: 10.1002/er
the presence of electrical field created by differentvoltages. As seen in Figure 4, the electrolysis ofwater and hydrolysis of sodium borohydrideincrease with increasing applied voltages betweenthe ranges of 1.5–16 DC voltages. To clarify thebehavior of electrolysis of water and hydrolysis ofNaBH4 shown in Figure 4, the following equationscan be proposed.
The electrolysis of water
Cathode : 4Hþ þ 4e� ! 2H2 ð1Þ
Anode : 4OH! O2 þ 2H2Oþ 4e� ð2Þ
In our previous study [30], the both hydrolysisof KBH4 and electrolysis of water were repre-sented by the following reactions:
Cathode: 4H2Oþ 4e� ! 2H2þ4OH� ð3Þ
Anode: 4OH� þ BH�4 ! O2 þ 4H2
þ 4e� þ BO�2 ðtotal anode reactionÞ ð4Þ
BH�4 þ 4H2O! O2 þ 6H2 þ BO�2
ðtotal electrolysis reactionÞ ð5Þ
0
500
1000
1500
2000
2500
20
Temperature (°C)
VH
2 (m
L)
30 40 50 60 70 80 90 100
Figure 2. The self-hydrolysis of 5ml of 30% NaBH4 at different temperatures (during 150min).
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
0
NaBH4%
Vga
s (m
l)
VanodeVcathode
5 10 15 20 25 30 35
Figure 3. The volume change of obtained gas at anode and cathode in the presence of electrical field (at the condition of7.0V, 301C, 5ml, during 60min).
O. SAHIN ET AL.560
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DOI: 10.1002/er
The electrolysis of water and hydrolysis ofNaBH4 can be represented by the same reactionmechanisms.
According to these reactions, the behavior ofelectrolysis and hydrolysis of NaBH4 solutionshown in Figure 4 can be explained. As shownin Figure 4, the collected gas in anode sectionincreases in a huge amount with increasing DCvoltages from 1.5 to 14V as the obtained gas isproduced with electrolysis of water and hydrolysisof sodium borohydride according to Equation (4).On the other hand, this increase was not observedin the cathode section because there was only theelectrolysis of water.
As a result, the excess of collected gas atanode section is produced from the hydrolysis ofsodium borohydride since electrical field intensityincreases the hydrolysis of sodium borohydride.
According to Equations (3) and (4),Vðgas from anodeÞ=Vðgas from cathodeÞ ratio is about 2.5.To confirm the suggested electrolysis and hydro-lysis reactions (Equations (3) and (4)), thehydrolysis of 10% NaBH4 aqueous solutionincluding 2% NaOH was carried out by applying3.5 voltages with platinum electrodes and theproduced gas both in anode and cathode wascollected separately. The obtained results indi-cate that the gas ratio anode/cathode approxi-mately takes the value of 2.5 as proposed fromEquations (3) and (4).
3.3. Effect of electrical field created by AC voltage
In this section, the effect of alternative current
(AC) voltage on the hydrolysis of NaBH4 solutionwithout electrolysis of water was investigated. Forthis purpose, triangle, square and sinusoidal waves
were separately used for 30% NaBH4 of 7mlsolution by applying 4.4V and 0.85A of current to
Pt electrodes at 301C. As can be seen in Figure 5,the collected gas volumes take the values of 910,190, 96ml for square, sinusoidal and triangle
waves, respectively. According to this result, themost effective wave type is square.
The results of hydrolysis of NaBH4 in the pre-
sence of electrical field created by AC voltage with
square wave as a function of time for different initial
NaBH4 percentages are shown in Figure 6. The
experiments were carried out without an alkali stabi-
lizer to clarify the hydrolysis of NaBH4 in electrical
field according to changes in NaBH4 concentration.
The rate of generated hydrogen increases with
increasing NaBH4 content in the solution.The other factor affecting the hydrolysis of
NaBH4 is temperature as shown in Figure 2. Thecombined effect of temperature and electrical field
created by AC voltage on the hydrolysis of NaBH4
is illustrated in Figure 7. In this figure, the accu-mulative hydrogen generation with respect to time
was also shown at temperatures of 20, 30, 40 and601C. According to Figure 7, by increasing the
0.0
0.5
1.0
1.5
2.0
2.5
0
Time (minute)
Obt
aine
d ga
s vo
lum
e at
ano
de (
L)
0
1
2
3
4
5
6
Obt
aine
d ga
s vo
lum
e at
cat
hode
(L
)
1.5 V (cathode)7.0 V (cathode)14.0 V (cathode)1.5 V (anode)7.0 V (anode)14.0 V (anode)
10 20 30 40 50 60 70
Figure 4. The volume change of gas at anode and cathode sections with time under electrical field created by differentvoltages (30% NaBH4 at 301C, without NaOH).
HYDROGEN PRODUCTION FROM SODIUM BOROHYDRIDE 561
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DOI: 10.1002/er
0
100
200
300
400
500
600
0
Time (minute)
Gas
vol
ume
(ml)
square
sinusoidal
triangle
20 40 60 80 100 120 140
Figure 5. The comparison effect of different AC wave types on 5ml of 30% NaBH4 solutions at 301C.
0
100
200
300
400
500
600
700
800
0
Time (minute)
Obt
aine
d ga
s vo
lum
e (L
)
10% NaBH4
20% NaBH4
30% NaBH4
50 100 150 200
Figure 6. The effect of electrical field created by AC voltage with square wave type on the hydrolysis of sodiumborohydride solutions including different percentages of NaBH4 (5ml of solutions, at 301C, V: 4.4V I: 0.805A).
0
500
1000
1500
2000
2500
0
Tme (minute)
Obt
aine
d ga
s vo
lum
e (m
L)
20 °C
30 °C
40 °C
60 °C
20 40 60 80 100 120 140
Figure 7. The effect of electrical field created by AC voltage with square wave type on the hydrolysis of sodiumborohydride solutions at different temperatures (5ml of 30% NaBH4 solution, V: 4.4V I: 0.805A).
O. SAHIN ET AL.562
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DOI: 10.1002/er
temperature in the presence of electrical field createdby AC voltage with square wave, the hydrolysis ofNaBH4 rapidly increases in comparison with purestate as shown in Figure 2. At temperature lowerthan 601C, the generated hydrogen volume increasesslowly for the first 20min of reaction becauseNaBO2 particles form with hydrolysis reaction.However, the non-zero-order feature is observedafter that time as the hydrogen volume changes withtime are not linear. On the other hand, at a tempera-ture of 601C, the hydrolysis of NaBH4 is differentfrom the hydrolysis at lower temperatures in thepresence of electrical field created by AC voltages.It is believed that NaBH4 hydrolysis reaction ishindered by NaBO2.
The kinetic of sodium borohydride hydrolysisreaction was investigated in the presence of differentcatalysts such as ruthenium (Ru) [13–18], platinum(Pt) [19,20], palladium (Pd) [20], nickel (Ni) [21,22],cobalt (Co) [21,23,24], Co–B [25,26], Ni–B [27],Ni–Co–B [28], carbon nanotubes (CNT) [29]. Theresult obtained in the presence of catalysts studiesshows that the kinetic models of the hydrolysis ofNaBH4 are mostly zero-order or first-order withexception of the work of Reference [18] and the acti-vation energy changes between 28 and 65kJmol�1.
One aim of this work is to determine an appro-priate kinetic model and the activation energy ofhydrolysis of sodium borohydride in the presence ofelectrical field created by AC voltage with squarewave. To analyze data given in Figure 7, the datamust be converted to reaction rate versus sodium
borohydride concentration or sodium borohydrideconcentration versus time for the hydrogen gene-ration as a function of time. The concentration ofNaBH4 as a function of time can be obtained fromthe equation of CNaBH4
5 nNaBH4/V.
In this study, the following three kineticsmodels were used to describe the behavior of thehydrolysis reaction of hydrogen generation byusing an integral method.
3.3.1. Zero-order. For a batch reactor with avolume V, the reaction rate per unit volume basedon zero-order kinetics can be described as
dCNaBH4
dt¼ �rNaBH4
¼ �kðTÞ ð6Þ
Integrating the differential Equation (6), weobtain
CNaBH4ðt¼0Þ � CNaBH4ðt¼tÞ ¼ kt ð7Þ
where CNaBH4ðt¼0Þ is the initial concentration ofsodium borohydride, CNaBH4ðt¼tÞ is the concentra-tion of sodium borohydride at any time, r is therate of reaction and k is the reaction rate constantbased on the solution volume.
A plot of CNaBH4ðt¼0Þ � CNaBH4ðt¼tÞ as a functionof time should give a straight line passing throughthe origin and the slope of line can be used tocalculate the zero-order rate constant (k).
Figure 8 shows the plot of CNaBH4ðt¼0Þ �CNaBH4ðt¼tÞ versus time for the temperatures of20, 30, 40 and 601C. Here, the maximum hydrogen
0
1
2
3
4
5
6
7
8
0
Time (minute)
20 °C
30 °C
40 °C60 °C
50 100 150 200 250
CN
aBH
4(t=
0) -
CN
aBH
4(t=
t)
Figure 8. Linear regressions based on zero-order by using the data of NaBH4 hydrolysis at different temperatures.
HYDROGEN PRODUCTION FROM SODIUM BOROHYDRIDE 563
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DOI: 10.1002/er
generation rate was observed from initial condi-tion to 100min. As can be seen in Figure 8, at alltemperatures where hydrolysis was performed,the zero-order reaction model does not fit thecurve very well since the plot of CNaBH4ðt¼0Þ�CNaBH4ðt¼tÞ versus time cannot be represented bylinear equation according to regression withcorrelation coefficients (R2). As a result, the hydro-lysis reaction of sodium borohydride in thepresence of electrical field does not obey thezero-order reaction model.
3.3.2. First-order. The reaction rate based on first-order kinetics can be described as
� rNaBH4¼ �
dCNaBH4
dt¼ kCNaBH4
ð8Þ
By integrating Equation (8), following equationis obtained
lnCNaBH4ðt¼0Þ
CNaBH4ðt¼tÞ
� �¼ kt ð9Þ
A plot of lnðCNaBH4ðt¼0Þ=CNaBH4ðt¼tÞÞ as a func-tion of time should give a straight line and theslope of line can be used to calculate the first-orderrate constant, k. Figure 9 shows that the plot oflnðCNaBH4ðt¼0Þ=CNaBH4ðt¼tÞÞ versus time at tempera-tures of 40 and 601C has a good linear regressionwith correlation coefficients of 0.9919 and 0.9929.The reason is that the higher temperature causeshigher reaction rate. High temperature signi-ficantly increases the effect of electrical field on thehydrolysis of sodium borohydride. Nevertheless,
the data given in Figure 9 do not obey the first-order reaction since the regression coefficients arenot linear at 20 and 301C.
3.3.3. nth-order reaction. For a batch reactor, thenth-order kinetics can be described as
� rNaBH4¼ �
dCNaBH4
dt¼ k � Cn
NaBH4ð10Þ
By separating and integrating Equation (10), weobtain
1
n� 1ðC1�n
NaBH4ðt¼0Þ � C1�nNaBH4ðt¼tÞÞ ¼ knt ðn#1Þ
ð11Þ
Therefore, a plot of 1=n� 1ðC1�nNaBH4ðt¼0Þ �
C1�nNaBH4ðt¼tÞÞ versus time should give a straight line
through the origin, and the slope of line can beused to calculate nth-order rate constant, kn.
In order to find Arrhenius constants (activationenergy, E, and pre-exponentional factor, A) forzero-order, first-order and nth-order reactionmodel, the plot of ln(k) versus 1/T for the tempera-tures of 20, 30, 40 and 601C was obtained and theresult is given in Figure 10. The activation energyand pre-exponential factor of zero-order, first-order and nth-order reaction models can beobtained from slope and intercept of the regres-sion line, being 40.37 kJmol�1, 7.241� 104;50.20 kJmol�1, 5.181� 105 and 52.78 kJmol�1,8.741� 105, respectively. The regression resultsindicate that the zero-order cannot describe thehydrogen generation rate at all temperatures, but
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
0
Time (minute)
ln(C
NaB
H4(
t=0/
CN
aBH
4(t=
t))
20 °C
30 °C40 °C60 °C
50 100 150 200 250
Figure 9. Linear regressions based on first-order by using the data of NaBH4 hydrolysis at different temperatures.
O. SAHIN ET AL.564
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DOI: 10.1002/er
the first-order can represent the hydrogen genera-tion rate from sodium borohydride over theexperiments during high temperatures of 40 and601C. On the other hand, the nth-order modelgives the best result according to linear regressionwith a correlation coefficient of 0.994. As can beseen in Figure 10, the obtained Arrhenius cons-tants for first-order model approach the constantof nth-order model values.
In addition, the hydrogen generation from thehydrolysis reaction of an alkaline NaBH4 solutioncan be used for PEM fuel cell application due to itshigh purity. The operation fuel cell temperaturenormally set at 601C was used to validate thekinetic models, which are zero-order, first-orderand nth-order. As can be seen from Figure 10, thefirst-order and nth-order give the best predictionat temperature higher than 301C.
Table I summarizes the following regressiondata for zero-order, first-order and nth-order at atemperatures range of 20–601C, the reaction rateconstants found by the slope of linear regressionand the correlation coefficients for regression.
4. CONCLUSION
In this study, the hydrolysis of sodium borohy-dride (NaBH4) was investigated depending ontemperature and intensity of electrical field createdby DC and AC voltages. The hydrolysis of sodiumborohydride with temperature increases exponen-tially. When an electrical field created by DCvoltages is applied to NaBH4 solution, the pro-duced hydrogen is two or more times higher thanin the electrolysis of water. The electrical field
ln(k)(zero-order) = -4856.01699/T + 11.19015
R2 = 0.96516
ln(k)(first-order) = -6038.5/T + 13.158
R2 = 0.983
ln(k)(nth-order) = -6348.162/T + 13.681R2 = 0.994
-9
-8
-7
-6
-5
-4
-3
-20.0029
1/T (K-1)
Ln
(k )
zero-order
first-order
nth-order
0.003 0.0031 0.0032 0.0033 0.0034 0.0035
Figure 10. The evaluation of rate equations of NaBH4 in zero-, first- and nth-orders under electrical field effectaccording to the Arrhenius equation.
Table I. Kinetic parameters of hydrolysis of sodium borohydride for different reaction models.
Zero-order First-order nth-order
T (1C) k (mol l�1 s�1) R2 k (s�1) R2 k ðl mol�1Þn�1 s�1 n R2
20 0.004195 0.9407 0.000555 0.9523 0.000335 1.25 0.55030 0.00773 0.883 0.001068 0.9114 0.000658 1.25 0.92240 0.01674 0.9643 0.002662 0.9920 0.001541 1.30 0.99460 0.0299 0.9643 0.006307 0.9923 0.004369 125 0.992
HYDROGEN PRODUCTION FROM SODIUM BOROHYDRIDE 565
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DOI: 10.1002/er
created by AC voltages having square, triangle andsinusoidal wave on hydrolysis of sodium boro-hydride solution without electrolysis shows thatthe effective wave type is a square wave. Hydro-lysis kinetics of NaBH4 were investigated in thepresence of electrical field created by AC voltageswith square wave at a temperature range of20–601C and zero-order, first-order and nth-orderkinetics were applied to the obtained data. Theactivation energy was found to be 50.20 and52.28 kJmol�1 for first-order and nth-order,respectively. Zero-order does not represent thehydrolysis kinetics of NaBH4 satisfactorily. It canbe concluded that the electrical field created by DCvoltages, which is not needed for catalytic activitysurface, may be used in the hydrolysis of sodiumborohydride.
NOMENCLATURE
PEM 5 proton exchange membranePEMFC 5 proton exchange membrane fuel
cellNaBH4 5 sodium borohydrideDH 5 enthalpy change (kJmol�1)DC 5 direct current (V)AC 5 alternative current (V)NaBO2 5 sodium metaborateC 5 concentration (mol l�1)n 5moleV 5 volume (L)r 5 rate of reaction ((mol L�1)min�1)k 5 reaction rate constantt 5 time (min)R2 5 correlation coefficientE 5 activation energy (kJmol�1)A 5 exponential constant
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