In the Classroom
Calculation of the Characteristic Performance Indicators in an Electrochemical Process
W
C. M. Sánchez-Sánchez, E. Expósito, J. Solla-Gullón, V. García-García, V. Montiel,* and A. Aldaz Departamento de Química Física, Universidad de Alicante, Ap. 99, 03080 Alicante, Spain; *
[email protected] Electrochemical engineering, a relatively young discipline, has some important interrelationships with chemical engineering (1–3) and electrochemistry (4–7). The main objectives of electrochemical engineering are the characterization and the optimization, both in design and operation mode, of the mechanisms and the processes related to the conversion of chemical and electrical energies. The electrochemical reactor constitutes the nucleus of any electrochemical process (8, 9), which can be defined as any mechanism where chemical reactions are generated at the expense of electrical energy or where electrical energy is produced from chemical reactions. As a discipline, electrochemical engineering has had a relatively slow development because of its traditional minor importance in the study of chemistry and chemical engineering. Fortunately, these deficiencies have been overcome and electrochemical engineering currently is developing rapidly in a large variety of fields. Among the examples of electrochemical synthesis implemented at an industrial scale are the synthesis of chlor–alkali, aluminium, and adiponitrile (an intermediate compound in the manufacture of Nylon; ref 10).
Other important processes include systems of electric energy generation (batteries and fuel cells) and sewage treatment (11– 13). Electrochemical engineering (14, 15), as it mainly addresses the development and optimization of industry-based processes, is essentially an applied discipline. Figures of Merit Generally, figures of merit are numerical quantities used to describe particular aspects of an instrument, technique, or approach. Here the definition of figures of merit focuses on the electrochemical process and is related to its yield. This concept constitutes a very useful tool to optimize the cost and the economic balance of this process (16). The most widely used figures of merit on the characterization of the electrochemical processes are summarized in Table 1 and discussed below.
Fractional Conversion of Reactant ( XA) This parameter is defined as the fraction of reactant consumed during the electrochemical process. For example, if a
Table 1. Summar y Involving the Figures of Merit Figures of Merit
Defining Equations
Fractional conversion of reactant (XA, dimensionless)
XA = 1 −
Yield (θP, dimensionless)
θP =
Current efficiency (φP, dimensionless)
φP
nA nAo
nP nAo
− nA
νA νP
m P νe F MP νP = Q 2680 Ecell avg
νe νP
Energy consumption (ECP, kW h kg᎑1)
kW h ECP = kg
Area time yield (PP, kg m᎑2 day᎑1)
kg νP PP 2 9.0 × 10-6 = φP (%) MP j ν m day e
Cell voltage (Ecell, V)
eq eq Ecell = Ecat − Ean − ηan − ηcat − I Rcell
φ P (% ) M P
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reactant, A, undergoes a electrochemical reaction to generate a product, P, νA A + νe e⫺
(1)
νP P
the fractional conversion of reactant is defined as
XA = 1 −
nA
(2)
nAo
where nA0 and nA are the initial and the final number of moles of reactant A, respectively. In the reactions where there is more than one initial reactant, the fractional conversion of each reactant can be defined in a similar manner.
Yield (θ P) The yield is defined as the ratio between the number of moles of product formed, nP, and the number of moles of reactant consumed, taking into account the stoichiometric coefficients in eq 1: moles of P formed νA moles of A consumed νP
θP =
θP =
nP nAo − nA
νA νP
charge used to form P total circulated charge
φP
530
φP MP
i +1
(9)
where i refers to the number of Ecell measurements until the moment when it is intended to evaluate the average cell potential, Ecellavg.
(4)
(5)
(6)
νe νP
o Ecell (i) + Ecell (i − 1) + … + Ecell
Ecell avg =
kg νP -6 PP 2 = φP (%) MP j ν 9.0 × 10 m day e
Energy Consumption (ECP, J kg᎑1) This parameter is defined as the energy required to obtain a specified quantity of product, normally expressed in mass. Although in the SI this parameter is given in units of J kg᎑1, in practice it is usually expressed in units of kW h kg᎑1, Ecell F
(8)
φ P (% ) M P
(3)
where F is Faraday’s constant (96487 C mol᎑1), mP is the mass of P generated in grams, Mp is the molar mass of P in grams mol᎑1 and Q is the circulated charge in coulombs. A value of φP lower than unity (or 100% when it is expressed as a percentage) may show the generation of by-products different from P, either the solvent electrolysis or that of the supporting electrolyte; for example, the formation of H2 by reducing H+ during metallic electrodeposition processes, or the O2 evolution starting from water during the Cl2 synthesis. In these two examples, a φP value lower than unity does not involve a θP value lower than one.
J W EC P = = mP g
νe νP
where Ecell is the cell voltage and Ecellavg is the averaged cell voltage, both measured in volts,
(7)
(10)
where j is the applied current density in A m᎑2.
Cell voltage ( Ecell) Another basic parameter in electrochemistry is the cell voltage. This complex parameter is formed by a combination of terms. Ecell = Ecat − Ean − I Rcell
(11)
eq eq Ecell = Ecat − Ean − ηan − ηcat − I Rcell
(12)
According to Faraday’s law, the current efficiency can be defined as m P νe F MP νP = Q
2680 Ecell avg
Area Time Yield ( PP, kg m᎑2 day᎑1) The product amount is defined at a specific current density and expressed in kg per unit time (days) and electrode area (m2). It is necessary to note that the time spent in other processes different from the electrochemical process is excluded from this figure of merit calculation
Current Efficiency (φ P) This parameter is defined as the ratio between the charge used to form the product and the total circulated charge (17): φP =
kW h ECP = kg
eq eq where ηcat, ηan, and Ecat , Ean constitute the cathodic (less than 0) and anodic (greater than 0) overpotentials and the equilibrium potentials of both cathode and anode reactions, respectively, all measured in volts. The current, I, circulating in the system is in units of amperes, and Rcell is the electrolytic cell resistance in ohms.
Example: Electrosynthesis of L-cysteine The different figures of merit are applied to an example of organic electrosynthesis, the L-cysteine (RSH) synthesis by electroreduction of L-cystine (RSSR) in acid media (18–20). The reaction scheme is O
H
O
O
H2N
HO
H2N 2eⴚ
OH NH2 S
H 2H
S
ⴙ
2
OH H HS
This synthesis is carried out as a laboratory experiment during the final years of the chemical engineering program. It is important to emphasize that data regarding this problem are
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In the Classroom
real. Using experimental data to calculate the figures of merit allows the students to use parameters and quantities affected by experimental error. A schematic representation of the experimental setup is shown in Figure 1 and the reactions taking place in the electrochemical reactor are shown in Figure 2. The electrochemical reactor employed in the experiments was a filter press
8
reactor with a geometric area of 20 cm2. The cathode was a Pb sheet. Metakem supplied the DSA-O2 anode. The separator was a perfluorinated cationic membrane, Nafion 450, from DuPont. The reagents, H2SO4 and L-cystine (99%), were obtained from Panreac PRS and from Diamalt, respectively. The solution temperature was 30 ⬚C. The catholyte is, at first, an aqueous solution of 385 mL of 0.470 M RSSR and 1 M H2SO4. During the electrolysis, 1-mL samples are taken from the catholyte tank for different percentages of circulated charge. These are analyzed spectrophotometrically in order to determine the RSH and RSSR concentration in the catholyte (Table 2). At the same time that catholyte samples are taken, the hydrogen volume collected is recorded and the cell voltage is measured. At the beginning of the experiment, the Ecell value was 4.21 V.
5
Hazards
1
7
6
6
4
3
Sulfuric acid is corrosive. It can cause severe irritation and corrosive damage if inhaled. It can also cause severe topical irritation and burns, which may result in permanent scarring. Extensive acid burns can result in death. Severity of injury depends on the concentration of the sulfuric acid solution and the duration of exposure. L-Cystine eye or skin contact may cause transient eye or skin irritation. Protective eyewear and clothing should be worn.
2
4
3
Figure 1. Schematic diagram of the experimental assembly: (1) catholyte reservoir, (2) anolyte reservoir, (3) heat exchanger, (4) magnetic pump, (5) electrochemical reactor, (6) flowmeter, (7) hydrogen volume measurement system, and (8) power supply.
Calculations If the cathode area is 20 cm2 and the current flow of the reactor is 2.0 A during the electrolysis, calculate, 1. RSSR fractional conversion of reactant (XRSSR) 2. RSH yield (θRSH)
ⴙ
ⴚ
3. Current efficiency for H2 and RSH (φH2 and φRSH)
2H + 2e
4. Energy consumption to synthesize RSH (ECRSH) 2 H2O
5. Area time yield of RSH (PRSH)
H2
ⴙ
for every value of circulated charge found in Table 2. The value of noRSSR and the necessary theoretical charge to reduce the reactants can be calculated and then it is possible to calculate the percentages of circulated charge for every sampling
H
O2 + 4 Hⴙ + 4 eⴚ
RSSR + 2 Hⴙ + 2 eⴚ
mol n oRSSR = (0.385L ) 0.470 = 0.181mol RSSR L
2 RSH
cation exchange membrane
anode
cathode
Figure 2. Charge transfer processes inside the electrochemical reactor.
Table 2. Ecell, H2 Volume, RSSR and RSH Concentrations at Different Values of Circulated Charge
Q /C
Ecell (i) /V
H2 Volume /mL
cRSSR /M
cRSH /M
8500
4.30
8.00 x101
0.36
0.23
17000
4.39
2.00 x102
0.26
0.43
25100
4.42
2
4.00 x10
0.18
0.58
34000
4.52
8.06 x102
0.12
0.73
Q t = n oRSSR
νe F νRSSR
C = (0.181 mol )(2) 96487 = 34900 C mol Thus, it is possible to know the percentage of theoretical circulated charge for the data in Table 2.
RSSR Fractional Conversion of Reactant ( XRSSR) The expression for XRSSR is as follows:
X RSSR = 1 −
n RSSR noRSSR
(13)
NOTE: The H2 volume is measured at 1atm and 25 ºC.
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Using the concentration of RSSR, cRSSR, and the previous expressions, the XRSSR value can be calculated at the different percentages of theoretical circulated charge as shown in Table 3.
RSH Yield (θRSH) The expression to calculate the product of interest yield, θRSH, is as follows, θRSH =
νRSSR νRSH
n RSH noRSSR − n RSSR
where is 181 mmoles, νRSSR is 1, and νRSH is 2. By substituting nRSSR and nRSH values at different Q t percentages, the θRSH results are calculated and shown in Table 4.
Current Efficiency for H2 and RSH (φ H2 and φRSH) The expressions that calculate φH2 and φRSH for every value of the circulated charge are
φH2 =
Q νH2
n ν F = RSH e Q νRSH
and φ RSH
(15)
The values of nRSH are shown in Table 4. The calculation of nH2 is carried out from the H2 volume and from the equation,
P VH2 = n H2 R T
Q /C
Qt (%)
cRSSR /M
8500
24
0.36
140
0.23
17000
49
0.26
100
0.45
25100
72
0.18
69
0.62
34000
97
0.12
46
0.75
(14)
noRSSR
nH2 νe F
Table 3. Calculation of the XRSSR Fractional Conversion of Reactant
(16)
where P is the gas pressure (1 atm in this case), VH2 the volume of H2 collected in liters, R is the ideal gas constant (0.082 atm L mol᎑1 K᎑1) and T the temperature (298 K in this example). The current efficiency values are shown in Table 5.
nRSSR /mmol
XRSSR
Table 4. Calculation of θRSH Yield Qt (%)
nRSSR /mmol
nRSH /mmol
θRSH
24
140
89
1.1
49
100
170
1.0
72
69
220
0.98
97
46
280
1.0
Table 5. Calculation of Current Efficiency in H2 and RSH φH2 (%) φRSH (%) nRSH H2 volume nH2 Qt (%) /mmol /mmol /mL 24
8.00 x101 2
3.3 8.2
89
7.5
170
100
49
2.00 x10
72
4.00 x102
16
220
12
9.3
85
96
97
8.06 x102
33
280
19
79
Table 6. Calculation of the Energy Consumption ECRSH φRSH (%) Qt (%) Ecell (i) Ecellave ECRSH /V /V /kW h kg᎑1
Energy Consumption To Synthesize RSH (ECRSH)
24
100
4.30
4.25
0.94
If the relevant data for the example are replaced in eq 7, the energy consumption may is defined as follows
49
96
4.39
4.30
0.99
72
85
4.42
4.34
1.1
97
79
4.52
4.38
1.2
EC RSH =
Ecell F
νe
νRSH φRSH MRSH
(17)
where MRSH is 121 g mol᎑1. Equation 17 provides the energy consumption in units of J g᎑1; to obtain the energy consumption in kW h kg᎑1, which are the most common units
2680 Ecell
νe
kW h νRSH = EC RSH φ RSH (%) MRSH kg
(18)
When calculating ECRSH, it is necessary to consider that the Ecell value constitutes a time function. Since sufficient data to obtain the Ecell(t) function are not available, the mean voltage for each percentage of circulated charge will be used as the mean value among the Ecell values already measured,
Table 7. Calculation of the RSH Area Time Yield, PRSH Qt (%)
φRSH (%)
PRSH /kg m᎑2 day᎑1
24
100
110
49
96
100
72
85
93
97
79
86
6 shows the results obtained for ECRSH.
RSH Area Time Yield ( PRSH) The last parameter to be calculated is the area time yield, which is defined as
(19)
kg νRSH -6 PRSH 2 = φRSH (%) MRSH j ν 9.0 × 10 (20) m day e
which is acceptable, since the Ecell variation during the experiment is not very sharp. Considering this last point, Table
where j is defined in units of A m᎑2 and φRSH as a percentage. Table 7 shows the results obtained for PRSH.
Ecell avg =
532
o Ecell (i) + Ecell (i − 1) + … + Ecell
i +1
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In the Classroom
Discussion The results obtained for the different figures of merit for the cysteine example are interpreted as follows: The XRSSR fractional conversion of reactant increases during the experiment. This result is expected since the more charge circulating in the system, the larger amount of RSSR is reduced. The values of θRSH were slightly different from 1. The electrochemical rupture of the L-cystine disulfide bond is a totally selective reaction in these experimental conditions, thus θRSH should be equal to 1. These unexpected values could be the result of the analytic method of RSH determination (21), which shows an uncertainty range of ±3%. The value of φRSH decreases from an initial value of 100% to 79%. On the contrary, φH2 increases from 7.5% to 19%. This result can be explained as a result of the decrease of RSSR concentration during the synthesis. This gives rise to a decrease in the current yield of the cysteine reaction and to a yield increase of the parallel hydrogen evolution reaction. The charge balance is closed, since the addition of both yields (φRSH and φH2) gives a value close to 100% for all percentages of circulated charge. The energy consumption, ECRSH, increases during the experiment because of two factors: an increase in Ecell and a decrease in the φRSH value. The area time yield, PRSH, decreases during the experiment. Again, this behavior is due to a decrease in φRSH during the synthesis, since a lower percentage of the circulated charge is used to synthesize the product. In addition, because the current is constant, more time will be needed to synthesize the same quantity of product. WSupplemental
Material
Derivations of the general equations to calculate some characteristic performance indicators in an electrochemical process are available in this issue of JCE Online. Literature Cited 1. Peppas, N. A. One Hundred Years of Chemical Engineering: From Lewis M. Norton to Present; Kluwer Ac. Pub.: London, 1989.
2. The Chemical Industry, 2nd ed.; Heaton, A., Ed.; Blackie: Glasgow, 1994. 3. An Introduction to Industrial Chemistry, 3rd ed.; Heaton, A., Ed.; Blackie: Glasgow, 1996. 4. Walsh, F. C. A First Course in Electrochemical Engineering; The Electrochemical Consultancy: Ramsey, England, 1993. 5. De Levie, R. In Advances in Electrochemistry and Electrochemical Engineering; Delahay, P., Ed.; J. Wiley & Sons: New York, 1967; Vol. 6, pp 329–397. 6. Newman, J. S; Tiedeman, W. In Advances in Electrochemistry and Electrochemical Engineering; Gerischer, H., Ed.; J. Wiley & Sons: New York, 1978; Vol. 11, pp 353–438. 7. Advances in Electrochemical Science and Engineering; Alkire, R. C., Kolb, D. M., Eds.; Wiley–VCH: Weinheim, Germany, 1999; Vol. 6. 8. Marchiano, S. L.; Arvia, A. J. In Electrochemical Reactors. Their Science and Technology. Part A; Ismail, M. I., Ed.; Elsevier: New York, 1989; pp 145–188. 9. Walsh, F. C.; Robinson, D. Interface 1998, 7, 40–45. 10. Wagenknecht, J. H. J. Chem. Educ. 1983, 60, 271–273. 11. Pletcher, D.; Walsh, F. C. Industrial Electrochemistry, 2nd ed.; Chapman and Hall: London, 1990. 12. Industrial Electrochemical Processes; Kuhn, A. T., Ed.; Elsevier: New York, 1971. 13. Electrochemistry for a Cleaner Environment; Weinberg, N. L., Genders, J. D., Eds.; Electrosynthesis Company: East Amherst, New York, 1992. 14. Alkire, R. C. J. Chem. Educ. 1983, 60, 274–276. 15. Electrochemical Engineering: Science and Technology in Chemical and Other Industries; Wendt, H., Kreysa, G., Eds.; Springer: Berlin, 1999. 16. Kreysa, G. J. App. Electrochem. 1985, 15, 175–179. 17. Bricker, C. E. J. Chem. Educ. 1989, 66, 954–955. 18. Sánchez-Cano, G.; Montiel, V.; Aldaz, A. Tetrahedron 1991, 47, 877–886. 19. Expósito, E.; González-García, J.; García-García, V.; Montiel, V.; Aldaz, A. J. Electrochem. Soc. 2001, 148, D24–D28. 20. Ralph, T. R.; Hitchman, M. L.; Millington, J. P.; Walsh, F. C. J. Electroanal. Chem. 1994, 375, 17–27. 21. Ralph, T. R.; Hitchman, M. L.; Millington, J. P.; Walsh, F. C. J. Electroanal. Chem. 1999, 462, 97–110.
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