Chemical equilibrium constants for the formation of carbamates in (carbon dioxide + piperazine + water) from 1H-NMR-spectroscopy

Article abstract of DOI:10.1016/S0021-9614(03)00076-4

H-NMR spectroscopic investigations were performed on aqueous solutions of carbon dioxide and piperazine at temperatures ranging from 283 to 333K. These investigations were performed to determine quantitatively the speciation in these solutions. The results were used to determine the chemical equilibrium constants for the formation of piperazine carbamate, piperazine dicarbamate and protonated piperazine carbamate.

Full text of DOI:10.1016/S0021-9614(03)00076-4

J. Chem. Thermodynamics 35 (2003) 1277–1289
www.elsevier.com/locate/jct
Chemical equilibrium constants for the
formation of carbamates in
(carbon dioxide + piperazine + water) from
1H-NMR-spectroscopy
ꢀ
Viktor Ermatchkov, Alvaro Perez-Salado Kamps, Gerd Maurer
*
ꢀ
Lehrstuhl f€ur Technische Thermodynamik, Universit€at Kaiserslautern, Postfach 3049,
Kaiserslautern D-67653, Federal Republic of Germany
Received 7 November 2002; accepted 19 March 2003
Abstract
1H-NMR spectroscopic investigations were performed on aqueous solutions of carbon di-
oxide and piperazine at temperatures ranging from (283 to 333) K to determine quantitatively
the speciation. The experimental results were used to determine the chemical equilibrium con-
stants for the formation of piperazine carbamate, piperazine dicarbamate and protonated
piperazine carbamate.
Ó 2003 Elsevier Science Ltd. All rights reserved.
Keywords: Chemical reacting aqueous electrolyte solutions; Chemical equilibrium constants; Carbon
dioxide; Piperazine; Carbamate
1. Introduction
Aqueous solutions of N-methyldiethanolamine (MDEA) are widely used for the
sweetening of sour gases, particularlyfor the selective removal of carbon dioxide
and/or hydrogen sulfide from gaseous effluents (e.g., natural gases). In such solutions
the sour gases are partiallyconverted to ionic species while MDEA is protonated. As
the absorption of carbon dioxide is hindered byslow kinetics, it is possible to favor
* Corresponding author. Fax: +49-631-205-3835.
E-mail address: gmaurer@rhrk.uni-kl.de (G. Maurer).
0021-9614/$ - see front matter Ó 2003 Elsevier Science Ltd. All rights reserved.
doi:10.1016/S0021-9614(03)00076-4

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V. Ermatchkov et al. / J. Chem. Thermodynamics 35 (2003) 1277–1289
the absorption of hydrogen sulfide over that of carbon dioxide. Process modifica-
tions attempt to improve the selective absorption of hydrogen sulfide by adding
modifiers (usuallyprimaryor secondaryamines) to the aqueous MDEA solution.
Piperazine (PIPH2) is a commonlyused modifier.
The reliable design of such separation equipment requires equilibrium data as de-
viation from equilibrium provides the driving force in that kineticallycontrolled pro-
cess. Correlating and predicting the (vapor + liquid) equilibrium for the simultaneous
solubilityof CO 2 and H2S in aqueous solutions of MDEA and piperazine at first re-
quires reliable information on the solubilityof the single gases in water and in the
aqueous solutions of the single amines as well as information on the equilibrium con-
stants of the chemical reactions.
In previous work [1,2], the solubilityof the single gases carbon dioxide and hy-
drogen sulfide in aqueous MDEA solutions was investigated at temperatures
ranging from (313 to 413) K, for MDEA molalities up to 8 mol ꢀ kgꢁ1 of water,
and pressures up to about 8 MPa. New experimental results were recentlypre-
sented for the solubilityof hdyrogen sulfide in aqueous solutions of piperazine
at temperatures between (313 and 393) K, for piperazine molalities up to
4 mol ꢀ kgꢁ1 of water, and pressures up to about 9 MPa [3]. Furthermore, the
protonation of N-methyldiethanolamine in aqueous solution was investigated at
temperatures from (278 to 368) K [4].
Piperazine is protonated and diprotonated in aqueous solutions in the presence of
a sour gas. Furthermore, carbon dioxide and piperazine react in aqueous solutions to
form (three) carbamate species: piperazine carbamate, piperazine dicarbamate and
protonated piperazine carbamate. The chemical equilibrium constants for the pro-
tonation of piperazine are available in the literature [5], whereas onlyrough esti-
mates have been published recentlyfor the chemical equilibrium constants for the
formation of the three carbamates [6,7].
In the present work the chemical reaction equilibrium for the formation of the
1
three carbamate species is studied by H-NMR spectroscopy. The experimental re-
sults are evaluated to determine species concentrations which furthermore are used
to determine the chemical equilibrium constants for the formation of piperazine car-
bamate, piperazine dicarbamate and protonated piperazine carbamate. The NMR-
investigations were carried out at temperatures ranging from (283 to 333) K at various
overall concentrations of piperazine and carbon dioxide.
2. Experimental
1H-NMR spectroscopywas applied to investigate solutions of (carbon diox-
ide + piperazine + deuterium oxide) to determine quantitativelythe speciation. A
Bruker DPX 400 NMR spectrometer (proton resonance frequencyof 400.13
MHz) was used for the experiments. Measurements were performed at
T ¼ ð283; 298; 313; and 333Þ K for piperazine molalities ranging from ð0:1 to
1:5Þ mol ꢀ kgꢁ1 of water. The aqueous solutions (with fixed piperazine molality) were

V. Ermatchkov et al. / J. Chem. Thermodynamics 35 (2003) 1277–1289
1279
loaded with up to one mol of carbon dioxide per mol of piperazine. Altogether 121
experiments were performed.
The aqueous piperazine solutions were prepared in a storage tank bydissolving
known amounts of piperazine in pure deuterium oxide (D2O). The stoichiometric
molalityof piperazine was determined gravimetricallywith a relative uncertainty
ranging from about Æ0:01 per cent (for the higher piperazine molalities) up to about
Æ0:1 per cent (for the lower piperazine molalities). Carbon dioxide was volumetri-
callycharged to an aqueous piperazine solution bymeans of a high precision dis-
placement pump. The mass of carbon dioxide filled into the cell was calculated,
assuming it was an ideal gas, with the experimental temperature and pressure
(T ꢂ 293 K, p ꢂ 0:1 MPa). The stoichiometric molalityof carbon dioxide is known
with a relative uncertaintyof at maximum Æ0:3 per cent. The liquid solutions were
filled into NMR pyrex tubes which were evacuated before. The charged cells were
sealed bymeans of a glass blowing burner. The cells were thermostated in a water
bath for about 24 h before theywere immersed into the spectrometer, which was
kept at the same temperature. That temperature was controlled with an accuracy
of about Æ0:1 K.
Carbon dioxide (mole fraction P 0.99995) was purchased from Messer–Griesheim,
Ludwigshafen, Germany. It was used without further purification. Piperazine (anhy-
drous, mass fraction P 0.99, Fluka Feinchemikalien GmbH, Neu-Ulm, Germany)
and D2O (mole fraction P 0.999, Sigma–Aldrich, Deisenhofen, Germany) were
separatelydegassed under vacuum.
Figure 1 shows the molecular structure of the piperazine compounds present in
(carbon dioxide + piperazine + deuterium oxide). When piperazine is dissolved in
deuterium oxide, the protons (i.e., the hydrogen atoms) bound in the NH amine
groups are exchanged bydeuterium atoms, producing a single peak in the water re-
gion (d ꢂ 5 ppm, cf. Chamberlain [8] where d is the chemical shift). Figure 2 shows a
1
typical H-NMR spectrum of an aqueous solution of CO2 and piperazine taken in
the present work. All peaks in figure 2 result from protons bound in CH2 groups
in piperazine species. Peaks 1 and 4 are assigned to protons bound in CH2 groups
in piperazine carbamate (PIPDCOOꢁ) as well as in protonated piperazine carbamate
(PIPDþ2 COOꢁ), peak 2 is assigned to protons bound in CH2 groups in molecular pi-
perazine (PIPD2), protonated piperazine (PIPDþ3 ) and diprotonated piperazine
(PIPD24þ), and peak 3 is assigned to protons bound in CH2 groups in piperazine
dicarbamate (PIPðCOOꢁÞ ).
2
This assignment results from the assumption, that anyprotonation (bydeute-
rium) of a molecule does not affect the chemical NMR environment of the H-atoms
bound in those CH2 groups. In order to confirm that assumption, we performed
1
some H-NMR measurements on (deuterium chloride + piperazine + deuterium ox-
ide), for molar ratios of DCl to piperazine up to about two. Those solutions contain
piperazine in molecular, in protonated as well as in diprotonated form. But – as ex-
pected – always only one additional peak appeared at d ꢂ 2:8 ppm.
The peak areas (the intensities) are proportional to the number of corresponding
protons (i.e., protons with same NMR chemical environment) in the solution (cf.
e.g., Chamberlain [8]). Therefore, the following equation must hold:

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V. Ermatchkov et al. / J. Chem. Thermodynamics 35 (2003) 1277–1289
FIGURE 1. Molecular structure of piperazine species in (carbon dioxide + piperazine + deutrium oxide).
FIGURE 2. 1H-NMR spectrum of (carbon dioxide + piperazine + deuterium oxide) at T ¼ 298 K
’
ðnꢁPIPH ꢂ 1:5 mol, nꢁCO ꢂ 0:8 mol, mD ¼ 1 kgÞ.
2O
2
2

V. Ermatchkov et al. / J. Chem. Thermodynamics 35 (2003) 1277–1289
1281
X
Ai ¼ k
Ni;jnj;
ð1Þ
j
where Ai is the peak area corresponding to protons with environment i, Ni;j is the
number of protons with environment i in component j, nj the number of moles of
component j, and k is a proportionalityconstant, which is independent of the proton
with environment i. This constant has the same numerical value for all peak areas in
a given spectrum, but has different values in different spectra.
Applying equation (1) to our system leads to the following equations:
ꢁ
þ2 COOꢁ
A1 ¼ 4kðnPIPDCOO þ nPIPD
Þ;
ð2Þ
ð3Þ
ð4Þ
þ
A2 ¼ 8kðnPIPD þ nPIPD þ nPIPD2þ Þ;
2
3
4
ꢁÞ2
A3 ¼ 8knPIPðCOO
;
and
ꢁ
þ2 COOꢁ
A4 ¼ 4kðnPIPDCOO þ nPIPD
Þ:
ð5Þ
No calibration is necessaryin order to obtain the proportionalityconstant k. It
follows from the mass balance for piperazine, and byaddition of equations 2 to 5
and was determined for everysingle spectrum:
ðA1 þ A2 þ A3 þ A4Þ
PIPH2
k ¼
:
ð6Þ
8nꢁ
From equations 2 to 6, the mole numbers of piperazine species corresponding to the
peak areas can be calculated and listed into tables 1–4. The moles of piperazine
carbamate and protonated piperazine carbamate maybe calculated from the peak
areas A1 or A4. We calculated them from the sum of both areas:
ꢁ
þ2 COOꢁ
A1 þ A4 ¼ 8kðnPIPDCOO þ nPIPD
Þ:
ð7Þ
In order to estimate the experimental uncertainty, the mean relative deviation in
these sum of mole numbers, following whether from equations (2) or (5), or from
equation (7) were calculated. This uncertaintyamounts to about (2 Æ 1:9) per cent.
But, when an experiment was repeated several times, the difference in the calculated
mole numbers (or sum of mole numbers), corresponding to the different peak areas
(or sum of peak areas) was never higher than one per cent.
As an example, figure 3 shows the experimentallydetermined amount-of-sub-
stances of piperazine species plotted versus the stoichiometric mole number of car-
bon dioxide in an about one molal aqueous piperazine solution at T ¼ 298 K.
The experimentallydetermined species concentrations were used to determine
the equilibrium constants for the formation of piperazine carbamate, dicarbamate
and protonated carbamate. The evaluation procedure is explained in the following
chapter.

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V. Ermatchkov et al. / J. Chem. Thermodynamics 35 (2003) 1277–1289
TABLE 1
Speciation in (carbon dioxide + piperazine + water) from 1H-NMR measurements at T ¼ 283:15K and
’
mD ¼ 1kg where nꢁ and n are the stoichiometric and the true number of moles of species i, respectively
2O
P
nꢁPIPH
nꢁCO
i ni
2
2
(mol)
(mol)
(mol)
i ¼ PIPD2; PIPDþ; PIPD2þ i ¼ PIPDCOOꢁ; PIPDþ2 COOꢁ
i ¼ PIPðCOOꢁÞ
3
4
2
1.4489
1.4687
1.4687
1.4775
1.4489
1.4489
1.4489
1.4489
0.9998
0.9996
0.9996
0.9996
0.9998
0.9998
0.9998
0.4990
0.4630
0.4630
0.4990
0.4630
0.4990
0.5122
0.2858
0.2858
0.2858
0.2858
0.2160
0.2160
0.2160
0.2160
0.1033
0.1033
0.1033
1.3974
1.2260
0.9824
0.8166
0.6810
0.5087
0.3418
0.2845
0.9651
0.8179
0.7425
0.6455
0.4881
0.3386
0.2361
0.5040
0.3917
0.3149
0.2555
0.2076
0.1684
0.1077
0.2611
0.1888
0.1255
0.0590
0.1695
0.1225
0.0734
0.0352
0.0732
0.0498
0.0235
0.4119
0.4967
0.6858
0.8203
0.8973
0.9923
1.1303
1.1748
0.3107
0.3931
0.4478
0.5030
0.6164
0.7172
0.7894
0.1846
0.2016
0.2353
0.3145
0.3063
0.3684
0.4220
0.1349
0.1652
0.1986
0.2411
0.1191
0.1366
0.1633
0.1888
0.0684
0.0745
0.0890
0.9905
0.8734
0.6619
0.5628
0.4812
0.4198
0.3052
0.2658
0.6566
0.5425
0.4779
0.4243
0.3384
0.2616
0.1993
0.3064
0.2428
0.2026
0.1651
0.1430
0.1229
0.0871
0.1451
0.1079
0.0804
0.0431
0.0892
0.0711
0.0494
0.0264
0.0324
0.0272
0.0140
0.0465
0.0986
0.1211
0.0945
0.0704
0.0368
0.0133
0.0082
0.0325
0.0639
0.0739
0.0723
0.0450
0.0210
0.0111
0.0080
0.0186
0.0251
0.0193
0.0136
0.0077
0.0031
0.0058
0.0127
0.0069
0.0016
0.0077
0.0083
0.0032
0.0008
0.0025
0.0016
0.0003
3. Correlation
Due to chemical reactions, carbon dioxide is dissolved in an aqueous solution of
piperazine not onlyin neutral, but also in non-volatile, ionic form. The following
chemical reactions are considered: the autoprotolysis of water (reaction I), the pro-
tonation and diprotonation of piperazine (reactions II, III), the formation and
dissociation of bicarbonate (reactions IV, V), and the formations of piperazine car-
bamate, piperazine dicarbamate and protonated piperazine carbamate (reactions VI,
VII, and VIII):

V. Ermatchkov et al. / J. Chem. Thermodynamics 35 (2003) 1277–1289
1283
TABLE 2
Speciation in the’ (carbon dioxide + piperazine + water) system from 1H-NMR measurements at
T ¼ 298:15 K and mD ¼ 1 kg where nꢁ and n are the stoichiometric and the true number of moles of spe-
2O
cies i, respectively
P
nꢁPIPH
nꢁCO
i ni
2
2
(mol)
(mol)
(mol)
i ¼ PIPD2; PIPDþ3 ; PIPD42þ
i ¼ PIPDCOOꢁ; PIPD2þCOOꢁ i ¼ PIPðCOOꢁÞ
0.9393
2
1.4489
1.4687
1.4687
1.4775
1.4489
1.4489
1.4489
1.4489
0.9998
0.9996
0.9996
0.9996
0.9998
0.9998
0.9998
0.4990
0.4630
0.4630
0.4990
0.4630
0.4990
0.5122
0.2858
0.2858
0.2858
0.2858
0.2160
0.2160
0.2160
0.2160
0.1033
0.1033
0.1033
1.3974
1.2260
0.9824
0.8166
0.6810
0.5087
0.3418
0.2845
0.9651
0.8179
0.7425
0.6455
0.4881
0.3386
0.2361
0.5040
0.3917
0.3149
0.2555
0.2076
0.1684
0.1077
0.2611
0.1888
0.1255
0.0590
0.0352
0.0734
0.1225
0.1695
0.0235
0.0498
0.0732
0.5096
0.5651
0.7465
0.8711
0.9347
1.0446
1.1676
1.2276
0.4220
0.4398
0.4888
0.5481
0.6485
0.7434
0.8135
0.2346
0.2361
0.2708
0.3299
0.3235
0.3820
0.4339
0.1472
0.1672
0.2006
0.2393
0.1915
0.1664
0.1420
0.1274
0.0905
0.0785
0.0698
0.8080
0.6087
0.5156
0.4493
0.3703
0.2673
0.2130
0.5777
0.4983
0.4432
0.3843
0.3093
0.2371
0.1777
0.2644
0.2107
0.1700
0.1519
0.1267
0.1099
0.0755
0.1333
0.1091
0.0796
0.0452
0.0240
0.0473
0.0686
0.0828
0.0126
0.0239
0.0321
0.0957
0.1134
0.0909
0.0649
0.0340
0.0140
0.0082
0.0615
0.0676
0.0672
0.0420
0.0192
0.0086
0.0162
0.0222
0.0172
0.0127
0.0071
0.0027
0.0053
0.0096
0.0056
0.0013
0.0005
0.0022
0.0053
0.0057
0.0002
0.0010
0.0014
H2O ꢀ Hþ þ OHꢁ;
PIPH2 þ Hþ ꢀ PIPHþ3 ;
ðIÞ
ðIIÞ
PIPHþ3 þ Hþ ꢀ PIPH42þ
;
ðIIIÞ
ðIVÞ
ðVÞ
CO2 þ H2O ꢀ HCOꢁ þ Hþ;
3
HCOꢁ3 ꢀ CO23ꢁ þ Hþ;

1284
V. Ermatchkov et al. / J. Chem. Thermodynamics 35 (2003) 1277–1289
TABLE 3
Speciation in (carbon dioxide + piperazine + water) from 1H-NMR measurements at T ¼ 313:15 K and
’
mD ¼ 1 kg where nꢁ and n are the stoichiometric and the true number of moles of species i, respectively
2O
P
nꢁPIPH
nꢁCO
i ni
2
2
(mol)
(mol)
(mol)
i ¼ PIPD2; PIPDþ3 ; PIPD42þ
i ¼ PIPDCOOꢁ; PIPD2þCOOꢁ i ¼ PIPðCOOꢁÞ
0.8371
2
1.4489
1.4687
1.4687
1.4775
1.4489
1.4489
1.4489
1.4489
0.9998
0.9996
0.9996
0.9996
0.9998
0.9998
0.9998
0.4990
0.4630
0.4630
0.4990
0.4630
0.4990
0.5122
0.2858
0.2858
0.2858
0.2858
0.2160
0.2160
0.2160
0.2160
0.1033
0.1033
0.1033
1.3974
1.2260
0.9824
0.8166
0.6810
0.5087
0.3418
0.2845
0.9651
0.8179
0.7425
0.6455
0.4881
0.3386
0.2361
0.5040
0.3917
0.3149
0.2555
0.2076
0.1684
0.1077
0.2611
0.1888
0.1255
0.0590
0.1695
0.1225
0.0734
0.0352
0.0732
0.0498
0.0235
0.6118
0.5995
0.8194
0.8666
0.9359
1.0300
1.1660
1.1899
0.4570
0.4526
0.4909
0.5213
0.6323
0.7335
0.7994
0.2968
0.2511
0.2780
0.3298
0.3202
0.3756
0.4232
0.1711
0.1783
0.2064
0.2435
0.1395
0.1474
0.1674
0.1895
0.0734
0.0802
0.0904
0.7514
0.5444
0.5190
0.4420
0.3775
0.2665
0.2481
0.5428
0.4676
0.4333
0.4122
0.3184
0.2430
0.1884
0.2021
0.1942
0.1660
0.1499
0.1324
0.1141
0.0869
0.1147
0.0980
0.0739
0.0408
0.0717
0.0631
0.0461
0.0261
0.0284
0.0223
0.0127
0.1178
0.1049
0.0919
0.0710
0.0414
0.0165
0.0109
0.0794
0.0754
0.0661
0.0491
0.0233
0.0119
0.0176
0.0190
0.0192
0.0104
0.0093
0.0020
0.0095
0.0055
0.0015
0.0047
0.0055
0.0025
0.0004
0.0015
0.0009
0.0002
PIPH2 þ HCOꢁ ꢀ PIPHCOOꢁ þ H2O;
ðVIÞ
3
PIPHCOOꢁ þ HCOꢁ ꢀ PIPðCOOꢁÞ þ H2O;
ðVIIÞ
3
2
and
PIPHCOOꢁ þ Hþ ꢀ PIPHþ2 COOꢁ:
The condition for chemical equilibrium yields the following equation for the equi-
librium constant K:
ðVIIIÞ

V. Ermatchkov et al. / J. Chem. Thermodynamics 35 (2003) 1277–1289
1285
TABLE 4
Speciation in (carbon dioxide + piperazine + water) from 1H-NMR measurements at T ¼ 333:15K and
’
mD ¼ 1kg where nꢁ and n are the stoichiometric and the true number of moles of species i, respectively
2O
P
nꢁPIPH
nꢁCO
i ni
2
2
(mol)
(mol)
(mol)
i ¼ PIPD2; PIPDþ3 ; PIPD42þ
i ¼ PIPDCOOꢁ; PIPD2þCOOꢁ i ¼ PIPðCOOꢁÞ
0.7077
2
1.4489
1.4687
1.4687
1.4775
1.4489
1.4489
1.4489
1.4489
0.9998
0.9996
0.9996
0.9996
0.9998
0.9998
0.9998
0.4990
0.4630
0.4630
0.4990
0.4630
0.4990
0.5122
1.3974
1.2260
0.9824
0.8166
0.6810
0.5087
0.3418
0.2845
0.9651
0.8179
0.7425
0.6455
0.4881
0.3386
0.2361
0.5040
0.3917
0.3149
0.2555
0.2076
0.1684
0.1077
0.7412
0.6714
0.7664
0.9874
1.0083
1.0906
1.1693
1.2301
0.5169
0.6594
0.6505
0.5487
0.7039
0.7770
0.8259
0.2919
0.2491
0.3024
0.3652
0.3661
0.3982
0.4384
0.6859
0.4337
0.3032
0.3679
0.2885
0.2557
0.1982
0.4828
0.1815
0.2019
0.2448
0.2526
0.1842
0.1514
0.2071
0.1195
0.1012
0.0998
0.0690
0.0894
0.0709
0.1114
0.2686
0.1870
0.0727
0.0698
0.0239
0.0206
0.1587
0.1471
0.2061
0.0433
0.0385
0.0225
0.0944
0.0594
0.0340
0.0278
0.0114
0.0029
FIGURE 3. Speciation in (carbon dioxide + piperazine’+ deuterium dioxide) at T ¼ 298 K resulting from
1H-NMR measurements at (nꢁPIPH ꢂ 1 mol and mD ¼ 1 kg) compared with the correlation.
2O
2
N, PIPðCOOꢁÞ ; j, (PIPDCOOꢁ þ PIPD2þCOOꢁ); and d, (PIPD2 þ PIPD3þ þ PIPD24þ).
2

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V. Ermatchkov et al. / J. Chem. Thermodynamics 35 (2003) 1277–1289
Y
KRðT Þ ¼
ami i;R
;
ð8Þ
i
where mi;R is the stoichiometric coefficient of species i in reaction R and ai is the
activityof species i. The balance equations for the number of moles of a species i in
the liquid phase is:
X
ni ¼ nꢁi þ
mi;RnR;
ð9Þ
R
where nR is the extent of reaction R. Solving this set of equations for a given tem-
perature and given stoichiometric numbers nꢁi of mixed components (i.e., CO2, pi-
perazine, and H2O) results in the ‘‘true’’ composition of the liquid phase, i.e., the
mole numbers of all neutral and ionic species. The calculation requires an activity
coefficient model for aqueous electrolyte solutions (e.g., Pitzer [9]), and the knowl-
edge of the temperature dependent chemical equilibrium constants KI to KVIII (on the
molalityscale, if Pitzer Õs GE equation is used).
Constants KI to KV were taken from literature. Details on the correlation equa-
ꢀ
tions for those reactions were given byP erez–Salado Kamps et al. [2] and Xia
et al. [3]. Temperature dependent constants KVI to KVIII were simultaneouslyfitted
to the 1H-NMR speciation data on the system (carbon dioxide + piperazine + water).
For that purpose, two assumptions were applied: on one hand, in PitzerÕs GE equa-
€
ꢀ
tion onlythe modified Debey–H uckel term was considered (e.g., Perez–Salado
Kamps et al. [2]), that is all interaction parameters were set to zero – the ionic
strength was always less than one molal. On the other hand, the reaction enthalpies
of reactions VI to VIII were assumed to be temperature independent, and the tem-
perature dependencyof the equilibrium constants for these reactions was described
with a two parameter equation:
BR
T
lg KRðT Þ ¼ AR þ
:
ð10Þ
The optimization was performed as follows. In a first step, the protonation constant
of piperazine carbamate (KVIII) was estimated (i.e., parameters AVIII and BVIII of
equation (10) were set to a reasonable starting number). According to this as-
sumption, numbers for KVI; i and KVII; i can be calculated from everysingle experi-
mental speciation data point i (i ¼ 1; 2; . . . ; 121, with the exception of data points
where no piperazine dicarbamate was detected). The resulting numbers for lg KVI; i
(and lg KVII; i) were regressed according to equation (10). Finally, a variation of
parameters AVIII and BVIII was performed in order to minimize the average relative
deviation between lg KVI; i and lg KVII; i and the corresponding linearilyregressed
equations for lg KVI and lg KVII. Although the optimization was repeated starting
from verydifferent numerical values for AVIII and BVIII, it always led to the same
results. The resulting numerical values for the coefficients of equation (10) are given
in table 5. Figure 4 shows the results of that correlation, including standard devia-
tions in lg KVI and lg KVII. At T ¼ ð283; 298; 313; and 333Þ K the following numer-
ical values (and standard deviations) are found for lg KVI: (1:80 Æ 0:09),
(1:52 Æ 0:08), (1:26 Æ 0:11), and (0:96 Æ 0:16), and for lg KVII: (0:44 Æ 0:21),
(0:34 Æ 0:18), (0:25 Æ 0:16), and (0:14 Æ 0:26).

V. Ermatchkov et al. / J. Chem. Thermodynamics 35 (2003) 1277–1289
1287
TABLE 5
Equilibrium constants for chemical reactions VI to VIII (on the molalityscale) (lg KR ¼ A þ B=(T=K)) and
temperature range of validity
Reaction
A
B
T/K
VI
)3.750
)1.587
4.354
1570.4
574.2
1517.0
283 to 333
283 to 333
283 to 333
VII
VIII
FIGURE 4. Experimental results for the chemical equilibrium constants K for the carbamate formations
in (carbon dioxide + piperazine + water), and comparison with literature data. D, This work reaction VI;
ꢁ, this work reaction VII; s, this work reaction VIII, ––––, correlation, this work; ––– and – ꢀ – ꢀ –, ref-
erences [6,7].
The molar Gibbs free energyand the molar enthalpyof reaction of reactions
VI to VIII can be calculated from equation (10) (with coefficients given in table 5)
applying the well-known thermodynamic relations:
DrGm ¼ ꢁR ꢀ T ꢀ ln K
ð11Þ
and
d lnK
DrHm ¼ ꢁR ꢀ
dð1=TÞ
:
ð12Þ

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V. Ermatchkov et al. / J. Chem. Thermodynamics 35 (2003) 1277–1289
At standard state (T0 ¼ 298:15 K) the results are (on the molalityscale): DrGꢃm ¼ ꢁ8:66
kJ ꢀ molꢁ1 and DrHꢃ ¼ ꢁ30:07 kJ ꢀ molꢁ1 for reaction VI; DrGꢃ ¼ ꢁ1:93 kJ ꢀ molꢁ1
m
m
and DrHmꢃ ¼ ꢁ10:99 kJ ꢀ molꢁ1 for reaction VII; and DrGꢃm ¼ ꢁ53:90 kJ ꢀ molꢁ1 and
DrHmꢃ ¼ ꢁ29:04 kJ ꢀ molꢁ1 for reaction VIII.
4. Discussion
With the new correlation equations for the three carbamate formation constants
the model is able to reliablydescribe the speciation in (carbon dioxide + pipera-
1
zine + deuterium oxide) resulting from H-NMR measurements. A typical example
is shown in figure 3 for an aqueous about one molal piperazine solution at T ¼
298 K. As expected (up to this point all interaction parameters were neglected), devi-
ations between experimental data and the correlation become larger with increasing
piperazine and carbon dioxide concentration, i.e. with increasing ionic strength.
As alreadymentioned, the chemical equilibrium constants for the formation of
the three carbamates have been estimated recentlybyBishnoi and Rochelle [6,7].
Bishnoi and Rochelle [6] orginalyfitted these constants to some experimental results
for the partial pressure of carbon dioxide above aqueous 0.6 M piperazine solutions
1
at T ¼ ð313 and 343Þ K (17 data points) and some H-NMR speciation data at
T ¼ 298 K (2 data points). Theyarbitrarilyassumed that the reaction enthalpies
in reactions VI and VII do not differ. In a second estimation [7], some additional ex-
perimental carbon dioxide partial pressures above aqueous 0.6 M piperazine and 4
M MDEA solutions at T ¼ ð313 and 343Þ K (13 data points) were included in the
fitting. The results from these publications differ considerably, in particular for KVI
and KVII, from the results presented here, as shown in figure 4.
Figure 5 gives the speciation in an aqueous one molal piperazine solution at
T ¼ 298 K, when up to 1:2 mol of carbon dioxide were added (per kg of water),
as predicted bythe model presented before. The new correlation equations for KVI
FIGURE 5. Predicted species distribution in (carbon dioxide + piperazine + water) at T ¼ 298 K with
(mꢁPIPH ¼ 1 mol ꢀ kgꢁ1).
2

V. Ermatchkov et al. / J. Chem. Thermodynamics 35 (2003) 1277–1289
1289
to KVIII were considered, and all interaction parameters in PitzerÕs model were set
to zero. Considerable amounts of all carbon dioxide and piperazine species can be
expected in those solutions. In order to extend the existing thermodynamic model
for describing phase equilibria for (carbon dioxide + hydrogen sulphide +
MDEA + water) [1,2] allowing for the presence of piperazine, in a next step, param-
eters describing interactions between carbon dioxide and piperazine (and all their
species) will have to be determined from experimental solubilitydata of carbon
dioxide in aqueous piperazine solutions. This work is now in progress.
5. Conclusions
Sour gas sweetening is often achieved byabsorption in aqueous solutions of amines.
The basic design of such absorption processes requires a thermodynamic model for the
solubilityof sour gases, e.g., carbon dioxide and hydrogen sulfide, in aqueous solutions
of one or more amines, e.g., methyldiethanolamine (MDEA) and piperazine. The pres-
ent work is an extension of previous work on the solubilityof the single gases carbon
dioxide and hydrogen sulfide in aqueous solutions of MDEA [1,2], as well as on the
solubilityof hydrogen sulfide in aqueous solutions of piperazine [3], and on the proton-
ation of MDEA in aqueous solution [4]. The equilibrium constants for the formation
of piperazine carbamate, dicarbamate and protonated carbamate were determined
1
from H-NMR spectroscopic investigations of (carbon dioxide +piperazine + water).
Those chemical equilibrium constants are required in order to enable an extension
of the thermodynamic model for describing phase equilibria for (carbon dioxide +
hydrogen sulphide + MDEA + water) allowing for the presence of piperazine.
Acknowledgements
We thank Prof C. G. Kreiter and Ms H. Ruzek (Universityof Kaiserslautern,
Department of Chemistry) for their kind support in the NMR spectroscopic
investigations.
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