Determination of CO2 concentration in aqueous solutions

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Sterically hindered primary amines

If we now have a closer look on the series of molecules n°12 to 14, which are all primary amines with an amino group linked to a quaternary carbon and exhibit an order n of 1.2, an increase of the pKa tends to increase the value of kAm, as it has been already pointed out with tertiary amine. However, these sterically hindered primary amines are faster to react with CO2 than tertiary amines having same pKa, as can be seen by comparing molecule n°6 with molecule n°12 (pKa = 9.72 – 9.75) or molecule n°13 with molecule n°5 (pKa = 9.48 – 9.50).

Comparison between acyclic and cyclic secondary amines

Molecules n°18 and 19 can be compared. Indeed these molecules are both secondary amines with the same number of carbon between nitrogen and the oxygen atoms. Linear diethanolamine (molecule n°18) reacts 10 times more slowly than cyclic morpholine (molecule n°19) at 100 mol.m-3 in spite of the fact that diethanolamine is more basic. It reveals that there is an important difference of behaviour between cyclic and acyclic amines.

Series with increasing steric hindrance

Series of monoamines n°7 to 11 corresponds to ethanolamines R-NH-CH2-CH2-OH with R being with increasing number: hydrogen (n°7), methyl (n°8), ethyl (n°9), n-butyl (n°10) and tert-butyl (n°11). For this series of molecules, the pKa varies between 9.44 and 10.12 with an increasing steric hindrance around the nitrogen group. This variation of pKa and steric hindrance is correlated with significant variations of kAm and n.
It is very interesting to notice that the effect of hindrance around the amino group on the order n is not monotonic: starting from 1.2 with monoethanolamine (molecule n°7), it first increases up to a maximum around 2 for ethylethanolamine (molecule n°9), and then decreases down to a value of 1 for tert-butylethanolamine (molecule n°11).
It is also possible to compare k0 of theses amines at a concentration of 100 mol.m-3: we see first an increase of the reaction rate from monoethanolamine to methylethanolamine, and an increasing negative effect of hindrance on k0 as the alkyl substituent of the secondary amine gets longer or more substituted, as k0 decreases by two orders of magnitude between methylethanolamine and tert-butylethanolamine. These observations are further discussed below with respect to the different mechanisms proposed in the literature.

Confrontation with mechanisms

The series of molecules n°7 to 11 is represented by Figure III-7. Corresponding pKa and steric hindrance quantified by Taft constants are given in Table III-4. A brief description of Taft constant is given in Chapter IX .2 in appendix. We now attempt to explain the evolution of kinetic constant and order with pKa and Taft constant, considering three hypotheses for the reaction mechanism: carbamic acid, zwitterion or termolecular mechanism.

Effect of steric hindrance

In the part Chapter III .3.3.1.4 we have shown that steric hindrance has a preponderant role to explain kinetic parameters. Conway et al. (2012b) have studied this effect and obtained the results summarized in Figure III-11. Without a descriptor of the steric hindrance for a molecule which could be calculated for their different linear and cyclic amines, they were not able to find a quantitative relationship between steric hindrance and the kinetics of reaction. However, the negative effect of steric hindrance is clearly observed on the second order kinetic constant of the carbamic acid model of the primary amines represented by red circles. This effect can be illustrated by the comparison between n-BA (n-butylamine) and SBA (sec-butylamine) (pKa = 10.6-10.7) on the one hand and with 1-AP (1-amino-2-propanol) and 2-AP (2-aminopropanol) on the other hand (pKa = 9.6).

Ethylenediamine

We compare the apparent kinetic constants from stopped flow data between 3-aminopropanol (kAm = 2.15 m3n.mol-n.s-1) and ethylenediamine (kAm = 5.95 m3n.mol-n.s-1). Indeed, these molecules have almost the same apparent order n ≈ 1.15 and similar values of pKa, respectively 10.00 and 9.92. Moreover they are both linear non hindered primary amine. With a 2.8 factor between the kinetic constant of these molecules, we observe the same effect than for piperazine which are both symmetric multi-amines.

Statistical compensation

In the temperature range of the stopped-flow experiments, the neperian logarithm of the kinetic constant (ln (kter1) and ln (kter2)) and the value of 1/T have a limited variation  which can account for uncertainty on the independent determination of pre-exponential factor and energy of activation. This indetermination can be a first explanation for the apparent compensation effect generally called the statistical compensation effect. This phenomenon is well described by Barrie (2012). We determine for each molecule the confidence ellipse area in order to evaluate the impact of statistical compensation effect on our parameters (Draper and Smith, 1998). The expression of the confidence ellipse area is given by Equation 25 where b is the vector of parameters (ln(A); Ea), β is the estimation of (ln(A) ; Ea) represented by the center of the ellipse, C is the covariance matrix between parameters, (p+1) = 2 is the number of parameters, s² is the residual variance, F; p; (n-p-1) corresponds to the F-distribution value with a confidence level of (1-) % and n is the number of data points used to estimate β.     ; ; ( 1) ‘ ( 1). 2 .       p n p p s F b β C b β.

Physico-chemical compensation

The statistical analysis shows that a part of the observed compensation effect may have a physical explanation. According to the transition state theory, activation energy can be related with activation enthalpy and pre-exponential factor with activation entropy according to Equation 26 and Equation 27 (Scacchi et al., 1996), where Δ‡H is the activation enthalpy, R is the gas constant, T the temperature (here we set at 298.15 K), kB is the Boltzmann constant, h is the Planck constant, Δ‡S is the activation entropy and ‡ 0 cn is the unitary concentration (1,000 mol.m-3) with (1-Δn‡) which is the molecularity of the process (which is 3). Values of activation enthalpy and entropy are given in Table III-6.

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Mass balances and equilibria

We calculate the molalities of 11 or 12 solutes as a function of time: Am, AmH+, CO2, H2CO3, HCO3 -, CO3 2-, HO- and H+, Cl-, HCO2H, HCO2 – in the case which do not form carbamate (tertiary and sterically hindered amines) and we add R2NCO2 – in the case of primary or secondary amines forming carbamates. For given conditions of total amine  concentration and loading ( , HCl and HCO2H  ), the molalities of all species at equilibrium are determined by the resolution of a system of 11 equations (12 with carbamates). These equations are presented below. First, there are five acid-base equilibria. The definition of equilibrium constants (mass action laws) gives the five equations presented in Table IV-1.

Table of contents :

CHAPTER I : GENERAL INTRODUCTION
CHAPTER II : STATE OF THE ART
1 Global warming
2 Carbon capture and storage
2.1 Storage
2.2 Transport
2.3 Capture
3 Amine scrubbing capture process
3.1 Description of the process
3.2 Natural gas treatment
3.3 Performance of the process
3.4 Choice of the solvent
3.5 Conclusion
4 The amine – carbon dioxide reaction
4.1 Definitions
4.2 Instantaneous reactions
4.3 Kinetically limited reactions
4.4 Conclusion
5 Experimental techniques
5.1 Measurement of CO2 absorption flow rate
5.2 Rapid mixing methods
5.3 Conclusion
6 Methods for data treatment
6.1 Numerical method
6.2 Analytical method
7 Conclusion
CHAPTER III : CRITICAL REVIEW OF THE LITERATURE 
1 Stopped-flow data
2 First order kinetic constants
3 Effect of the concentration
3.1 Analysis of the raw data
3.2 Tertiary amines
3.3 Primary and secondary amines
3.4 Multi-amines
4 Effect of temperature
4.1 Statistical compensation
4.2 Physico-chemical compensation
5 Conclusion and scope of this work
CHAPTER IV : METHODOLOGY
1 Experimental techniques
1.1 Stopped-flow technique
1.2 Acid-base titration
2 Characterisation of apparent kinetic constants
2.1 Numerical method
2.2 Analytical method
2.3 Experimental optimization
2.4 Method of data treatment
2.5 Uncertainty of the apparent kinetic constant
3 Characterisation of the constants of the kinetic model
3.1 Semi-empirical model
3.2 Uncertainty of the constants of the kinetic model
4 Design of experiments
4.1 General features
4.2 Tertiary amines
4.3 Primary and secondary amines
4.4 Multi-amines
5 Conclusion
CHAPTER V : INTERPRETATION OF EXPERIMENTAL RESULTS
1 Overview
1.1 Definitions
1.2 Amines of the class A
1.3 Amines of the class B
2 Tertiary and sterically hindered secondary amines
2.1 Comparison with results from literature
2.2 Alkanolamines
2.3 Alkylamines
2.4 Other tertiary amines
2.5 Secondary amines
2.6 Conclusion
3 Primary amines
3.1 Effect of the basicity
3.2 Effect of the steric hindrance
3.3 Enantiomerism
3.4 Conclusion
4 Acyclic secondary amines
4.1 Change of degree of substitution
4.2 Effect of the basicity
4.3 Effect of the steric hindrance
4.4 Conclusion
5 Cyclic secondary amines
5.1 Effect of the basicity
5.2 Effect of the steric hindrance
5.3 Conclusion
6 Multi-amines
6.1 N,N,N’,N’-Tetramethylethylenediamine
6.2 1-Methylpiperazine
6.3 Piperazine
6.4 Conclusion
7 Discussion
8 Conclusion
CHAPTER VI : QSPR MODELLING
1 General points
2 QSPR descriptor model
2.1 Descriptors
2.2 QSPR model
2.3 Conclusion
3 Results
3.1 Modelling of tertiary and sterically hindered amines
3.2 Modelling of primary and secondary amines
4 Discussion
4.1 Tertiary and sterically hindered amines
4.2 Primary and secondary amines
5 Conclusion
CHAPTER VII : GENERAL CONCLUSION AND PERSPECTIVES
CHAPTER VIII : BIBLIOGRAPHIC REFERENCES
CHAPTER IX : APPENDICES
1 Bibliography
1.1 Kinetic constants and orders at 25°C
1.2 Bibliography: variation of kter1 and kter2 with temperature
1.3 Bibliography: kinetic constants k1 and k2
2 Taft constant
3 Experimental method
3.1 Determination of CO2 concentration in aqueous solutions
3.2 Experimental optimization
4 Additional information concerning the numerical model
4.1 Thermodynamic parameters
4.2 Kinetic parameters
4.3 Conductivity parameters
5 Additional information concerning the analytical model
5.1 Tertiary amines
5.2 Primary and secondary amines
6 List of studied molecules
6.1 Primary amines
6.2 Secondary amines
6.3 Tertiary amines
6.4 Multi-amines
6.5 Acidic solutions
6.6 Gas
7 Kinetic results of each studied amine for each concentration .
8 Thermodynamic and kinetic parameters of each molecule
9 Molecular descriptors
9.1 Complete list of molecular descriptors
9.2 Values of molecular descriptors for primary amines
9.3 Values of molecular descriptors for secondary amines
9.4 Values of molecular descriptors for tertiary amines
10 Nitrogen accessible surface
10.1 Algorithm to calculate the nitrogen accessible surface
10.2 Values of nitrogen accessible surface of studied monoamines
11 QSPR model
11.1 Justification of the proportion of data in each set
11.2 Justification of the number of model used
12 Coefficients of the second order models
12.1 Kinetic constant k1 tertiary and sterically hindered amines
12.2 Kinetic constant k1 primary and secondary amines
12.3 Kinetic constant k2 primary and secondary amines
13 Results of the QSPR modelling
13.1 Tertiary and sterically hindered amines
13.2 Primary and secondary amines
14 French detailed summary (résumé détaillé en français)

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