Calculations of Henry's law constants for organic species using relative Gibbs free energy change

Accepted Manuscript Title: Calculations of Henry’s Law Constants for Organic Species Using Relative Gibbs Free Energy Change Author: Xia Zhang Yue Zeng PII: DOI: Reference:

S0378-3812(14)00315-X http://dx.doi.org/doi:10.1016/j.fluid.2014.05.024 FLUID 10125

To appear in:

Fluid Phase Equilibria

Received date: Revised date: Accepted date:

18-1-2014 15-5-2014 21-5-2014

Please cite this article as: X. Zhang, Y. Zeng, Calculations of Henry’s Law Constants for Organic Species Using Relative Gibbs Free Energy Change, Fluid Phase Equilibria (2014), http://dx.doi.org/10.1016/j.fluid.2014.05.024 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Calculations of Henry’s Law Constants for Organic Species Using Relative Gibbs Free Energy Change Xia Zhang, Yue Zeng∗

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Key Laboratory of Chemical Biology and Traditional Chinese Medicine Research of Ministry of Education, College of Chemistry and Chemical Engineering, Hunan Normal University, Changsha, Hunan 410081,

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P.R.China

Abstract: An effective approach is established to estimate Henry’law constant values (H) using density

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functional theory (DFT) at the level of B3LYP/6-311+G(d,p) along with a polarizable continuum model (PCM). The 319 H values for the eight categories of small organic molecules (43 alcohols, 50

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amines, 24 aldehydes, 32 ketones, 33 organic fluorides, 72 organic chlorides, 32 organic bromides and 33 organic nitrates) are estimated, respectively. The Henry’s law constant values estimated by this

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procedure are in good agreement with the experimental results with the standard deviations of 1.38 lnH unit for alcohols, 1.94 lnH unit for amines, 1.55 lnH unit for aldehydes, 1.18 lnH unit for ketones, 1.24

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lnH unit for organic fluorides, 1.44 lnH unit for organic chlorides, 1.49 lnH unit for organic bromides and 0.95 lnH unit for organic nitrates, respectively.

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1. Introduction

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Keywords: Small organic molecule, Henry’s law constant, DFT

Henry’s law constant (HLC) describes an ability of a chemical molecule to distribute

between gaseous and aqueous phase, and plays a key role in physical chemistry [1]. It is a key property in the process of describing a chemical substance’s environmental behavior [2-4]. So many attentions have been devoted to seeking the estimation methods of HLC values. Conventionally, the most important property-property relationships (PPR) [5] for the estimation of HLC values are given by the vapor pressure/aqueous solubility ratio. This method has a thermodynamical background and therefore a broad range of applicability. However the results obtained by this approach depend strongly on the measured quality of the vapor pressure and aqueous solubility data. Unfortunately such data is often unavailable or not ∗

To whom all correspondence should be addressed. E-mail: [email protected]. Project (21275051) was supported by the National Natural Science Foundation of China

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reliable. In 1975 Hine and Mookerjee reported the group contribution method [6], however, this method only can be used to a part of compounds owing to missing fragment constants. The EPICS (Equilibrium Partitioning in Closed Systems) method, which proposed by Gosset in

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1987, involves carefully weighing the amount of the volatile compound added to both of the

sealed bottles and working with ratios of masses [7]. This method needs ascertain the exact

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ratio of the masses added to both bottles, so it would be impossible to accurately determine the Henry’s law constants. In 1993 Robbins reported the static headspace method, [8] in

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which the exact concentration of the volatile compound need not to be known. Experimentally, this method involves the measurement of the equilibrium headspace peak

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areas of one or more compounds by gas chromatography from aliquots of the same solution in three separate enclosed vials with different headspace-to-liquid volume ratios. In addition

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the bond method by Meylan and Howard [9] can be applied to some compounds with distinct experimental HLC values. However, there are some shortcomings in this method. One is the

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missing differentiation of isomers, which is an inherent problem of all fragment methods. Another point is the comparably bad performance for the most of the organochlorines.

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Perhaps the experimental HLC data presented here could be used for a further improvement

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of the bond method by introducing additional class specific correction factors [5]. Usually, LSER method (Linear solvation energy relation ship) [10] by Dearden is also used to estimate HLC values for more compounds. In 2009 H. S. Simon Ip [11] performed offline analysis of aliquots of glyoxal solution by ion chromatograph (IC), and glyoxylic acid and glycolic acid solutions by high performance liquid chromatography. In 2013, J. Duncan Kish [12] presented an improved method by coupling a bubble column system with a gas cell in an infrared spectrometer. This method can be applicable to different classes of atmospheric organics regardless of the presence of heteroatoms or aqueous phase dissociation. Nowadays by means of computers with high computing power theoreticians can also use thermodynamic methods in conjunction with the advanced computational algorithm to calculate the HLC values. Density functional theory (DFT) is a reliable tool which can be used to theoretically study thermodynamic processes, such as surface adsorption and chemical equilibrium. In our previous study [13], pKa values of carboxylic acids in aqueous solution

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were calculated using density functional theory methods. In this work, we report theoretically estimation of Henry’s law constants for 319 compounds covering eight categories (alcohols, amines, aldehydes, ketones, organic fluorides, chlorides, bromides and organic nitrates) in aqueous solution with density functional theory, and the polarizable continuum model (PCM)

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[14] used to describe the solvent effect.

2. Theory and Computational Methods

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2.1 Thermodynamic Theory

The Henry’s law constant H is a way of describing the solubility in water. Usually H is

PD CD

(1)

an

H=

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defined as:

where, CD is the concentration of specie D in the aqueous phase, PD is the partial pressure of species D in the gas phase. The solvation equation of species D into aqueous solution is (2)

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GD D( g ) ⎯Δ⎯ ⎯ → D(aq)

From Eq.(2), we can get the relationship of Henry’s law constant H and solvation 0

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standard Gibbs free energy change, ΔGD, as follow: CD = RTlnH PD

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ΔGD0 = - RT ln K C = - RT ln

(4)

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Then ln H = ΔGD0 / RT

(3)

where R is gas constant and T is temperature. Our previous researches shown that there is a prodigious error when the thermodynamic

properties (e.g., pKa) of some equilibrium processes are directly computed by Gibbs free energy changes ΔGD(calc.) from density functional theory [13]. For this reason the relative

Gibbs free energy change of two interchange reactions can be used to calculate these thermodynamic properties [13]:

GR1 ( calc.) D( g ) + DR1 (aq) ⎯Δ⎯ ⎯⎯→ D(aq) + DR1 ( g )

(5)

G R2 ( calc.) DR2 ( g ) + DR1 (aq) ⎯Δ⎯ ⎯⎯→ DR2 (aq ) + DR1 ( g )

(6)

where DR1 and DR2 are two reference substances whose thermodynamic property is known. The relative Gibbs free energy change, ΔGr = ΔGR1(calc.)/ΔGR2(calc.), can be defined as

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ΔGr =

ΔGD (calc.) − ΔGDR1 (calc.) ΔGR1 (calc.) ln H − ln H R1 = = ΔGR 2 (calc.) ΔGDR 2 (calc.) − ΔGDR1 (calc.) ln H R 2 − ln H R1

(7)

(ln H R 2 − ln H R1 ) ]ΔGD (calc.) ΔGDR 2 (calc.) − ΔGDR1 (calc.)

+ [ln H R1 −

(ln H R 2 − ln H R1 ) ΔGDR1 (calc.)] ΔGD R 2 (calc.) − ΔGDR1 (calc.)

(8)

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ln H = [

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Then Henry’s law constant H can be expressed by Eq.(8)

When the selection of the two reference substances, DR1 and DR2, is appropriate, the

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accurate Henry’s law constant value H can be obtained from Eq.(8).

(ln H R 2 − ln H R1 )

ΔGD (calc.) − ΔGD (calc.) R2

B=

R1

(ln H R 2 − ln H R1 )

ΔGD (calc.) − ΔGD (calc.) R2

R1

(9)

R1

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We finally arrive at

RT

ΔGD (calc.)

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A = ln H R1 −

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With

lnH = BΔGD(calc.)/RT+A

(10)

(11)

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where A and B can be calculated from Eq.(9) and Eq.(10) by ΔGDR1(calc.), ΔGDR2(calc.), and

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HR1 and HR2 of the two reference substances, DR1 and DR2.

2.2 Theoretical Calculations of Gibbs free energy Changes, ΔG(calc.) A total of 319 molecular systems with inclusion of 43 alcohols, 50 amines, 24 aldehydes,

32 ketones, 33 organic fluorides, 72 organic chlorides, 32 organic bromides and 33 organic nitrates, respectively, were initially optimized with DFT hybrid exchange-correlation energy density functional, B3LYP [15], which consists of the Becke’s three parameterized exchange energy density functional and the Lee-Yang-Parr correlation functional. For both core and valence-shell electrons, we employed the People’s basis set of split-valence triple-zeta plus (d,p)-type polarization, 6-311+G(d,p) [16]. The solvation effect was considered by using a polarizable continuum model (PCM) [17]. All calculations were performed with the Gaussian 09 Revision B.01 package[18]. The

experimental Henry’s law constant H taken from reference [5, 20-23].

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3. Results and Discussion 3.1 Determine of the parameters A and B in Eq. (11) It can been seen from Eq.(9) and Eq.(10) that the determine of the parameters A and B depend on the choice of the two reference compounds, DR1 and DR2, which is very important

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to the calculated accuracy. In our research the mathematical statistics, whose goal was the

attain of the smallest standard deviation, was used to find out the most appropriate reference

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compounds in the same category using Origin Software. Our data analysis by the mathematical statistics for alcohols, amines, aldehydes, ketones, organic fluorides, organic

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chlorides, organic bromides and organic nitrates indicates that the most accurate calculated values of lnH can be obtained when CH2OHCH2CH2OH and CH3CH2CHOH(CH2)2CH3 are

for

amines,

C6H5CHO

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chosen as the two reference substances for alcohols, 1-Naphthylamine and (CH3CH2CH2)2NH and

CH3CH2CH2CHO

for

aldehydes,

C6H5COCH3

and

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p-CH3C6H5COCH3 for ketones, o-C6H4F2 and CH2=CF2 for organic fluorides, CH2ClCH2Cl and C6HCl5 for organic chlorides, CH2BrCH2Br and CH3Br for organic bromides,

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1,8-octanediol dinitrate and 1-butyl nitrate for organic nitrates. The parameters A and B in Eq.(11) can be calculated by inserting ΔG(calc.)B and lnH(exp.) of the two reference

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compounds, which are listed in Table S-1 in the supplementary material section, into Eq.(9)

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and Eq.(10), respectively. Then, the expressions of the lnH calculation are as follows: for the alcohols and phenols: ln{H/[atm/(mol⋅L-1)]} = 0.5561ΔGD(calc.)/RT + 4.75

(12)

for amines

ln{H/[atm/(mol⋅L-1)]} = 1.743ΔGD(calc.)/RT + 8.34

(13)

for aldehydes:

ln{H/[atm/(mol⋅L-1)]} = 1.787ΔGD(calc.)/RT + 14.65

(14)

for ketones: ln{H/[atm/(mol⋅L-1)]} = 2.415ΔGD(calc.)/RT + 19.98

(15)

for organic fluorides: ln{H/[atm/(mol⋅L-1)]} = 1.772ΔGD(calc.)/RT + 14.90

(16)

for organic chlorides: ln{H/[atm/(mol⋅L-1)]} = 1.528ΔGD(calc.)/RT + 12.00

(17)

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for organic bromides: ln{H/[atm/(mol⋅L-1)]} = 1.843ΔGD(calc.)/RT + 12.82

(18)

for organic nitrates: ln{H/[atm/(mol⋅L-1)]} = 0.6545ΔGD(calc.)/RT + 9.57

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3.2 Examination to Eq. (11)

(19)

Fig. 1 exhibits the plot of the experimental lnH values, [lnH(exp.)], vs. ΔGD(calc.)/RT,

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and the straight lines from Eq.(12)-(19) are also placed on Fig.1 for all eight categories. It can

and ΔGD(calc.)/RT for each of the eight categories.

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be observed from Fig. 1 that a strong linear correlation between the experimental lnH values

The Gibbs free energy changes ΔGD(calc.) computed by this work, the experimental lnH

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values, lnH(exp.), the calculated values lnH(calc.), and the deviations Δ(lnH) calculated by Eq.(12)-(19) are listed in Table S-2 to Table S-9 for 319 organic compounds, respectively. Fig.

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2 plot the deviation Δ(lnH) vs. lnH(exp.). It can be seen from Table S-2 to Table S-9 and Fig. 2 that a good agreement is found between the experimental values and the calculated values

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using the relative Gibbs energy changes. The standard deviations and the maximum deviations are 1.38 and 3.15 for 43 alcohols, 1.94 and -3.18 for 50 amines, 1.55 and -2.97 for

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24 aldehydes, 1.18 and 2.13 for 32 ketones, 1.24 and -3.24 for 33 organic fluorides, 1.44 and

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3.48 for 72 organic chlorides, 1.50 and -3.13 for 32 organic bromides, 0.95 and -2.40 for 33 organic nitrates, respectively.

3.3 Examination to constants A and B in Eq. (11) In principle, the calculation of Henry’s law constants must employ the standard Gibbs

free energies (G0D ). The comparison of Eq.(11) with Eq.(4) shows that the parameters A and B

are introduced into Eq.(4) to achieve a good calculation result when GD(calc.) instead of G0D is directly employed to calculate lnH by Eq.(4). so the most main reason for introducing the

parameters A and B is that the Gibbs free energies (GD(calc.)) calculated by DFT is not standard Gibbs free energies (G0D ). If GΔD represents the difference between the two, i.e., 0

G D = GD(calc.) + GΔD

(20)

Our previous investigations for the pKa calculation of acids by DFT have shown that 0

there are still systemic errors in the calculations of standard Gibbs free energies (G D ) by 0

Eq.(20) [24]. To reduce the impact of these systemic errors on the calculated accuracy of G D

Page 6 of 17

values, the scaling factor, SF, can be introduced into Eq. (20) to obtain good agreement between the calculated value and experimental one, i.e., 0

G D = SF[GD(calc.) + GΔD]

(21)

Inserting Eq. (21) into Eq. (4), we have (22)

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lnH = SFΔGD(calc.)/RT+ SFΔGΔD

By comparing Eq. (22) with Eq. (4), we observe that the slope B and the intercept A in

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Eq. (4) can be simply seen as a scaling factor SF and a parameter related to the difference 0

between standard Gibbs free energy G D and Gibbs free energy GD(calc.) calculated by DFT. 0

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It is well known that G D and GD(calc.) is the Gibbs free energy of particle D under the standard state and the “live alone” state (i.e., the state of the individual particle D stayed in an 0

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infinite amount of solvent), respectively. Distinctly the the difference of between G D and GD(calc.) comes mainly from the interaction between same solute molecules.

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The Dimer binding free energy ΔGDim of simplest molecule in the same category is chosen as a rough indicator of the interaction between the same solute molecules to observe

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and study the effect of the interaction between solute molecules on both the slope B and the intercept A. Table 1 shows the slope B, the intercept A and the Dimer binding free energy

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ΔGDim calculated by DFT in gas-phase. Fig. 3 exhibits the plot of the relationships between

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the Dimer binding free energy ΔGDim with both the slope B and intercept A for the eight categories studied in this work. It is seen that a reasonable linear relationship is obtained, which means that the slope B and the intercept A in Eq. (11) are two correction factors related to the interaction between the solute molecules. The different categories of compounds with different functional group reveal the different characteristic of intermolecular interaction, which leads to the different parameters A and B.

4. Conclusion

In this study a relative Gibbs energy method is established to estimate lnH values for alcohols, amines, aldehydes, ketones, organic fluorides, organic chlorides, organic bromides and organic nitrates using density functional theory and polarizable continuum solvation model. The results of the calculated lnH values show that when CH2OHCH2CH2OH and CH3CH2CHOH(CH2)2CH3 are chosen as the two reference compounds, DR1 and DR2, for alcohols, and 1-Naphthylamine and (CH3CH2CH2)2NH for amines, C6H5CHO and

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CH3CH2CH2CHO for aldehydes, C6H5COCH3 and p-CH3C6H5COCH3 for ketones, o-C6H4F2 and CH2=CF2 for organic fluorides, CH2ClCH2Cl and C6HCl5 for organic chlorides, CH2BrCH2Br and CH3Br for organic bromides, 1,8-octanediol dinitrate and 1-butyl nitrate for organic nitrates, accurate results of lnH values can be obtained with the standard deviation of

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1.38 lnH unit for alcohols, 1.94 lnH unit for amines, 1.55 lnH unit for aldehydes, 1.18 lnH unit for ketones, 1.24 lnH unit for organic fluorides, 1.44 lnH unit for organic chlorides, 1.49

cr

lnH unit for organic bromides and 0.95 lnH unit for organic nitrates. In summary we have successfully established a computational procedure, by which lnH values of some organic

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species, such as alcohols, amines, aldehydes, ketones, organic fluorides, organic chlorides,

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organic bromides and organic nitrates, can be rapidly and reliably predicted.

Acknowledgment

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This project (NO. 21275051) was supported by the National Natural Science Foundation of China .

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References

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[1] John J. Carroll, Henry’s Law: A Historical View[J]. Journal of chemical education. 70 (1993) 91-92. [2] K. C. Hornbuckle, J. D. Jeremiason, C. W. Sweet and S. J. Eisenreich. Seasonal Variations in Air-Water

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Exchange of Polychlorinated Biphenyls in Lake Superior. Environ. Sci. Technol. 28 (1994) 1491-1501.

[3] J. Schreitmtiller and K. Ballschmiter, Air-Water Equilibrium of Hexachlorocyclohexanes and Chloromethoxybenzenes in the North and South Atlantic. Environ. Sci. Technol. 29 (1995) 207-215 .

[4] J. Staudinger and P. V. Roberts, A Critical Review of Henry’s Law Constants for Environmental Appli- cations. Crit. Rev. Environ. Sci. Technol. 26 (1996) 205-297.

[5] Altschuh J, Bruggemann R, Santl H, etal. Henry’s law constants for a diverse set of organic chemicals: Experimental determination and comparison of estimation methods. Chemosphere 39 (1999) 1871-1887. [6] J. Hine and P. K. Mookerjee, The Intrinsic Hydrophilic Character of Organic Compounds. Correlations in Terms of Structural Contributions, J. Org. Chem. 40 (1975) 292-298. [7] Gos sett, J. M. Measurement of Henry’s Law Constants for C1, and C2 Chlorinated Hydrocarbons. Enuiron. Sci. Technol. 21 (1987) 202-208. [8] Robbins G A, Wang S, Stuart J D, Using the Static Headspace Method to Determine Henry’s Law Constants.

Page 8 of 17

Anal. Chem. 65 (1993) 3113-3118. [9] W. M. Meylan and P. H. Howard, Bond Contribution Method for Estimating Henry’s Law Constants, Environ. Toxicol. Chem. 1991, 10 (10): 1283-1293.

constant from molecular structure[J] . Environ Toxicol Chem. 22 (2003) 1755-1770.

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[10] John C. Dearden , G. Schüürmann. Quantitative structure-property relationships for predicting Henry’s law

[11] Ip.H.S., Huang X.H., Yu. J.Z. Effective Henry’s law constants of glyoxal, glyoxylic acid, and glycolic acid[J] .

cr

Geophysical Research Letters 36 (2009) 1-5.

organics[J]. Atmospheric Environment 79 (2013) 561-565.

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[12] J. Duncan Kish, Chunbo Leng. An improved approach for measuring Henry’s law coefficients of atmospheric

[13] Y. Zeng, X.L. Chen, Estimation of pKa values for carboxylic acids, alcohols, phenols and amines using

an

changes in the relative Gibbs free energy, Fluid Phase Equilibria 313(2012) 148–155.

[14] For recent applications of the PCM to molecular properties, see, for example: (a) Cammi, R. J.Chem. Phys. ,

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109(1998) 3185. (b) Cammi, R.; Mennucci, B.; Tomasi, J. J. Am. Chem. Soc. 120(1998) 8834. (c) Cammi, R.; Mennucci, B.; Tomasi, J. J. Phys. Chem. A 102 (1998) 870. (d) Cammi, R.; Mennucci, B.; Tomasi, J. J. Chem.

d

Phys. 110 (1999) 7627. (e) Mennucci, B.; Cammi, R.; Tomasi, J. Int. J. Quantum Chem. 75 (1999) 767. (f) Tomasi, J.; Cammi, R.; Mennucci, B. Int. J. Quantum Chem. 75(1999) 783. (g) Cammi, R.; Mennucci, B.;

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(2001) 7287.

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Tomasi, J. J. Phys. Chem. A 104(2000) 4690. (h) Mennucci, B.; Martinez, J., Tomasi, J. J.Phys. Chem. A 105

[15] A. D. Becke, Phys. Rev. A 38 (1988) 3098-3100. [16] V. A. Rassolov, M. A. Ratner, J. A. Pqple, P. C. Redfern, L. A. Curtiss, J. Comput. Chem. 22 (2001) 976-984. [17] J. Tomasi, B. Mennucci, E. Cancès, J. Mol. Struct. (THEOCHEM) 464 (1999) 211-226. [18] A. D. Becke, Phys. Rev. A 38 (1988) 3098-3100. [19] R. Adam Kenneth, New Density Functional and Atoms in Molecules Method of Computing Relative pKa Values in Solution[J]. Phys. Chem. A 106(2002) 11963–11972.

[20] Denise Yaffe, Yoram Cohen, A Fuzzy ARTMAP–-Based Quantitative Structure-Property Relationship (QSPR) for the Henry’s Law Constant of Organic Compounds[J]. Chem. Inf. Comput. Sci. 43 (2003) 85–112 [21] Rolf Sander. Compilation of Henry’s Law Constants for Inorganic and Organic Species of Potential Importance in Environmental Chemistry. Max-Planck Institute of Chemistry.http://www.mpch-mainz.mpg.de /˜sander/res/henry.html.1999 Feb,3.

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[22] R.Lide David , CRC Handbook of Chemistry and Physics(87th Edition). In the United Stated of America on acid-free paper , CRC Press, 2006. [23] N. Nirmalakhandan et al, R. A. Brennan, Predicting henry’s law constant and the effect of temperature on henry’s law constant. War. Res. 31(1997) 1471–1481.

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M

an

us

cr

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[24] Y. Zeng, H.Y. Qian, X.L. Chen, Z.L. Li, S.C. Yu, X.X. Xiao, Chinese J. Chem. 28 (2010) 727–733.

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Fig.1 Linear relationships between ∆GD(calc.)/RT and lnH(exp.) for alcohols, amines, aldehydes,

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ketones, organic fluorides, organic chlorides, organic bromides and organic nitrates.

Page 11 of 17

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Fig. 2 The plot of the deviation Δ(lnH) vs. lnH(exp.) for for alcohols, amines, aldehydes, ketones,

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organic fluorides, organic chlorides, organic bromides and organic nitrates.

Page 12 of 17

4

Intercept A Slope B Linear fitting

15

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35 7 6

10

8

5

cr

2 1 7 6 8 8.5

2 0 6.0

1 6.5

7.0

7.5

8.0

4

5 3

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Intercept A or Slope B

20

9.0

9.5

10.0

3

an

Dimer binding energy ΔGDim×10 /a.u.

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Fig. 3 The plot of intercept A and slope B in Eq. (11) vs dimer binding free energies ΔGDim in gas-phase for eight categories.

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Table 1 The samples and dimer binding energies ΔGDim for eight category substances studied in this work Type

Intercept A

Slope B

Sample

∆GDim×103/a.u.

1

alcohol and phenol

4.748

0.5561

CH3CH2CH2OH

6.42

2

amine

8.342

1.743

CH3NH2

6.83

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NO.

3

aldehyde

14.65

1.787

CH3CHO

9.09

4

ketone

19.98

2.415

CH3COCH3

9.69

5

organic fluoride

14.90

1.772

CH3F

9.16

6

organic chloride

12.00

1.528

CH3Cl

8.43

7

organic bromide

12.82

1.843

CH3Br

8.51

8

organic nitrate

9.566

0.6545

CH3ONO2

8.46

Note: Intercept A and Slope B are listed in this table to be compared with ΔGDim

Page 13 of 17

Graphical Abstract GD D ( g ) ⎯Δ⎯ ⎯ → D (aq )

us

cr

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ln H = ΔGD0 / RT

An effective approach is established to estimate Henry’law constant values (H) using density

an

functional theory (DFT) at the level of B3LYP/6-311+G(d,p) along with a polarizable continuum model (PCM). The 319 H values for the eight categories of small organic molecules (alcohols, amines,

M

aldehydes, ketones, organic fluorides, organic chlorides, organic bromides and organic nitrates) are estimated, respectively. The Henry’s law constant values estimated by this procedure are in good agreement with the experimental results with the standard deviations of 1.38 lnH unit for alcohols, 1.94

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lnH unit for amines, 1.55 lnH unit for aldehydes, 1.18 lnH unit for ketones, 1.24 lnH unit for organic

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fluorides, 1.44 lnH unit for organic chlorides, 1.49 lnH unit for organic bromides and 0.95 lnH unit for

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organic nitrates, respectively.

Note: our paper is about numerical calculation of Henry’s Law constant values, it is enough that a few equations are need as Graphical Abstract.

Page 14 of 17

Figure(s)

Figure Captions

-32

-24

-16

-8

-20

-15

-10

-5

0

-12

-9

-6

-12

5 0

(Amine)

-8

-6

(ketones)

(Aldehyde)

0

-5

0

0

-5

-4

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-7 -5

-10

Y=0.4625X+3.645 R=0.91 SD=1.38

15

-21

Y=1.731X+8.673 R=0.92 SD=1.94

-10

Y=1.783X+14.39 R=0.92 SD=1.55

Y=1.962X+16.43 R=0.83 SD=1.18

6

10

(Organofluorine)

-8

us

-10

cr

-14

-1

(Organochloride)

10

(Organobromine)

(Organonitrates)

4

an

5

10

5

0

0 -10

-5

GD(calc.)/RT

0

-5

M

Y=1.260X+13.43 R=0.93 SD=1.24

2

0

5

Y=1.621X+12.69 R=0.85 SD=1.44 -9

-6

-3

ed

ln{H(exp.)/[atm/(molL )]}

-1

ln{H(exp.)/[atm/(molL )]}

(Alcohol) 0

-10

4

GD(calc.)/RT

-5

0

Y=1.367X+15.17 R=0.94 SD=1.49 -9

-6

-3

GD(calc.)/RT

-2 -20

Y=0.6663X+9.641 R=0.92 SD=0.95 -15

-10

-5

GD(calc.)/RT

Ac

ce pt

Figure 1. Linear relationships between ∆GD(calc.)/RT and lnH(exp.) for alcohols, amines, aldehydes, ketones, organic fluorides, organic chlorides, organic bromides and organic nitrates.

Page 15 of 17

-10

-5

0

-24

-16

-8

0

-10

-5

0

5

3

3

5

2

1

1

1

1

0 0

0

0 -1

-1

-2

-2

ip t

(lnH)

0

2

2

-1

-1

-2 -3

-2

cr

-3

3

3

2

3 2 1

1 1

0

0

1

0

an

0

us

2 2

(lnH)

-5 2

-1

-1

-1 -2

-1

-2

-2 -3

-2

0

5

10

15

-6

0

M

-3

6

lnH(exp.)

12

-10

-5

0

5

lnH(exp.)

10

-2

0

2

4

6

lnH(exp.)

ed

lnH(exp.)

Ac

ce pt

Figure 2. The plot of the deviation Δ(lnH) vs. lnH(exp.) for for alcohols, amines, aldehydes, ketones, organic fluorides, organic chlorides, organic bromides and organic nitrates.

Page 16 of 17

Research highlights: ● The relative Gibbs free energy method is proposed to estimate Henry’law constant values for the eight categories of organic molecules. ● In our paper Henry’law constant values can be directly calculated using DFT, and no thermodynamic cycle is required.

ip t

● The standard deviation of our estimation is 1.38, 1.94, 1.55, 1.18, 1.24, 1.44, 1.49, 0.95 lnH unit,

Ac ce p

te

d

M

an

us

cr

respectively, for eight categories.

1

Page 17 of 17