Chemical Engineering Science 61 (2006) 6199–6212www.elsevier.com/locate/ces

A theoretical study of solvent effects on Kolbe–Schmitt reaction kinetics

Ioana Stanescu∗, Luke E.K. AchenieDepartment of Chemical Engineering, University of Connecticut, 191 Auditorium Road, Storrs, CT 06269-3222, USA

Received 23 June 2005; received in revised form 11 April 2006; accepted 18 May 2006Available online 26 May 2006

Abstract

A theoretical DFT study was employed to confirm the Kolbe–Schmitt reaction mechanism and investigate solvent effects on this reaction. Theuse of a solvent in the Kolbe–Schmitt reaction is desirable to facilitate a homogeneous reaction mixture and potentially improve the reactionrate. The candidate solvents were designed using computer aided molecular design (CAMD) and tested using DFT solvation calculations.The results from the quantum mechanical calculations were then used to determine the rate constants for each elementary step, the overallreaction yields and the corresponding residence time. The methodology was tested on the reaction without solvent, with solvents reported inthe literature, and with the designed solvents. The study revealed that in the presence of solvents with high dielectric constant the reactionbecomes reversible, leading to low product yields.� 2006 Elsevier Ltd. All rights reserved.

Keywords: Kolbe–Schmitt reaction; Density functional theory; Rate constant; Conventional transition state theory; Computer aided molecular design; Solventdesign

1. Introduction

Aromatic hydroxy carboxylic acids are important intermedi-ates in the synthesis of numerous products, including pharma-ceuticals, antiseptic agents, fungicidal agents, dyes, polyesters,high-polymeric liquid crystals, color-developing agents, andtextile assistants. The most conventional method for preparingthese acids is the Kolbe–Schmitt reaction. Usually, this reac-tion is carried out by introducing dry carbon dioxide underpressure over dry alkali metal aryloxides or by rapidly passingcarbon dioxide through the melted alkali metal aryloxide. TheKolbe–Schmitt reaction has also been reported to take placein solution or suspension, allowing intensified stirring of thereaction mixture. The conditions of the Kolbe–Schmitt reac-tion vary over a wide range, depending on the starting alkalimetal aryloxide, the procedure used for carrying out the reac-tion, the use of solvents or suspension media, the degree ofdryness (presence of water), and a few other factors. A detailedreview of research on the Kolbe–Schmitt reaction can be foundin Lindsey and Jeskey (1957).

∗ Corresponding author. Tel.: +1 860 486 4600; fax: +1 860 486 2959.E-mail address: ioana_stanescu_ro@yahoo.com (I. Stanescu).

0009-2509/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.doi:10.1016/j.ces.2006.05.025

Kolbe (1860) first prepared salicylic acid by heating sodiumphenoxide with carbon dioxide at atmospheric pressure, andacidifying the resulting sodium salicylate solution (Fig. 1).Kolbe obtained yields below 50%. In the course of the reaction,despite absolutely dry conditions, half of the initial amount ofphenol distilled (prior to the Kolbe–Schmitt reaction phenol isneutralized with sodium hydroxide and water is removed). Phe-nol distills usually from the reaction mixture at low CO2 pres-sure and high temperature, when the side reactions presentedin Fig. 2 occur (Rieckmann, 2004; Lindsey and Jeskey, 1957).

Schmitt (1885) proposed a modification of the Kolbe reactionin which carbon dioxide introduced under pressure significantlyimproved the yield. For example, Baine et al. (1954) reportedobtaining 79% yield of salicylic acid at 125 ◦C and a carbondioxide pressure of 80–135 atm. Under these conditions no phe-nol is lost and salicylic acid is obtained in an almost stoichio-metric amount. This modification, known as the Kolbe–Schmittreaction, remains the standard method for preparing a wide va-riety of hydroxy aromatic acids.

In the present-day industrial process for manufacturing sal-icylic acid, the reaction takes place in the gas-solid phase.Here dry sodium phenoxide is contacted with carbon dioxideat 5 atm and temperatures up to 100 ◦C. After absorption of

6200 I. Stanescu, L.E.K. Achenie / Chemical Engineering Science 61 (2006) 6199–6212

O

Na

+OH

O

ONa

SodiumPhenoxide

CarbonDioxide

SodiumSalicylate

+ by products

CO2

Fig. 1. Kolbe–Schmitt reaction.

ONa

+

OH

O

ONa

O

O

ONa

Na + OH

2OH

O

ONa

O

O

ONa

Na+ OH + CO2

Fig. 2. Side reactions.

approximately one molar equivalent of carbon dioxide, the tem-perature is raised and held at 150–160 ◦C for several hours. Oneof the practical challenges in carrying out the Kolbe–Schmitt re-action in the solid state is the difficulty of achieving absolutelyanhydrous conditions and maintaining the metal aryloxide in afinely divided state. Agglomeration of particles during carbona-tion and inefficient mixing leads to less than optimal yields andlocal overheating with formation of undesirable by-products.The reaction mixture is either a powdery solid or a viscous liq-uid (paste), and much effort has been made to improve the re-actor design for better stirring of the reaction mixture and forenhancing the contact surface between the reactants. The useof an inert solvent or suspension medium may overcome thesedifficulties by facilitating a homogeneous reaction mixture, im-proving the stirring of the reaction mixture, and, in a numberof cases, enabling the reaction to be carried out under milderconditions (Lindsey and Jeskey, 1957). In addition, Ullmann’sEncyclopedia, 1997 indicates that the process can be carriedout continuously in a suitable medium, mitigating the disad-vantage that the classical Kolbe–Schmitt procedure is mostlyconducted batchwise.

2. Methodology and results

2.1. Validation of the Kolbe–Schmitt reaction mechanism

2.1.1. BackgroundDespite great efforts and numerous hypotheses proposed to

elucidate the Kolbe–Schmitt reaction mechanism, this subjectstill remains unresolved. Early researchers suggested that thereaction occurs via an intermediate complex “sodium phenylcarbonate” (PhO · CO2Na) that forms at room temperature(Kolbe, 1860; Schmitt, 1885). Hessler (1907), citing Tijmstra(1905), asserted that the complex formed between CO2 andPhONa is not “phenyl sodium carbonate,” because this species

readily looses carbon dioxide at 120 ◦C. Tijmstra assumes asimple addition of carbon dioxide to sodium phenoxide, form-ing a “phenyl sodium-�-carbonic acid” (Ph(ONa) · COOH).Johnson (1933) and Luttringhaus (1945) indicated that the ini-tial chelate rearranges with the formation of a cyclic interme-diate, followed by hydrogen atom migration in the synthesisof ortho substituted products. Gilman et al. (1945) proposeda different mechanism involving phenyl sodium carbonate andmetallated compounds.

Hales et al. (1954a,b), using infra-red absorption spectra,found evidence of formation of a weak chelate complex be-tween PhONa and CO2 (PhONa · CO2). The authors showedthat this complex dissociates into the original reactants at lowpressure (atmospheric or sub-atmospheric pressure) when tem-perature is raised to 80 ◦C, however, it does not dissociate underthe conditions of the Kolbe–Schmitt reaction at 120–160 ◦Cwhen pressure exceeds 4 atm. This study indicates that, uponthermal activation, the chelate complex suffers an intramolec-ular rearrangement followed by displacement of the orthohydrogen by electrophilic attack. Hales et al. excluded orthometallated aryloxides and dimetallated intermediates from thereaction mechanism, explained by the absence of disodiumsalicylates products.

Ayres (1966) suggested that the chelate complex further re-arranges into a � complex with C-alkylation in the ortho posi-tion, followed by proton transfer to the phenolic oxygen. Ayresalso showed that the chelate decomposes into CO2 and PhONaon addition of solvents (such as acetone, known to form com-plexes with phenoxides). Kunert et al. (1997) investigated thestructure of solvent free sodium phenoxide by means of FT-IRand DTA, indicating the presence of the PhONa · CO2 com-plex, as well as a further intermediate. They concluded that di-rect carboxylation could be excluded from the Kolbe–Schmittreaction mechanism.

Kosugi et al. (2003) indicated that the reaction proceeded bydirect carboxylation of the aromatic ring and that the PhONa ·CO2 complex was not an intermediate in this process. Thus,chelate formation constitutes a competing reaction with theformation of salicylic or p-hydroxybenzoic acid. Their studiesfocused mainly on the carbonation of potassium phenoxide andan exact mechanism based on their hypothesis has not beenpresented.

Markovic et al. (2002) employed quantum mechanical cal-culations using Gaussian 98 software package and proposed acomplete mechanism including three intermediates and threetransition states:

PhONa + CO2 → B → TS1 (o-TS1, p-TS1) → C

→ TS2 → D → TS3 → Sodium salicylate (E).

They indicated PhONa · CO2 chelate as the first inter-mediate, showing that carbon dioxide can only attack atthe –O–Na site. The chelate undergoes intramolecular re-arrangement, followed by electrophilic attack with dis-placement of the ortho hydrogen atom. Intermediate Cexhibits a similar structure to that of the chelate com-plex suggested by Hales et al. (1954a,b). Markovic’s studyalso provides a quantitative explanation for the low yields

I. Stanescu, L.E.K. Achenie / Chemical Engineering Science 61 (2006) 6199–6212 6201

Fig. 3. The Kolbe–Schmitt Reaction Mechanism. The ground states are the optimized geometries obtained using B3LYP/LAV3P** level of theory. The transitionsstates geometries were found using the transition state search option in Jaguar 4.2, starting from the optimized structures of the reactants and products. Thelabels of the structures along the reaction path (intermediates and transition states) are the same as Markovic’s notations (Markovic et al., 2002).

of p-hydroxybenzoic acid by-product and the equilibrium be-havior of the Kolbe–Schmitt reaction.

2.1.2. Methodology and results from DFT calculationsTo confirm the mechanism proposed by Markovic et al.

(2002), quantum mechanical calculations were performed usingthe Jaguar 4.2 program package (Jaguar 4.2 User’s guide, 2002).DFT calculations, geometry optimization and transition statesearch for the different structures along the reaction path wereconducted at B3LYP/LAV3P** level of theory. After a series oftests with LAV2D**, LACVP**, LAV3P** and LAV3P∗∗ ++basis sets, LAV3P** was finally selected for the calculations,taking into account the trade-off between accuracy and com-putational effort. The LAV3P** basis set is more accurate thanLAV2D**, while LACVP** results were very different fromthose reported by Markovic et al. (2002), offering no possi-bility for comparison. Adding the diffuse functions providedby LAV3P∗∗ + + basis set did not notably modify the results;however, the computational effort increased significantly. Thecalculations performed using LAV3P** were robust and easilyreproducible, the average CPU time being around 6200 s for theoptimization calculations and around 9900 s for the transitionstate searches, using a single node of a Beowulf Linux Cluster(with the AthlonTM MP 1800 + at 1.53 GHz).

Calculations were performed for normal conditions (0 ◦Cand 1 atm) to compare with Markovic’s results. For deriving therate constants we selected 150 ◦C and 4 atm as the conditionsfor the Kolbe–Schmitt reaction, used in industrial process today(Lindsey and Jeskey, 1957; Ullmann’s Encyclopedia, 1997).

The results support the mechanism proposed by Markovicet al. (2002). Optimized geometries and transition states are pre-sented in Fig. 3. Starting from reactants placed in the workspacerelatively far from each other and optimizing this initialgeometry (varying the distances and angles), complex B isobtained as the optimized structure, having the lowest energyaround the initial geometry. Also, intermediate C was obtainedas the optimized structure if the initial reactants were placedrelatively close to each other such that direct substitutionwould be the most probable; however there is no indicationthat direct substitution is plausible in this situation. No newC–C bond in ortho or para position in a structure with lowenergy around this initial geometry appears after optimization.Based on a HOMO-LUMO analysis, Markovic concludes thatthe reactive site in the first step is the O–Na bond. Our inves-tigations showed that the initial chelate formation is likely tooccur, since CO2 is a weak electrophile and the O–Na bond ishighly polarized. In addition, this mechanism is verified by anexamination of charges on the ortho C atom in sodium phe-noxide and on the C atom in CO2 compared with the chargeson the same atoms in complex B. The ortho position in thearomatic ring has a partial charge of −0.45467 in PhONaand of −0.37888 in complex B. The C atom in CO2 has apartial charge of +0.63824, while in complex B the chargeis +0.90266. Therefore, the chelate formation facilitates thesubsequent electrophilic attack and the reaction is more likelyto follow this mechanism than direct carboxylation.

The energy profile along the reaction path follows the samepattern as that reported by Markovic et al. (2002), however, the

6202 I. Stanescu, L.E.K. Achenie / Chemical Engineering Science 61 (2006) 6199–6212

E

TS3

DTS2C

o-TS1B

A

E

TS3

DTS2

Co-TS1B

A

-495.75

-495.70

-495.65

-495.55

-495.50

Reaction coordinate

En

erg

y (H

F)

-192.04

-92.04

7.96

107.96

207.96

307.96

407.96This work (B3LYP/ lav3p**)

-495.60

Markovic et al. 2002

Rel

ativ

e E

ner

gy

(kJ

/mo

l)

Fig. 4. Potential energy diagram. The first curve represents the energies of dif-ferent structures along the Kolbe–Schmitt reaction path reported by Markovicet al. (2002). The curve below represent the energies of the optimized struc-tures and transition states calculated in this work at B3LYP/LAV3P** levelof theory.

Table 1Thermodynamic properties for the optimized structures and transition statesin the Kolbe–Schmitt reaction 150 ◦C and 4 atm

Structure S (cal/mol K) H (kcal/mol) G (kcal/mol)

CO2 51.7477 3.4495 −18.4475PhONa 94.9783 9.0794 −31.1106

Reactants (A) 146.7260 12.5289 −49.5581B 111.8003 12.1358 −31.1725o-TS1 119.5505 13.2716 −37.3162p-TS1 120.1996 13.2837 −37.5787C 113.3663 12.4217 −35.5493TS2 108.6233 12.1929 −33.7752D 112.9425 12.1539 −35.6377TS3 110.8080 12.6103 −34.2781E 106.6871 11.5448 −33.5999

Results from DFT calculations using Jaguar 4.2.

energies obtained using LAV3P** basis set in Jaguar are lowerby an average of 0.069 HF (Fig. 4). We suspect that the con-stant offset can mostly be attributed to the differences betweenthe LANL2DZ basis set in the Gaussian 98 package, used inMarkovic’s work, and LAV3P** in the Jaguar 4.2 package,used in this work. For the structures along the reaction path,the calculated thermodynamic properties, namely heat capac-ity, enthalpy, entropy and Gibbs free energy of the moleculesare presented in Table 1. These properties later allowed us toestimate the rate constants for each elementary reaction usingthe thermodynamic formulation of the transition state theory.With a confirmed reaction mechanism, we were able to calcu-late the same set of properties for the Kolbe–Schmitt reactionconducted in the presence of solvents.

2.2. Solvents in the Kolbe–Schmitt reaction

2.2.1. Reported solvents for the reactionA wide variety of organic compounds has been reported as

solvents or suspension media for the Kolbe–Schmitt reaction.An obvious choice of solvent would be water, since it dis-solves the alkali metal aryloxides. However, water inhibits the

carbonation of monohydric phenols and therefore it shouldbe removed from the reactants prior to reaction. This adverseeffect may be due to strong chelation of water moleculeswith alkali metal aryloxides, preventing the initial addition ofcarbon dioxide. Another cause may be the hydrolysis of thealkali salt to phenol and sodium hydroxide. Subsequently,introducing carbon dioxide leads to the formation of sodiumbicarbonate, the phenol remaining unchanged (Lindsey andJeskey, 1957). Hydrocarbons are among the most commonsolvents, but they generally may be used only as suspensionmedia in the Kolbe–Schmitt reaction since metal aryloxidesoften are not soluble in this type of solvent. Moseley et al.(1955) reported xylene as suspension media for the reactionconducted continuously, while kerosene, light oil and gasolinewere indicated as dispersants by Ueno and Tetsuya (1974).

A series of other possible solvents have been identified inthe literature. The Kolbe–Schmitt reaction can be performed inexcess phenol, as proposed by Wacker (1932), Dow Chemical(1964) and Jansen and Wolff (1983). Barkley (1958) presenteda series of experiments carried out in the presence of higheralcohols (e.g. isooctanol, isodecyl alcohol), and carbonation ofmetal aryloxides in cyclic diethers (dioxane) and heterocyclicamines (pyridine and quinoline) has also been reported (Lindseyand Jeskey, 1957). Aprotic polar solvents such as DMF andDMSO were employed as solvents for carboxylation of phenolderivatives by Hirao et al. (1967), enabling the reaction to behomogeneous at 100–180 ◦C. Kunert et al. (1997) investigatedthe structure of sodium phenoxide crystals and its complexeswith THF and TMU (N, N, N ′, N ′-tetramethyl urea). Furuyaet al. (1998) proposed a process for preparing hydroxybenzoicacids by using a mixture of alkali metal compound, phenol andan aprotic polar solvent (amides, dimethyl sulfoxide or sul-folane). While these are all potential solvents, data limitationsdid not permit computations for these cases.

Additional solvents proposed in literature provided the fo-cus for our solvation calculations. Wideqvist (1954) indicatedthat alkali salicylates are readily soluble in acetone, ethanoland methanol. Glycols (ethylene glycol, glycerol) and 1-butanolhave also been used as solvents for the Kolbe–Schmitt reac-tion. Glycerol has been employed as a solvent for carbonationsat atmospheric pressure, when the reaction mixture is heatedat 130–210 ◦C with alkali bicarbonate in a stream of carbondioxide. Fry (1950) suggested lower dialkyl ketones (insolublein water) as solvents for alkali phenolates and conducted theKolbe–Schmitt reaction for sodium phenoxide in diisobutyl ke-tone. With sodium phenoxide as the starting reactant, data usingthese solvents are indicated in Table 2. The yields of salicylicacid achieved by using these solvents are significantly lower(in some cases no product was obtained) in comparison withthe current solvent-free Kolbe–Schmitt reaction, which givesup to 97% yield. As posited by Isemer, cited by Lindsey andJeskey (1957), the data indicate that carbonation proceeds mostreadily in solvents having low dielectric constants.

2.2.2. Solvent designIn addition to solvents identified in the literature, a system-

atic computer-aided molecular design (CAMD) algorithm was

I. Stanescu, L.E.K. Achenie / Chemical Engineering Science 61 (2006) 6199–6212 6203

Table 2Carbonation of sodium phenoxide in various solvents (adapted from Lindsey and Jeskey, 1957)

Solvent Dielectric constant Temperature (◦C) Pressure (atm) Salicylic acid yield (%)

Methanol 31.2 140 22 No productEthanol 25.8 140 6 No product1-Butanol 19.2 155 10 7.5Glycol 41.2 140 6 No productGlycerol 56.2 170 10 No productXylene (suspension) 2.6 138 1 33.5Diisobutyl ketone – 150 1 18.9

employed to find new/alternative solvents that may exhibit bet-ter performances in this reaction. The CAMD algorithm utilizesfunctional group information to generate structures (molecules)and applies a group-contribution method to estimate the prop-erties of the designed compounds, which are then evaluatedwith respect to the specified set of desired properties. Thus,this methodology leads to the identification of solvents havingdesired types and properties. Some of the most important contri-butions to this approach of CAMD have been presented by Ganiet al. (1991), Venkatasubramanian et al. (1994), Constantinouet al. (1996), Duvedi and Achenie (1996), Churi and Ache-nie (1996), Marcoulaki and Kokossis (1998), Harper and Gani(2000) and Wang and Achenie (2002). In this study, we usedProCAMD version 1.41 tool within the Integrated ComputerAided System (ICAS) version 7.0 (2004) (Gani, 1999–2004).

The design of solvents to be used in the Kolbe–Schmitt reac-tion takes into account several criteria, which translate into a setof desired properties applied as constraints in the selection ofthe feasible alternatives. The candidate solvents were designedto have specific types such that they are inert toward the reactioncomponents (reactants and products). Substances such as acidsand halogenated compounds were excluded due to their poten-tial reactivity toward the alkali metal aryloxides. Amines werealso excluded due to their potential toxicity, which is undesir-able in a pharmaceutical process. Additionally, the candidatesolvents must be liquid under the reaction conditions; thereforetheir melting and boiling point become property constraints inthe design procedure.

Since organic salts such as metal aryloxides and salicylatesare not present in common databases and their properties notreadily available or easy to predict (e.g. solubility parame-ter), the characteristics of mixtures between these compoundsand the designed solvents are difficult to estimate (miscibil-ity, solvent power, selectivity etc.). However, according to thesimple solubility parameter theory it is assumed that if thesolubility parameter of a solvent is around the same valueto that of the solute, they will be miscible (“like dissolveslike”). The product sodium salicylate was selected as the so-lute. Therefore, a solvent with high solubility for this compoundwill stabilize it within the reaction mixture, thereby improv-ing its yield. Taking into account the solubility parameter ofsodium salicylate reported by Barra et al. (2000) to be 30.81(MPa)1/2, the candidate solvents must have a solubility param-eter around the same value. It is also known that water is a good

solvent for sodium salicylate, therefore the solubility parame-ter limits considered for solvent design were between 30 and48 (MPa)1/2.

The resulting design criteria are as follows

• Types of compounds: Acyclic, aromatic and cyclic alcohols,phenols, aldehydes, ketones, ethers and esters, compoundscontaining double and triple bonds;

• Compounds can contain 2–10 groups, 0–3 functional groups,0–3 same functional groups;

• Solvents contained in ProCAMD common solvent databasewere also included; as user specified compounds;

• Melting point: Tm < 420 K;• Boiling point: Tb > 425 K;• Total solubility parameter: 30–48 (MPa)1/2 (target value 31

(MPa)1/2).

Additionally, partial solubility parameters were estimated inthe solvent design step and included in an analysis based onthe Teas graph presented in Fig. 5. A simple method to vi-sualize potentially suitable solvents for a particular substanceis to place them on a triangular diagram (Teas graph) ac-cording to their Hansen partial solubility parameters: �H , �D ,�P Barton, 1991). For sodium phenoxide, according to Barraet al. (2000), the partial solubility parameters determined em-pirically are: �H =16.58 (MPa)1/2, �D =16.55 (MPa)1/2, �P =20.01 (MPa)1/2 (point marked 1 in Fig. 5). The same studypresented another set of partial solubility parameters, calcu-lated using a group contribution method: �H =20.16 (MPa)1/2,�D = 21.18 (MPa)1/2, �P = 11.23 (MPa)1/2 (point marked 1*in Fig. 5). The solubility region is determined approximatelyby drawing a contour around the solute in the Teas diagram.In this case, the contour was sketched such that water is in-cluded inside the solubility region. Compounds situated in theclose vicinity of the solute are the most likely to dissolve it. Itcan be observed from Fig. 5 that glycols, alcohols and dihy-droxy aromatic compounds are among the suitable solvents forsodium phenoxide, which confirms the results from the solventdesign step and is consistent with the solvents reported in theliterature.

Molecular weight and liquid density are input data requiredby the DFT solvation calculations as solvent specifications;hence these properties are also evaluated during the solventdesign runs. The dielectric constant is also an input parameter

6204 I. Stanescu, L.E.K. Achenie / Chemical Engineering Science 61 (2006) 6199–6212

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.9

<delta >H

<delta >P

<delta >D

2423

1112

9

13

6

1514

17

16

24

7

84 19

9

21

1822

3

20

1

1*

1*- Sodium Salicylate (calc.)2- Water 3- Xylene 4- Methanol 5- Ethanol 6- 1-Butanol 7- Phenol 8- Ethylene glycol 9- Diethylene glycol 10- Propylene glycol 11- Glycerol 12- 1,3,5-Pentanetriol 13- Cyclopropanediol 14- Pyrogallol 15- o-Hydroquinone 16- Resorcinol 17- Acetone 18- Diisobutylketone 19- 1,4-Dihyroxy-2-butanone 20- Ethanol amine 21- Furfural 22- Salicylic acid 23-DMS 24- Dimethylsulfone

1 - Sodium Salicylate (exp.)

Fig. 5. Teas graph based on Hansen partial solubility parameters.

in Jaguar 4.2 solvation calculations; however, this property isnot available in ProCAMD. Consequently, dielectric constantswere estimated using ProPred 3.6 tool within ICAS (2004),based on Constantinou and Gani group-contribution technique(Constantinou et al., 1996).

The results from the solvent design step are presented inTable 4. All the acyclic compounds are listed together withtheir properties. Only one example of the cyclic compoundsand two examples of the aromatic compounds are given sincethese compounds cannot be found in common databases, mak-ing their properties unavailable and difficult to estimate, inparticular their dielectric constants. The cyclic compounds de-signed contain 2–3 hydroxyl groups or 2 hydroxyl groups and acarbonyl group, placed around small rings (3–4 carbon atoms).These cyclic compounds are likely to be strained and possi-bly unstable under the reaction conditions. The aromatic com-pounds contain 2–3 hydroxyl groups or 2 hydroxyl groupsand a carbonyl or carboxylic group, their functionalities be-ing similar to those of acyclic or cyclic compounds. Aromaticcompounds are oftentimes toxic, hence undesirable in a phar-maceutical process. Considering these factors, only the acycliccompounds were further analyzed with respect to their effectson the Kolbe–Schmitt reaction.

2.2.3. Methodology and results from solvation calculationsThe effect of each solvent on the geometries along the

reaction path was investigated by using an implicit solvent

technique. This requires specifying the solvent dielectric con-stant, molecular weight and density in the Jaguar 4.2 programpackage solvation tab. Jaguar (Jaguar 4.2 User’s Guide, 2002)uses a self-consistent reaction field (SCRF) method and aPoisson–Boltzmann solver to describe solvated structures. TheSCRF method first calculates the gas phase wave function andelectrostatic potential and then transfers the electrostatic po-tential into a set of atomic charges. The Poisson–Boltzmannsolver represents the solvent as a continuum of uniform dielec-tric constant, a layer of charges around the molecular surface,and determines the reaction field from the atomic charges. Thesolvent point charges thus derived are used in a new quantummechanical wave function calculation, repeating this procedureuntil self-consistency is achieved.

Solvation energies were computed for minimum-energy sol-vated structures and solvated transition states. Thus, the groundstates (reactants, product and intermediates) were optimizedin solution, while for the solvated transition states only singlepoint energy calculations were performed due to the consider-able computational effort. For example, when 1,2-ethanediol isused as solvent, the average CPU time for energy-minimizationof the ground states in solution was approximately 22,700 s,3.6 times the CPU time needed for the gas phase optimization.For the single point energy calculations of the solvated transi-tion states, the average CPU time was approximately 20,400 s,while transition state searches would require 30–50 iterationsto converge.

I. Stanescu, L.E.K. Achenie / Chemical Engineering Science 61 (2006) 6199–6212 6205

Table 3Designed solvents using ProCAMD

Designed solvent Solubility �H �D �P Normal Normal Molecular Liquid Dielectricparameter (MPa1/2) (MPa1/2) (MPa1/2) melting boiling weight density constant(MPa1/2) point (K) point (K) (kg/kmol) (kg/dm3)

Acyclic compoundsNumber of compounds designed: 11711; Number of compounds selected: 9; Total time used to design: 0.85 s1,3-Propylene glycol 30.51 23.51 17.00 9.77 235.53 453.47 76.09 1.05 33.68Compound 2 2CH3 1CH2 1CH 1C 3OH 30.70 24.42 17.39 8.61 274.95 527.88 120.15 1.19 32.99a

Compound 3 1CH3 2CH2 2CH 3OH 30.85 24.27 17.19 8.51 268.97 533.19 120.15 1.18 32.37a

Compound 4 1CH3 3CH2 1C 3OH 31.16 24.47 17.86 8.64 281.91 533.25 120.15 1.20 34.17a

1,3,5-Pentanetriol 31.30 24.33 17.65 8.54 276.33 538.42 120.15 1.18 33.36a

1,4-Dihydroxy-2-butanone 31.37 22.35 18.07 12.43 275.35 510.72 104.10 1.24 35.59a

1,2,3-Butanetriol 32.86 26.50 17.33 10.14 261.87 518.82 106.12 1.24 34.10a

Glycerol (1,2,4-Butanetriol) 33.37 26.57 17.89 10.19 269.74 524.43 106.12 1.25 37.62a

1,2-Ethanediol 33.48 26.74 17.16 12.64 225.56 431.87 62.07 1.11 37.7

Cyclic compoundsNumber of compounds designed: 122 866; Number of compounds selected: 10; Total time used to design: 14.64 s1,2-Cyclopropanediol 34.40 27.28 15.81 13.15 223.12 438.77 74.08 1.38 b

Aromatic compoundsNumber of compounds designed: 3 416 848; Number of compounds selected: 41; Total time used to design: 39.82 so-Hydroquinone (1,2-Benzenediol) 30.10 16.82 20.04 8.01 371.39 592.30 180.20 1.24 b

Pyrogallol (1,2,3-Benzenetriol) 30.94 17.32 20.50 8.21 371.39 603.67 180.20 1.24 b

aEstimated using ProPred 3.6;bDielectric constants not available. Difficulties in estimating their values.

Table 4Potential energy of the solvated geometries (HF)

Solvent Methanol Ethanol 1-Butanol Ethylene glycol Glycerol

StructureCO2 −188.58660537639 −188.58641264511 −188.58619013033 −188.58661089363 −188.58663372578PhONa −307.26738984264 −307.26389850918 −307.25838820476 −307.26773993709 −307.26707110702

Reactants (A) −495.85399521903 −495.85031115429 −495.84457833509 −495.85435083072 −495.85370483280B −495.87263767809 −495.86984110472 −495.86377939579 −495.87245645537 −495.87363535774o-TS1 −495.82195448393 −495.81845444750 −495.81443250333 −495.82140382598 −495.82120881401C −495.83868274771 −495.83126221793 −495.82517303152 −495.83527368333 −495.83399758800TS2 −495.81163203388 −495.80841437079 −495.80423368283 −495.81149608253 −495.81134600266D −495.83500927258 −495.83006881325 −495.82394319247 −495.83428735933 −495.83332071755TS3 −495.73692069282 −495.73354983520 −495.72990018607 −495.73664766833 −495.73638360987E −495.87536549901 −495.87169819725 −495.87169819725 −495.87531104679 −495.87343782360

Solvent Diisobutyl ketone 1,3-Propylene glycol 1,4-Dihydroxy-2-butanone

StructureCO2 −188.58776691990 −188.59006896961 −188.58657290023PhONa −307.24634904996 −307.26637584784 −307.26566314691

Reactants (A) −495.83411596986 −495.85293283685 −495.85223604714B −495.84828111400 −495.87213657768 −495.87219948488o-TS1 −495.80449191321 −495.82010071643 −495.82032667732C −495.81443295991 −495.83311720263 −495.83253288356TS2 −495.79380406257 −495.81040149448 −495.81044150219D −495.81175929135 −495.83236367794 −495.83206527937TS3 −495.71970202956 −495.73550482782 −495.73545254629E −495.85324099972 −495.87223713398 −495.87161871254

Results from DFT calculations.

DFT solvation calculations were performed using solventsreported in the literature (Table 2) and the designed solvents forwhich the necessary data were available (Table 3). The energies

for each solvated structure along the reaction path are presentedin Table 4, and a graphical example is presented in Fig. 6 forthe case of methanol.

6206 I. Stanescu, L.E.K. Achenie / Chemical Engineering Science 61 (2006) 6199–6212

E

TS3

DTS2C

o-TS1

B

A

E

TS3

DTS2o-TS1

B

A C

-495.90

-495.85

-495.80

-495.75

-495.70

-495.65

-495.60

-495.55

-495.50

Reaction coordinate

En

erg

y (H

F)

-585.87

-385.87

-185.87

14.13

214.13

414.13

Rel

ativ

e E

ner

gy

(kca

l/m

ol)

No Solvent Solvent: Methanol

Fig. 6. Energy diagram for Kolbe–Schmitt reaction with methonal as solventand without solvent, respectively.

Table 5Thermodynamic properties of solvated structures: S (cal/mol K), H (kcal/mol) G (kcal/mol) and solvation energy (kcal/mol)

Solvent Methanol Ethanol 1-Butanol Ethylene Glycerol 1,3-Propylene 1,4-Dihydroxy- Diisobutylglycol glycol 2-butanone ketone

StructureCO2 S 51.7885 51.7900 51.7849 51.7911 51.7871 51.8209 51.7879 51.7823

H 3.4599 3.4603 3.4590 3.4605 3.4595 3.4688 3.4597 3.4584G −18.5444 −18.4547 −18.4538 −18.4549 −18.4542 −18.4592 −18.4543 −18.4533S.E. −2.6811 −2.6248 −2.5607 −2.6825 −2.6888 −2.7089 −2.6714 −2.4433

PhONa S 90.6425 87.3172 87.2947 90.3582 87.6886 90.4726 87.4746 93.803H 9.3035 9.9472 9.3352 9.2658 9.3959 9.2623 9.3656 9.1299G −29.0519 −27.6010 −27.6035 −28.9693 −27.7096 −29.0212 −27.6493 −30.2994S.E. −49.4639 −48.5127 −47.0230 −49.5298 −49.3421 −49.1841 −49.0455 −43.7396

Reactants (A) S 142.431 139.107 139.080 142.149 139.476 141.664 139.263 144.963H 12.763 13.408 12.794 12.726 12.855 11.521 12.825 12.588G −47.596 −46.056 −46.057 −47.424 −46.164 −42.025 −46.104 −48.753S.E. −52.145 −51.138 −49.584 −52.212 −52.031 −51.851 −51.717 −46.183

B S 110.3060 109.8415 113.8361 107.9298 109.2169 112.0213 111.8203 115.3116H 12.2233 12.2237 12.1826 12.1028 12.2000 12.3189 12.3089 12.2422G −34.4526 −34.2557 −35.9871 −33.5677 −34.0151 −35.0829 −35.0079 −36.5519S.E. −47.8947 −47.2821 −45.4546 −47.8581 −48.0195 −47.8763 −47.8941 −41.7096

o-TS1 S 118.3279 113.3600 113.9970 113.2606 119.5554 113.2751 119.2694 114.5049H 13.4270 13.4836 13.5112 13.4797 13.4973 13.4864 13.4897 13.5150G −36.6435 −34.4846 −34.7267 −34.4466 −37.0926 −34.4028 −36.9791 −34.9377S.E. −39.9398 −38.9191 −37.7602 −39.7736 −39.7270 −39.4028 −39.4709 −34.8453

C S 117.1783 116.9158 115.1133 114.8351 113.4456 120.0099 113.6554 117.8421H 13.7294 13.4825 13.2249 13.3069 13.5344 13.3228 13.3457 13.3832G −35.8547 −35.9905 −35.4853 −35.2856 −34.4701 −37.4594 −34.7476 −36.4817S.E. −41.8175 −39.8910 −38.3077 −41.0043 −40.9159 −37.4594 −44.9701 −35.4838

TS2 S 106.7144 103.0480 107.2198 106.9896 107.7994 106.7971 107.4585 106.7998H 12.3921 12.4595 12.4068 12.4048 12.4202 12.3948 12.4127 12.3933G −32.7641 −31.1453 −32.9633 −32.8679 −33.1951 −32.7964 −33.0584 −32.7990S.E. −42.5969 −41.6567 −40.4230 −42.5576 −42.5048 −42.2387 −42.2401 −37.3509

D S 110.7770 111.5654 111.0622 109.9111 116.0556 110.9953 116.6646 115.2498H 12.4580 12.4856 12.5062 12.4036 12.4948 12.4934 12.5035 12.4388G −34.4172 −34.7234 −34.4898 −34.1053 −36.6184 −34.4743 −36.8631 −36.3292S.E. −46.8171 −45.5436 −44.1130 −46.6422 −46.4876 −46.2548 −50.1413 −40.8395

TS3 S 109.0687 109.0722 108.8412 108.7968 109.4836 110.0625 109.1734 108.4086H 12.8274 12.8357 12.7996 12.8176 12.8376 12.8786 12.8264 12.7884G −33.3250 −33.3182 −33.2565 −33.2198 −33.4904 −33.6943 −33.3703 −33.0847S.E. −43.0795 −42.0951 −41.0593 −42.9949 −42.9257 −42.6711 −42.6551 −38.0478

E S 113.2792 110.2593 110.2593 111.2801 111.6464 112.2988 113.2596 109.6898H 11.9969 11.8862 11.8862 11.9568 12.0450 12.0146 12.0476 11.8838G −35.9372 −34.7700 −34.7700 −35.1313 −35.1982 −35.4047 −35.8783 −34.5314S.E. −43.6725 −42.7294 −42.7294 −43.6572 −43.1593 −42.8357 −46.4474 −37.6761

The results illustrate that the energies for all the solvatedgeometries are lower than that for the same structures in theabsence of solvent, demonstrating that the solvents stabilizethe species along the reaction path. As expected, polar solventshave greater impact on the reactive species’ energies (Table 4),thermodynamic properties and solvation energies (Table 5),and consequently on the reaction rate constants. In the caseswhere solvents have low dielectric constants, the differences inpotential energy are less significant, indicating that the struc-tures along the reaction path are less stable in these solvents.As illustrated in Fig. 7, all solvents reduce �G‡ for the firstreaction step, suggesting that the solvents would improve thisrate determining step. The second step, which proceeds prac-tically without an energy barrier in solid phase, shows a small

I. Stanescu, L.E.K. Achenie / Chemical Engineering Science 61 (2006) 6199–6212 6207

A

B

o-TS1

C

TS2

D

TS3

E

-50

-48

-46

-44

-42

-40

-38

-36

-34

-32

-30

Reaction coordinate

G (k

cal/

mol

)

No Solvent Solvent: MethanolEthanol 1-ButanolEthylene Glycol GlycerolDiisobutyl ketone 1,3-Propylene Glycol1,4-Dihydroxy-2-butanone

Fig. 7. Free Gibbs energy diagram for Kolbe–Schmitt reaction with solvents,and without solvent, respectively.

barrier with solvents like 1-butanol, 1,3-propylene glycol anddiisobutyl ketone. The �G‡ barrier also increases slightly inthe third step with methanol, 1,3-propylene glycol and glyc-erol as solvents, while ethanol appear to have a more importantimpact. In the fourth step �G‡ increases in the presence of di-isobutyl ketone, 1,4-dihydroxy-2-butanone and glycerol. Notethat the free Gibbs energy of sodium salicylate decreases for allsolvents, indicating that the product is stabilized in solution aswe anticipated. However, no direct conclusion can be derivedfor the solvent effects on the overall reaction rate and yield atthis point. A solvent’s performance will be determined by itsability to increase the rate constant, to displace the equilibriumtowards the product, and/or to improve mass transfer (the latternot being investigated in this study).

The thermodynamic properties of the species along theKolbe–Schmitt reaction path determined using DFT calcu-lations presented in Table 5 were used to calculate the rateconstants for each of the four elementary reaction steps.

2.3. Determination of rate constants and kinetic analysis

2.3.1. Rate constant estimation using transition state theoryIn order to perform a kinetic analysis of the Kolbe–Schmitt

reaction, the rate constants for each elementary step must bedetermined. Given the results from the DFT calculations, tran-sitional state theory was found to be the most suitable methodto estimate the rate constants (Foresman and Frisch, 1993).According to thermodynamic formulation of the conventionaltransition state theory (CTST) (Laidler, 1987), the rate constant

for an elementary reaction can be calculated as in Eq. (1)

k = kBT

he−�‡

G/RT = kBT

he−�‡

S/Re−�‡H/RT . (1)

Another formulation of the transition state theory, using po-tential energy surfaces and partition functions, was also tested.However, the results proved to be inconclusive, therefore it wasdetermined that using the thermodynamic formulation of CTSTwas the best approach for this research.

2.3.2. Kinetic modelConsidering the Kolbe–Schmitt reaction mechanism, the

overall reaction can be represented as a series of four consec-utive elementary steps, starting with the reactants and leadingto the product sodium salicylate, and also a parallel pathway,branching from intermediate B and leading to the sodium saltof para-hydroxybenzoic acid. The Kolbe–Schmitt carboxyla-tion is considered an equilibrium reaction (Ullmann’s Ency-clopedia, 1997; Moseley et al., 1955), thus all the elementarysteps are considered reversible as presented in Fig. 8.

When using sodium phenoxide as the starting material, theresulting salicylic acid is usually analyzed after hydrolysisof its sodium salt. Under the conditions of the present-dayindustrial process (150–160 ◦C and 5 atm), the product doesnot contain any other byproducts except for small amounts ofp-hydroxybenzoic acid, 2-hydroxy-isophthalic aid, 4-hydroxy-isophthalic acid and the un-reacted starting materials (Lindseyand Jeskey, 1957; Markovic et al., 2002; Jansen and Wolff,1983). Salicylic acid being the major product and only smallquantities of p-hydroxybenzoic acid being formed can beexplained if the reaction is considered thermodynamicallycontrolled. In this case, the transition state formed by theelectrophilic attack in the para position (p-TS1) is the earlytransition state having lower energy and leading to sodiumpara-hydroxybenzoate (called the kinetic product). On theother hand, the transition state formed by electrophilic attackin the ortho position (o-TS1) is the late transition state hav-ing higher energy and leading to sodium salicylate (called theequilibrium product). Taking into account that the experimen-tal residence times for the Kolbe–Schmitt reaction are high,normally between 0.5 and 25 h (Hales et al., 1954b; Lindseyand Jeskey, 1957; Ayres, 1966; Sarkar et al., 1973; Jansen andWolff, 1983; Kirk-Othmer Encyclopedia, 1991; Ullmann’s En-cyclopedia, 1997; du Pont, 1999; Rieckmann, 2004); it is mostlikely that the process is thermodynamically controlled and theequilibrium product (sodium salicylate) is the major product.

The kinetic analysis can therefore be simplified by disregard-ing the side reactions (Fig. 2) and the parallel pathway (for-mation of sodium p-hydroxybenzote product). This leads to aseries of four consecutive elementary steps (1, 2, 3 and 4 inFig. 8).

Also, for the purposes of the kinetic analysis, the reactionwas assumed to be pseudo-homogeneous and carried out in abatch manner, with no significant volume change in the reactionphase. Assuming that the first step is a second order reac-tion (bimolecular), and all the other steps are first order reac-tions (unimolecular), the kinetic model results in the following

6208 I. Stanescu, L.E.K. Achenie / Chemical Engineering Science 61 (2006) 6199–6212

PhONa + CO2 B C D E (Sodium Salicylate)

p-C ... Na (p-HBA) (Sodium p-hydroxybenzoate)

k1

k-1

k2

k-2

k3

k-3

k4

k-4

k5 k-5

Fig. 8. Series of consecutive and simultaneous reactions in the Kolbe–Schmitt reaction mechanism.

system of ordinary differential equations (ODEs) describing thevariation of concentrations for all the species involved in thereaction mechanism

d[PhONa]dt

= −k1[PhONa][CO2] + k−1[B], (2)

d[CO2]dt

= −k1[PhONa][CO2] + k−1[B], (3)

d[B]dt

= k1[PhONa][CO2] − k−1[B] − k2[B] + k−2[C], (4)

d[C]dt

= k2[B] − k−2[C] − k3[C] + k−3[D], (5)

d[D]dt

= k3[C] − k−3[D] − k4[D] + k−4[E], (6)

d[E]dt

= k4[D] − k−4[E]. (7)

The above system of ODEs was integrated numerically us-ing Matlab version 6.5.1 Release 13 (2003) (Matlab Manu-als, 1994–2004). Since the order of magnitude of different rateconstants can be significantly different, thus generating a stiff

Table 6Rate constants for elementary steps in the absence of solvent and in solution calculated according to the thermodynamic formulation of CTST

Solvent No solvent Methanol Ethanol 1-Butanol Ethylene glycol Glycerol

RateConstants (s−1)

k1 3.276142E + 05 1.597263E + 06 1.447883E + 07 5.549468E + 07 6.147515E + 05 4.685795E + 06k−1 2.372875E + 20 4.866998E + 19 5.369131E + 18 1.400832E + 18 1.264556E + 20 1.659030E + 19k2 1.128494E + 14 1.193465E + 14 1.157628E + 13 1.969181E + 12 2.507364E + 13 3.425771E + 14k−2 7.209632E + 13 2.252926E + 13 1.471070E + 12 3.576708E + 12 3.250611E + 12 1.994217E + 14k3 1.063935E + 12 2.234253E + 11 2.772570E + 10 4.392725E + 11 4.972890E + 11 1.935575E + 12k−3 9.576846E + 11 1.234459E + 12 1.251203E + 11 1.435170E + 12 2.023985E + 12 1.511688E + 11k4 1.750262E + 12 2.405375E + 12 1.658103E + 12 2.034160E + 12 3.075855E + 12 2.147649E + 11k−4 1.975273E + 13 3.946200E + 11 1.568482E + 12 1.457604E + 12 9.078372E + 11 1.156850E + 12

Solvent Diisobutyl ketone 1,3-Propylene glycol 1,4-Dihydroxy-2-butanone

RateConstants (s−1)

k1 4.404227E + 06 3.485350E + 06 1.638921E + 07k−1 1.765094E + 19 2.230443E + 19 4.743287E + 18k2 1.293115E + 12 4.133742E + 12 9.192894E + 13k−2 1.405737E + 12 2.448708E + 11 1.252797E + 14k3 1.104836E + 11 3.443233E + 10 1.182683E + 12k−3 1.324578E + 11 1.198755E + 12 9.554967E + 10k4 1.860449E + 11 3.487444E + 12 1.384684E + 11k−4 1.577990E + 12 1.024087E + 12 4.467318E + 11

system of ODEs, the ode23s and ode15s functions in Matlabwere used for integration.

2.3.3. ResultsApplying the thermodynamic formulation of the conventional

transition state theory, the rate constants for each of the fourconsecutive elementary steps considered in the Kolbe–Schmittreaction mechanism were determined. The set of rate constantswere calculated for the reaction with and without solvent, andare presented in Table 6.

The results of the kinetic analysis of the reaction withoutsolvent proved to be in good agreement with the experimentaldata (Fig. 9). Considering that in the classical Kolbe–Schmittprocedure the product is in the solid state, and thus in a separatephase than the reaction mixture, the last elementary step ofthe reaction was assumed irreversible. Using the rate constantsgiven by the thermodynamic formulation of TST, at 150 ◦C and4 atm, a 97% yield of salicylic acid would be obtained after6.41 h. This corresponds with the observed residence time forthe Kolbe–Schmitt reaction of 0.5–25 h for a yield up to 97%.

While the mechanism of the Kolbe–Schmitt reaction includesfour steps, Fig. 9 indicates that the reaction apparently proceedsin a single step. This can be explained by examining the

I. Stanescu, L.E.K. Achenie / Chemical Engineering Science 61 (2006) 6199–6212 6209

0 0.5 1 1.5 2 2.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Con

cent

ratio

ns

[PhONa][CO2][B][C][D][E]

Time [s] x 104

Fig. 9. Variation of concentrations in time for different structures along theKolbe–Schmitt reaction path.

reaction conditions and the values of the rate constants (Table6). In the classical approach, the chelate formation betweensodium phenolate and carbon dioxide under normal conditionsor at temperatures up to 120 ◦C requires a few hours for theabsorption of an equimolar quantity of CO2 (Hessler, 1907;Hales et al., 1954b; Lindsey and Jeskey, 1957; Kunert et al.,1997). Then, the reaction mixture is heated for another fewhours at 140–160 ◦C with additional carbon dioxide to con-vert the chelate into sodium salicylate. Jansen and Wolff (1983)suggested that the Kolbe–Schmitt reaction can be carried outin one step at temperatures above 165 ◦C instead of two dis-tinct steps, increasing pressure from 5 bar to about 8–10 barsduring the latter part of the reaction. This procedure allowsthe introduction of carbon dioxide at a higher rate, the stoi-chiometric amount being reacted in a shorter period of time(1–6 h instead of 10–25 h). For our calculations we consideredreaction conditions of 150 ◦C and 4 atm for all the elemen-tary steps, including the chelate formation. In agreement withJansen and Wolff’s findings, the chelate (B) formed in the firststep under these conditions seems to be instantly converted intosodium salicylate, the overall reaction appearing as a single step(Fig. 9). While the overall reaction is slow, which can be at-tributed primarily to the lower rate constant for the first step,the intermediates (C and D) disappear very fast after they form.This may explain why there is a controversy surrounding thestructure of these intermediates and very little empirical evi-dence of their presence in the reaction mixture.

In contrast to the solvent-free Kolbe–Schmitt reaction, theresults obtained in the presence of solvent indicate an increasein the reaction rate for the chelate formation, with a correspond-ing decrease in the rate of the reverse reaction (Table 6). Forthe second and third elementary steps, solvents have a smallimpact on the rate constants. However, these are fast steps andthey do not have a major influence on the overall reaction rate.The fourth step appears to be the key in the kinetic analysis todetermine the solvent effects on the Kolbe–Schmitt reaction.

In the absence of solvent, the fourth step of the mechanismcan be considered irreversible. Taking into account that mostsolvents were selected such that they will dissolve the product(sodium salicylate), creating a homogeneous reaction mixture,the assumption of irreversibility for the fourth reaction step isno longer valid when the solvent is present. If the irreversibilityassumption were valid, the overall reaction rates would sub-stantially improve for all the solvents studied; however, thisconclusion would contradict the empirical data, which indicatelow yields of salicylic acid when the reaction is carried outwith solvents (Table 2). Thus, in performing the kinetic analy-sis, the fourth elementary step was considered reversible in thepresence of solvent, the sodium salicylate product remainingin the reaction mixture. Solving the kinetic model shows thatno product is formed in the presence of solvents, even whenthe residence time is allowed to increase by a few orders ofmagnitude.

3. Discussion and conclusions

This work presents, to the best of our knowledge, the firsttheoretical kinetic study of the Kolbe–Schmitt reaction. Theavailable experimental data associated with this reaction in-clude only limited information, such as the amount or yieldof salicylic acid obtained after hydrolysis of sodium salicy-late under certain reaction conditions, and/or the correspond-ing residence time. No reaction rates data could be found inthe literature. Sarkar et al. (1973) presented their investigationsregarding the influence of different variables on the extent ofcarboxylation using sodium phenoxide as the starting material.Their study illustrates the variation of the conversion as a func-tion of residence time, presenting the experimental data in agraphical form, yet no rate expression was derived. A groupcontribution technique has been used by Ota (1976) to deter-mine the thermodynamic properties and analyze the equilib-rium of the Kolbe–Schmitt reaction, however, the alkali metalions were not included in the thermodynamic analysis. There-fore, the significant differences determined by the presence ofdifferent metal ions, in terms of reaction yield and productsdistribution, cannot be explained based on Ota’s work. Underthese circumstances, it is not possible to derive the rate con-stants empirically and compare them with theoretical findings,the only reference being the overall yield and residence time.

We proposed a theoretical methodology to study the kineticsof the Kolbe–Schmitt reaction and to determine the effects ofsolvents on this reaction. DFT calculations at B3LYP/lav3p**level of theory were performed to confirm the reaction mecha-nism, and to compute the energies and thermodynamic proper-ties of the optimized structures and transitions states along thereaction path. The results supported Markovic’s four-step reac-tion mechanism model (Markovic et al., 2002). Rate constantsfor each elementary step were estimated using the thermody-namic formulation of the conventional transition state theory,both in the absence and presence of solvent. The effect of sev-eral solvents reported in literature was investigated, the resultsbeing in good agreement with experimental data. This workgives a theoretical justification for previous empirical results,

6210 I. Stanescu, L.E.K. Achenie / Chemical Engineering Science 61 (2006) 6199–6212

confirming Isemer’s suggestion that solvents having low di-electric constant are more suitable for the carbonation of alkalimetal aryloxides. When low dielectric constant compounds areused as a reaction medium, however, the reaction is primar-ily taking place in suspension and the solvent is in reality adiluent.

A CAMD technique was employed to identify alternativesolvents capable of creating a homogeneous reaction mixture,while at the same time promoting the reaction. The most im-portant design criteria were considered to be the solubility pa-rameter, together with the melting and boiling points, selectedsuch that the solvent is capable of dissolving and stabilizing theproduct and is liquid under the reaction conditions. The resultsfrom the design step revealed that compounds containing 2–3hydroxyl groups or 2 hydroxyl groups and a carbonyl or car-boxyl group were potentially suitable solvents for sodium phe-noxide. Two of the designed solvents were found to be identicalwith compounds summarized by Lindsey and Jeskey (1957).Kinetic analysis of the reaction carried out in the presence ofthe designed solvents demonstrated that, although the solventsare capable of dissolving the product (sodium phenoxide) andimprove the reaction’s rate constants, there was no improve-ment in product yield. This can only be explained by reactionreversibility.

The results of this study point to the reversibility of the finalstep as being the key to Kolbe–Schmitt reaction product yield.In the classical solvent-free reaction procedure, the fourth stepof the reaction mechanism is irreversible. The presence of sol-vent, however, by retaining the product in the reactive phase,allows a reverse reaction that displaces the equilibrium towardsthe reactants. Our findings theoretically demonstrate that theeffect of solvents with high dielectric constants and high solu-bility parameters on the Kolbe–Schmitt reaction is not favor-able. Solvents with high dielectric constants, even though theycan increase reaction rates, tend to allow reversibility to such adegree that no product is obtained. For example, glycerol andglycol, the solvents studied that had the highest dielectric con-stants, yield no product (Table 2). Comparatively, the presenceof solvents having low dielectric constants, while resulting inhigher product yields, still favor the reversibility of the re-action’s final step for much of the product. They thus showsignificantly lower product yields than the traditional, solvent-free procedure. For example, when xylene is used, althoughthe reaction does not reach the high yields of up to 97% givenby the conventional Kolbe–Schmitt procedure, yields 33.5%(Table 2). These solvents, having low dielectric constantsand low solubility parameters, behave like dispersants for theorganic sodium salts and allow the reaction to proceed insuspension; under these conditions, the quantum mechanicalmodel is inadequate for the study of the reaction. For solventshaving an intermediate value of dielectric constant our kineticanalysis shows that, if the fourth step of the reaction is con-sidered reversible, no product is obtained. However, experi-mentally the salicylic acid yield is 7.5% in case of 1-butanoland 18.9% in case of diisobutyl ketone (Table 2). Therefore,we can conclude that a fraction of the product is likely toprecipitate from the reaction mixture, and for this fraction the

process can be considered irreversible. The other fractionremains in solution and undergoes reversible reaction. Theamount of salicylic acid obtained experimentally is thus deter-mined by the un-dissolved portion, the result of the reactiontaking place in suspension, where the fourth step is irreversible.For this case too, the proposed theoretical methodology cannotbe applied to reaction carried out in suspension, which is be-yond the scope of this study. In addition, given the insufficientsolubility data for organic salts such as sodium phenoxide andsodium salicylate, it is difficult to estimate the fractions ofreactant and product solvated and the fractions dispersed insuspension.

Some differences between experimental data and our theo-retical results may appear due to mass transfer limitations, sincethe Kolbe–Schmitt reaction can proceed with the sodium phe-noxide in solid or molten state, or in solution or suspension,when carbon dioxide gas is introduced under pressure. Carbondioxide diffuses into the liquid phase or is absorbed at the sur-face of the solid where the reaction takes place. The overallrate constant and residence time will be ultimately determinedby coupled kinetic and diffusion mechanisms, more investiga-tions being required to evaluate the influence of mass trans-fer. Diffusion effect on the Kolbe–Schmitt reaction has beeninvestigated only for 2-naphtol suspension in kerosene oil byPhadtare and Doraiswamy (1969). The parameters for the pro-posed model were derived empirically, and therefore cannotbe extended for other reactants and reaction conditions. An-other difficulty in studying the diffusion arises from the lackof available properties or estimation techniques for the organicsalts involved. Thus, for the purposes of this analysis, masstransfer was neglected, considering that the results of the ki-netic model are in satisfactory agreement with the experimentalevidence.

Future studies could improve the accuracy of the results byapplying an explicit solvent method or an implicit–explicitsolvent method such as those presented by Gregersen et al.(2005) or Mucsi et al. (2005). In these cases the computa-tional effort could be significantly higher and semi-empiricalalgorithms may be required. The consideration of explicit sol-vent model may alter the obtained results. Another possibledevelopment may be obtained by designing a combination ofsolvents capable of creating a phase split, separating a reactivephase from the phase containing the product. In other words,the aim would be to identify a solvent for sodium phenox-ide/carbon dioxide system and a second solvent for sodiumsalicylate, immiscible with the first solvent. This approachintroduces several difficulties. For example the solubility pa-rameter of sodium phenoxide is not available; however, it isprobably close to the solubility parameter of sodium salicylate.If a group contribution technique would be used to estimatethe solubility parameters for sodium phenoxide and sodiumsalicylate, the contributions of the Na+ ion will likely not bevery different, since it replaces an H atom from the –OH groupin phenol and from the –COOH group in salicylic acid. Notingthat phenol has a solubility parameter of 24.1 MPa1/2 (Barton,1991) and the estimated value for salicylic acid is 21.07 MPa1/2

(using ProPred 3.6), solubilities of the sodium salts of these

I. Stanescu, L.E.K. Achenie / Chemical Engineering Science 61 (2006) 6199–6212 6211

compounds will also be similar. Thus, a good solvent forsodium phenoxide will also dissolve sodium salicylate; and asolvent designed for sodium salicylate is likely to be misciblewith a solvent designed for sodium phenoxide. Under thesecircumstances, designing a combination of solvents to generatea phase split in the reaction mixture is probably not a realisticalternative.

Further investigations may consider estimating the effects ofother types of solvents, such as aprotic polar solvents, or ex-amining in more depth the solubility of alkali metal aryloxides,carbon dioxide and hydroxy aromatic acids salts in differentmedia. These studies could provide the means to calculate thefraction of product that precipitates from the reaction mixture.Additional insights may be obtained by employing more so-phisticated methods to evaluate the rate constants, by includ-ing side reactions in the kinetic analysis and by coupling masstransfer with the reaction kinetics. The latter must be supportedby experimental efforts to provide physical properties and dif-fusion data for alkali salts of aromatic compounds used in theKolbe–Schmitt reaction. Any solvent designed to improve prod-uct yields for the Kolbe–Schmitt reaction, however, must ad-dress the tendency of the solvents to allow reversibility duringthe reaction’s final step.

Notation

G free Gibbs energy, kcal mol−1

�‡G Gibbs free energy of reaction, kcal mol−1

h Planck constant = 6.626176E−34 J sH enthalpy, kcal mol−1

�‡H enthalpy of reaction, kcal mol−1

k rate constantkB Boltzmann constant = 1.380662E

−23 m2 kg s−2 K−1

R universal constant of gases = 1.987 cal mol−1

S entropy, cal mol−1K−1

�‡S entropy of reaction, cal mol−1K−1

S.E. solvation energy, kcal/molT temperature, KTm melting pointTb boiling point�H hydrogen bonding component of Hansen solubility

parameter, MPa1/2

�D dispersion component of Hansen solubilityparameter, MPa1/2

�P polar component of Hansen solubilityparameter, MPa1/2

Acknowledgements

The authors would like to thank Dr. Gani’s group at CAPEC(Department of Chemical Engineering, Technical University ofDenmark) for allowing us to use ICAS for the solvent designsection of this study.

References

Ayres, D.C., 1966. Carbanions in Synthesis. Oldbourne P., London,pp. 168-173.

Baine, O., Adamson, G.F., Barton, J.W., Fitch, J.L., Swayampati, D.R., Jeskey,H., 1954. The Kolbe–Schmitt reaction. II. The carbonation of phenols.Journal of Organic Chemistry 19, 510–514.

Barkley, L.B. (Monsanto Chemical Co.), 1958. Carboxylation of phenols. USPatent 2,824,892.

Barra, J., Pena, M.A., Bustamante, P., 2000. Proposition of group molarconstants for sodium to calculate the partial solubility parameters of sodiumsalts using the van Krevelen group contribution method. European Journalof Pharmaceutical Science 10, 153–161.

Barton, A.F.M., 1991. CRC Handbook of Solubility Parameters and OtherCohesion Parameters. second ed. CRC Press, Boca Raton, FL.

Churi, N., Achenie, L.E.K., 1996. Novel mathematical programming modelfor computer aided molecular design. Industrial & Engineering ChemistryResearch 35 (10), 3788–3794.

Constantinou, L., Bagherpour, K., Gani, R., Klein, J.A., Wu, D.T., 1996.Computer aided product design: problem formulations methodology, andapplications. Computers & Chemical Engineering 20, 685–702.

Dow Chemical Co., 1964. Salicylic acid and its alkali metal salts. BritishPatent 949,988.

Duvedi, A.P., Achenie, L.E.K., 1996. Designing environmentally saferefrigerants using mathematical programming. Chemical EngineeringScience 51 (15), 3727–3739.

Foresman, J.B., Frisch, Æ., 1993. Exploring Chemistry with ElectronicStructure Methods. second ed. Gaussian, Inc., Pittsburgh, PA.

Fry, D. J. (Ilford Ltd.), 1950. Hydroxy aromatic carboxylic acids. BritishPatent 638,196.

Furuya, M., Nagatomo, A., Wada, M. (Mitsui Toatsu Chemicals, Inc., Japan),1998. Preparation of hydroxybenzoic acids. European Patent 834,494 A1.

Gani, R., 1999–2004. ICAS Documentation. Computer aided processengineering center. Department of Chemical Engineering. TechnicalUniversity of Denmark, Lyngby, Denmark.

Gani, R., Nielsen, B., Fredenslund, A., 1991. A group contribution approachto computer-aided molecular design. A.I.Ch.E. Journal 37 (9), 1318–1332.

Gilman, H., Arntzen, C.E., Webb, F.J., 1945. Organometallic compounds inthe Kolbe and Reimer–Tiemann reactions. Journal of Organic Chemistry10, 374–379.

Gregersen, B.A., Khandogin, J., Thiel, W., York, D.M., 2005. Smooth solvationmethod for d-orbital semiempirical calculations of biological reactions.2. Application to transphosphorylation thio effects in solution. Journal ofPhysical Chemistry B 109 (19), 9810–9817.

Hales, J.L., Jones, J.I., Lindsey, A.S., 1954a. Mechanism of Kolbe–Schmittreaction. Chemistry & Industry 49.

Hales, J.L., Jones, J.I., Lindsey, A.S., 1954b. Mechanism of the Kolbe–Schmittreaction. I. Infrared studies. Journal of the American Chemical Society,Abstracts, 3145–3151.

Harper, P.M., Gani, R., 2000. A multi-step and multi-level approach forcomputer aided molecular design. Computers & Chemical Engineering 24,677–683.

Hessler, J.C., 1907. Some recent work in organic chemistry. Journal of theAmerican Chemical Society 29 (1), 88–89.

Hirao, I., Ota, K., Sueta, S., Hara, Y., 1967. Carboxylation of phenolderivatives. IV. Synthesis of p-hydroxybenzoic acid and salicylic acidfrom alkali phenoxides in N ,N -dimethylformamide. Yuki Gosei KagakuKyokaishi 25 (5), 412–416.

Jaguar 4.2. User’s guide, 2002. Schrodinger, Inc., Portland, OR.Jansen, G., Wolff, P., 1983. Chemical process. US Patent 4,376,867.Johnson, J.R., 1933. Abnormal reactions of benzylmagnesium chloride. II.

The mechanism of the o-tolyl rearrangement. Journal of the AmericanChemical Society 55, 3029–3032.

Kirk–Othmer Encyclopedia of Chemical Technology, 1991. Wiley, New York.Kolbe, H., 1860. Ueber Synthese der Salicylsaure. Ann. 113, 125.Kosugi, Y., Imaoka, Y., Gotoh, F., Rahim, M.A., Matsui, Y., Sakanishi, K.,

2003. Carboxylations of alkali metal phenoxides with carbon dioxide.Organic and Biomolecular Chemistry 1, 817–821.

6212 I. Stanescu, L.E.K. Achenie / Chemical Engineering Science 61 (2006) 6199–6212

Kunert, M., Dinjus, E., Nauck, M., Sieler, J., 1997. Structure and reactivityof sodium phenoxide. Following the course of the Kolbe–Schmitt reaction.Chemische Berichte/Recueil 130 (10), 1461–1465.

Laidler, K.P., 1987. Chemical Kinetics. third ed. Harper Collins Publishers,New York.

Lindsey, A.S., Jeskey, H., 1957. The Kolbe–Schmitt reaction. ChemicalReviews 57, 583–620.

Marcoulaki, E.C., Kokossis, A.C., 1998. Molecular design synthesis usingstochastic optimisation as a tool for scoping and screening. Computers &Chemical Engineering 22, S11–S18.

Markovic, Z., Engelbrecht, J.P., Markovic, S., 2002. Theoretical study ofthe Kolbe–Schmitt reaction mechanism. Zeitschrift für Naturforschung 57(9–10), 812–818.

Matlab Manuals, 1994–2004. MathWorks, Inc.Moseley, J.C., Edyvean, W., Hartley, J. (“Shell” Refining & Marketing Co.,

Ltd.), 1955. Aromatic hydroxy carboxylic acids. British Patent 738,359.Mucsi, Z., Szabo, A., Hermecz, I., Kucsman, A., Csizmadia, I.G., 2005.

Modeling rate-controlling solvent effects. The pericyclic Meisenheimerrearrangement of N -propargylmorpholine N -oxide. Journal of theAmerican Chemical Society 127 (20), 7615–7631.

Ota, K., 1976. Thermodynamic consideration for the Kolbe–Schmitt reactionby estimating methods of group contributions. Memoirs of the KyushuInstitute of Technology, Engineering 6, 165–175.

Phadtare, P.G., Doraiswamy, L.K., 1969. Kolbe–Schmitt carbonation of2-naphtol. Confirmation of the Mass Transfer Model and Process

Optimization. Industrial & Engineering Chemistry Process Design andDevelopment 8 (2), 165–173.

Rieckmann, T., 2004. Salicylic Acid. Fachhochschule Köln, University ofApplied Sciences Cologne, Department of Plant Design and ChemicalEngineering, MEng/Reaction Kinetics 〈www.av.fh-koeln.de/professoren/rieckmann/chemischeprozesstechnik/lab_na-phenolate/na-phenolate.html〉.

Sarkar, K., Maiti, B.R., Sen Gupta, P., Roy, N.C., 1973. Carboxylation ofsodium phenate to sodium salicycilate. Indian Journal of Technology 11(4), 187–188.

Schmitt, R., 1885. Beitrag zur kenntniss der Kolbe’schen salicyl-saure-synthese. Journal für Praktische Chemie 31, 397.

Ueno, R., Tetsuya, N. (Ueno Pharmaceutical Co.), 1974. Process for theproduction of p-hydroxybenzoic acid. US Patent 3,816,521.

Ullmann’s Encyclopedia of Industrial Chemistry, 1997. fifth ed. Wiley-VCH,Weinheim, Germany.

Venkatasubramanian, V., Chan, K., Caruthers, J.M., 1994. Computer-aidedmolecular design using genetic algorithms. Computers & ChemicalEngineering 18 (9), 833–844.

Wacker, A., 1932. Manufacture of aromatic oxy-carboxylic acids. BritishPatent 384,619.

Wang, Y., Achenie, L.E.K., 2002. Computer aided solvent design for extractivefermentation. Fluid Phase Equilibria 201 (1), 1–18.

Wideqvist, S., 1954. Some aspects of Kolbe’s synthesis of salicylic acid.Arkiv for Kemi 7 (26), 229–240.