\makeatletter \@ifundefined{HCode} {\documentclass[screen,CRCHIM,Unicode,Thematic]{cedram} \newenvironment{noXML}{}{} \def\tsup#1{$^{{#1}}$} \def\tsub#1{$_{{#1}}$} \def\ndash{\text{--}} \usepackage[T1]{fontenc} \def\thead{\noalign{\relax}\hline} \def\tbody{\noalign{\relax}} \def\endthead{\noalign{\relax}\hline} \def\xsection#1{} \def\tabnote#1{\vskip4pt\parbox{.98\linewidth}{#1}} \RequirePackage{etoolbox} \def\jobid{crchim20240110} %\graphicspath{{/tmp/\jobid_figs/web/}} \graphicspath{{./figures/}} \newcounter{runlevel} \let\MakeYrStrItalic\relax \csdef{Seqnsplit}{\\} \def\refinput#1{} \def\back#1{} \def\rmDelta{\Delta} \def\ubreak{\break} \let\Lbreak\break \def\botline{\\\hline} \def\mn{\phantom{$-$}} \def\0{\phantom{0}} \def\inlinefig#1{\includegraphics{#1}} \usepackage{multirow} \def\nrow#1{\@tempcnta #1\relax% \advance\@tempcnta by 1\relax% \xdef\lenrow{\the\@tempcnta}} \def\morerows#1#2{\nrow{#1}\multirow{\lenrow}{*}{#2}} \def\xmorerows#1#2{#2} \usepackage{hyperref} \DOI{10.5802/crchim.324} \datereceived{2024-02-19} \daterevised{2024-05-15} \datererevised{2024-06-17} \dateaccepted{2024-06-19} \ItHasTeXPublished } {\documentclass[crchim]{article} \usepackage[T1]{fontenc} \def\CDRdoi{10.5802/crchim.324} \let\newline\break \def\xmorerows#1#2{\morerows{#1}{#2}} \let\ubreak\relax \makeatletter \def\CDRsupplementaryTwotypes#1#2{} } \makeatother \usepackage{upgreek} \dateposted{2024-07-17} \begin{document} %\copyeditor{RK} \begin{noXML} %\makeatletter %\def\TITREspecial{\relax} %\def\cdr@specialtitle@english{French Network on Solvation (GDR 2035 SolvATE)} %\def\cdr@specialtitle@french{R\'eseau th\'ematique sur la solvatation (GDR 2035 SolvATE)} %\makeatother \CDRsetmeta{articletype}{research-article} \title{On the phase behavior of sorbitol/water/H\textsubscript{2}/CO\textsubscript{2} mixtures at high pressures and temperatures by in~situ infrared spectroscopy} \alttitle{Thermodynamique des m\'{e}langes sorbitol/eau/H\textsubscript{2}/CO\textsubscript{2} \`{a} haute pression et haute temp\'{e}rature par spectroscopie infrarouge in situ} \author{\firstname{Isaline} \lastname{Bonnin}} \address{Institut des Sciences Mol\'{e}culaires (ISM), Univ. Bordeaux, CNRS, Bordeaux INP, ISM, UMR 5255, F-33400 Talence, France} \address{Institut de Chimie des Milieux et Mat\'{e}riaux de Poitiers (IC2MP), Univ. de Poitiers, UMR CNRS 7285, 1 rue Marcel Dor\'{e}, 86073 Poitiers Cedex 9, France} \author{\firstname{Rapha\"{e}l} \lastname{Mereau}\CDRorcid{0000-0002-0357-4654}} \addressSameAs{1}{Institut des Sciences Mol\'{e}culaires (ISM), Univ. Bordeaux, CNRS, Bordeaux INP, ISM, UMR 5255, F-33400 Talence, France} \author{\firstname{Karine} \lastname{De Oliveira Vigier}\CDRorcid{0000-0003-3613-7992}} \addressSameAs{2}{Institut de Chimie des Milieux et Mat\'{e}riaux de Poitiers (IC2MP), Univ. de Poitiers, UMR CNRS 7285, 1 rue Marcel Dor\'{e}, 86073 Poitiers Cedex 9, France} \author{\firstname{Thierry~}\lastname{Tassaing}\CDRorcid{0000-0003-4114-170X}\IsCorresp} \addressSameAs{1}{Institut des Sciences Mol\'{e}culaires (ISM), Univ. Bordeaux, CNRS, Bordeaux INP, ISM, UMR 5255, F-33400 Talence, France} \email[T. Tassaing]{thierry.tassaing@u-bordeaux.fr} \shortrunauthors \thanks{Region Nouvelle Aquitaine, University of Poitiers, MITI of CNRS, INCREASE Federation, GDR 2035 SolvATE} \begin{abstract} The thermodynamic behavior of multi-component system, which includes sorbitol dissolved in water under CO\textsubscript{2} and H\textsubscript{2} pressure, is investigated by {in situ} infrared spectroscopy. Our study focuses on the gas phase of binary, ternary, and quaternary systems at temperatures ranging from 40~\textdegree{}C to 220~\textdegree{}C and at CO\textsubscript{2} pressures between 30 and 120 bar, while maintaining a constant pressure of H\textsubscript{2} at 30 or 60 bar. The influence of addition of sorbitol in the liquid aqueous phase and of H\textsubscript{2} in the CO\textsubscript{2}-rich gas phase on the mutual solubility of CO\textsubscript{2} and water is evaluated. In our experimental conditions (\textit{T}< 220~\textdegree{}C and \textit{P}< 120 bar), it is found that in such multi-component system, a water-rich liquid phase always coexists with a CO\textsubscript{2}-rich gas phase. Presence of sorbitol in the water-rich phase and H\textsubscript{2} in the CO\textsubscript{2}-rich phase has a limited impact on the mutual solubility of water and CO\textsubscript{2}. Furthermore, sorbitol is not soluble in the CO\textsubscript{2}-rich phase and instead remains in the water-rich liquid phase over the thermodynamic range investigated. \end{abstract} \begin{altabstract} Le comportement thermodynamique du syst\`{e}me multi-composants, qui comprend du sorbitol dissous dans l'eau sous pression de CO\textsubscript{2} et H\textsubscript{2}, est \'{e}tudi\'{e} par spectroscopie infrarouge in situ. Notre \'{e}tude se concentre sur la phase gazeuse des syst\`{e}mes binaires, ternaires et quaternaires dans une large gamme de temp\'{e}ratures allant de 40~\textdegree{}C \`{a} 220~\textdegree{}C et sous une pression de CO\textsubscript{2} comprise entre 30 bar et 120 bar, tout en maintenant une pression constante de 30 ou 60 bar de H\textsubscript{2} L'influence de l'addition de sorbitol dans la phase aqueuse liquide et de H\textsubscript{2} dans la phase gazeuse riche en CO\textsubscript{2} sur la solubilit\'{e} mutuelle du CO\textsubscript{2} et de l'eau est \'{e}valu\'{e}e. Dans nos conditions exp\'{e}rimentales (\textit{T}< 220~\textdegree{}C et \textit{P}< 120 bar), nous constatons que dans un tel syst\`{e}me multi-composants, une phase liquide riche en eau coexiste toujours avec une phase gazeuse riche en CO\textsubscript{2}. La pr\'{e}sence de sorbitol dans la phase riche en eau et de H\textsubscript{2} dans la phase riche en CO\textsubscript{2} a un impact limit\'{e} sur la solubilit\'{e} mutuelle de l'eau et du CO\textsubscript{2}. De plus, le sorbitol n'est pas soluble dans la phase riche en CO\textsubscript{2} et reste dans la phase liquide riche en eau dans la gamme thermodynamique \'{e}tudi\'{e}e. \end{altabstract} \keywords{\kwd{Sorbitol} \kwd{CO\textsubscript{2}} \kwd{Hydrogen} \kwd{Water} \kwd{High pressures} \kwd{Infrared spectroscopy}} \altkeywords{\kwd{Sorbitol} \kwd{CO\textsubscript{2}} \kwd{Hydrog\`{e}ne} \kwd{Eau} \kwd{Hautes pressions} \kwd{Spectroscopie infrarouge}} \maketitle \vspace*{20pt plus 1pt minus 1pt} \twocolumngrid \end{noXML} \section{Introduction} In the context of biomass valorization towards substitution of petroleum-based materials, sorbitans represent bio-sourced alternatives to a large number of petroleum-based molecules; and can be used in a wide range of applications such as additives, pharmaceuticals and monomers for polymer industries~\cite{1,2,3,4}. In particular, the hydrogenation of glucose into sorbitol and the dehydration of sorbitol with various catalytic systems have been studied in depth~\cite{5,6}. However, the synthesis of these diols remains, to this day, a technological challenge due to the cost of energy-consuming processes, use of expensive and toxic solvents as well as the intensive \mbox{purification} steps. To this regard, it is worthwhile to develop ``one-pot'' protocols for the obtention of sorbitans starting from glucose combining heterogeneous catalytic hydrogenation and an acid-catalyzed dehydration reaction~\cite{5,7}. Conventionally, strong mineral acids are used and they limit the selective obtention of sorbitans to favor its dehydration to isosorbide (produced by double dehydration of sorbitol). Being non-toxic and non-corrosive, gaseous CO$_{2}$ has attracted attention in replacing environmentally unsafe mineral acid catalysts thanks to the reversible control of reaction mixture's~pH. In order to study this one-pot reaction (hydrogenation and dehydration), we combined in situ spectroscopic analysis with molecular modeling to better understand the mechanisms and the kinetics in the formation of different reactions' intermediates~\cite{8,9,10}. However, the thermodynamics of these multi-component mixtures are not clearly known. We recall that the aqueous dehydration of sorbitol was performed under H$_{2}$ and CO$_{2}$ pressure (between 30 and 120 bar); and at high temperature (up to 220~\textdegree{}C). The phase behavior and the mutual solubility of all the components of this multi-component mixture depend strongly upon the pressure/temperature conditions which in turn can significantly influence the selectivity and yield of the sorbitans synthesis during hydrogenation and dehydration occurring in the liquid phase. The aim of this paper is to determine the thermodynamic behavior of binary, ternary, and quaternary systems composed of sorbitol/water/H$_{2}$/CO$_{2}$ at temperatures ranging from 40~\textdegree{}C to 220~\textdegree{}C; at CO$_2$ pressure between 30 bar to 120 bar; H$_{2}$ pressure at 30 or 60 bar. Additionally, we have focused our investigation on the gas phase using infrared spectroscopy which performs well {in situ} and {in operando} investigations. Of particular note, the evolution of the intensity of selected vibrational modes of CO$_{2}$ and H$_{2}$O have also been analyzed as a function of temperature and pressure in order to determine the evolution of H$_{2}$O and CO$_{2}$ concentrations in binary, ternary, and quaternary mixtures. From the results obtained, it was possible to show that in such multi-component system, a water-rich liquid phase coexists with a CO$_{2}$-rich gas phase under our experimental conditions ($T < 220$~\textdegree{}C and $P < 120$ bar). In addition, it was found that sorbitol remains in the water-rich liquid phase over the thermodynamic range investigated.\looseness=-1 \section{Experimental setup} \subsection{High pressure in situ infrared absorption setup} The {in situ} analysis of sorbitol--water--CO$_{2}$--H$_{2}$ mixture was done with IR spectroscopy in one\break high-pressure cell ({Figure~\ref{fig1}}). Due to strong absorption of water, the liquid-phase analysis is best performed using ATR-FTIR equipment which can withstand high temperature and pressure. Due to the lack of such equipment, we have focused our study on the gas phase using a home made HP cell which can withstand high temperature of about 250~\textdegree{}C and pressure up to 20 MPa. The home-made stainless-steel cell is composed of three cylindrical windows (one sapphire window for visual observation and two silicon windows for IR absorption with a pathlength of 26 mm). Windows were positioned on the flat surface of an inconel plug with a Kapton foil placed between the window and the plug to compensate for imperfections at the two surfaces (unsupported area principle). Flat Kapton rings were used to ensure sealing between the plug and the cell body. Heating was achieved using four cartridge heaters inside the body of the cell and a thermocouple located close to one cartridge was used to regulate the temperature with an accuracy of ${\rmDelta}T = \pm 0.5$~\textdegree{}C. The cell was connected via a stainless capillary to a pressurizing system which allows the regulation of pressure with an accuracy of $\rmDelta P = \pm 0.1$ bar. \begin{figure*} {\vspace*{1pt}} \includegraphics{fig01} \caption{\label{fig1}Design of the high-pressure experimental device with a high-pressure cell coupled with IR spectrometer for the {in situ} measurements of the CO$_{2}$-rich phase of the sorbitol/water/H$_{2}$/CO$_{2}$ mixtures.} \end{figure*} For IR absorption measurements, a Nicolet 6700 FTIR spectrometer equipped with a Globar source, a KBr/Ge beamsplitter and a DLaTGS/KBr thermal detector was used to determine the spectral range, from 400 to 6500 cm$^{-1}$. Single beam spectra with 4 cm$^{-1}$ resolution were obtained by Fourier transformation of 100 accumulated interferograms in order to improve the signal to noise ratio. \subsection{Experimental procedure} For the quaternary mixture, the lower part of the cell was filled with 1~ml of an aqueous solution of 30 wt\% of sorbitol (purchased from Sigma Aldrich (${>}$98\% purity)). The experiments were performed by initially adding a predetermined pressure of H$_{2}$ (purchased from Air Liquid (99.9999\% purity)); CO$_{2}$ (purchased from Air Liquid (99.95\% purity)) was then added to this high-pressure cell using a manual pump (TOP industrie) up to the desired pressure. We mention that the notation 30/30 bar CO$_{2}$/H$_{2}$ means that 30~bar of H$_{2}$ is introduced and then the cell was filled with CO$_{2}$ until the total pressure reached 60 bar. Making the hypothesis that both CO$_{2}$ and H$_{2}$ behave as ideal gases and that their pressures can be added, we assumed that 30 bar of CO$_{2}$ was added to the cell. The cell volume (8~ml) is fixed and only the pressure can be adjusted. {\vspace*{3pt}} \subsection{Infrared absorption spectra and calibration} {\vspace*{3pt}} {Figure~\ref{fig2}} illustrates (for the case of a binary H$_{2}$O/CO$_{2}$ mixture) the spectral changes of the infrared absorption spectra in the CO$_{2}$-rich phase that occur with an increase of the temperature from 40 to 220~\textdegree{}C at a constant pressure of 60 bar. \begin{figure*} \includegraphics{fig02} \caption{\label{fig2}Infrared spectra of the CO$_{2}$-rich phase of the H$_{2}$O--CO$_{2}$ binary system at a constant pressure of CO$_{2}$ of 60 bar; and temperature from 40~\textdegree{}C to 220~\textdegree{}C.} \end{figure*} In that region, fundamental and combination bands of CO$_{2}$ and H$_{2}$O were observed. However, only the spectral range between 2500 and 3200 cm$^{-1}$, and between 4500 and 7500 cm$^{-1}$ are of interest for our purpose under our experimental conditions. Indeed, the strong absorption of CO$_{2}$ and H$_{2}$O precludes any quantitative analysis outside this spectral range. For CO$_{2}$, the region from 4750 to 5200 cm$^{-1}$ with overlapping peaks of CO$_{2}$ at 4800 cm$^{-1}$, 4950~cm$^{-1}$ and 5100 cm$^{-1}$ are of interest and correspond to the combination modes $4\nu _{2}+ \nu _{3}$, $\nu _{1}+ 2\nu _{2}+ \nu _{3}$ and $2\nu _{1}+ \nu _{3}$, respectively. $\nu _{1}$, $\nu _{2}$ and $\nu _{3}$ are the fundamental vibrational modes of CO$_{2}$ with \mbox{symmetric} stretch, bending mode and antisymmetric stretch, respectively~\cite{11,12,13,14}. The weak peak observed at 6950 cm$^{-1}$ is assigned to the $3\nu _{3}$ overtone of~CO$_{2}$.\looseness=-1 For H$_{2}$O, the band at 1600 cm$^{-1}$ which is saturated at temperatures above 120~\textdegree{}C is related to the bending mode $\nu _{2}$ of water~\cite{15}. The profile at 5300~cm$^{-1}$ having an increasing intensity with the temperature, is assigned to the $\nu _{2}+ \nu _{3}$ combination mode of water~\cite{16,17}. In 7000--7500 cm$^{-1}$ spectral range, the profile with a doublet structure observed at 7200~cm$^{-1}$ with an enhanced intensity with temperature is assigned to the $2\nu _{3}$ overtone of water. In order to quantify the concentration of CO$_{2}$, we selected the vibrational mode $2\nu _{1}+ \nu _{3}$ of CO$_{2}$ and determined its epsilon value from its integrated area (from 4900 to 4740 cm$^{-1}$). This was selected as it negligibly overlaps with any contribution of water. We, then measured the infrared absorption spectra of neat gaseous CO$_{2}$ at constant pressures of 30, 60 and 120 bar at 40, 80, 120, 160, 200 and 220~\textdegree{}C. Knowing the concentration of CO$_{2}$ (in mol${\cdot}$L$^{-1}$) from the NIST database (NIST Chemistry Webbook~\cite{18}), the pathlength of the cell ($l$) and measuring the integrated area ($A$) in 4900 to 4740 cm$^{-1}$ range; the molar extinction coefficient (epsilon $=$\ $\varepsilon{}$) values are then calculated by applying the Beer--Lambert law: $A = \varepsilon\cdot l\cdot c$ (see Table~\ref{tab1}). For all temperatures and pressures, it can be seen that there is a significant variation of the epsilon values with increase in pressure. Hence, these values are used as reference for the same given temperature and pressure to determine CO$_{2}$ concentration in all analyzed mixtures. \begin{table*} \caption{\label{tab1} Molar extinction coefficients (in L${\cdot}$mol$^{-1}{\cdot}$cm$^{-2}$) of the $2\nu_{1}+ \nu_{3}$ mode of CO$_{2}$~integrated in 4900 to 4740 cm$^{-1}$ range} \begin{tabular}{lcccccc} \thead & {40~\textdegree{}C} & {80~\textdegree{}C} & {120~\textdegree{}C} & {160~\textdegree{}C} & {200~\textdegree{}C} & {220~\textdegree{}C} \\ \endthead {30 bar CO}$_{2}$ & 2.010 & 2.101 & 2.114 & 2.014 & 1.931 & 1.806 \\ {60 bar CO}$_{2}$ & 1.916 & 2.013 & 1.970 & 1.903 & 1.791 & 1.675 \\ {120 bar CO}$_{2}$ & 1.341 & 1.645 & 1.688 & 1.646 & 1.532 & Saturate \botline \end{tabular} \end{table*} By the same token, to quantify the concentration of water, selecting a vibrational mode of water and determining its epsilon value is required. In water--CO$_{2}$ mixtures, the molar fraction of CO$_{2}$ can be calculated from the concentration of CO$_{2}$ and water. We selected the $\nu_{2} + \nu_{3}$ combination mode of water and used its integrated area from 5800 to 5347 cm$^{-1}$ to calculate the concentration of water. We emphasize that only the high frequency wing of the mode of water has been considered for integration as the low frequency range is superimposed with a contribution of CO$_{2}$. Then, the epsilon of this band associated with water is fitted to obtain an experimental molar fraction of water calculated from the experimental water and CO$_{2}$ concentration, that is consistent with the molar fraction in the literature~\cite{19,20}. As shown in the {Figure~\ref{fig3}}, a good fit is obtained in the whole temperature and pressure range specific to this study when a unique epsilon value of water is used and found to be equal to 140~L${\cdot}$mol$^{-1}{\cdot}$cm$^{-2}$. Thus, we have evaluated a relative uncertainty of ${\pm}$5\% on the concentration measurements using our setup and data processing methodology. \begin{figure} %\vspace*{-2pt} \includegraphics{fig03} %\vspace*{-2pt} \caption{\label{fig3}Comparison of the molar fraction of CO$_{2}$ in the CO$_{2}$-rich phase of H$_{2}$O--CO$_{2}$ mixtures calculated from our infrared spectra with literature data.} %\vspace*{-4pt} \end{figure} Finally, it is worth noting that if sorbitol is soluble in the CO$_{2}$-rich phase, one should observe a peak in the alkane region (in the range 2800--3000 cm$^{-1}$) related to C--H stretching vibrations with a detection limit of about 10$^{-4}$--10$^{-5}$\ $g_{\mathrm{sorbitol}}/g_{\mathrm{CO}_{2}}$. We emphasize that the initial total amount of sorbitol is excessive in comparison to the minimum amount of sorbitol that could be detected. In a few experiments, the collision-induced IR spectral band of H$_{2}$ is also observed at about 4150~cm$^{-1}$ (see Figures~\ref{fig5} and~\ref{fig12} in the results and discussion section). This band has been reported previously for H$_{2}$ diluted in monoatomic gases under high pressure conditions~\cite{21,22}. Indeed, as the H$_{2}$ stretching vibration is inactive in IR spectroscopy, the observed H$_{2}$ spectrum in the CO$_{2}$-rich phase is due to an induced dipole moment of the H$_{2}$ molecule that results from its interaction with the surrounding CO$_{2}$ molecules. Therefore, the induced molar extinction coefficient of the H$_{2}$ peak strongly depends on the temperature and pressure and precludes the use of this peak for quantitative analyses~\cite{23}. \section{Results and discussion} \subsection{H$_2$O--CO$_{2}$ binary system} Preliminary studies are done in H$_2$O--CO$_{2}$ binary system to analyze the influence of water on the CO$_{2}$ concentration in the CO$_{2}$-rich phase based on the pressure of CO$_{2}$ and temperature. Infrared spectra of the gas phase of the binary system are illustrated in {Figure~\ref{fig2}} and has been described in earlier sections. Beer--Lambert law is applied to determine the evolution of the concentration of CO$_{2}$ in the CO$_{2}$-rich phase of the H$_{2}$O--CO$_{2}$ binary mixture and compare it with the concentration of neat CO$_{2}$ in the same thermodynamic range from 40 to 220~\textdegree{}C at constant CO$_{2}$ pressures (30, 60 and 120 bar as shown in {Figure~\ref{fig4}}). \begin{figure} \includegraphics{fig04} \caption{\label{fig4}Temperature versus CO$_{2}$ concentration at constant pressure in neat CO$_{2}$ and in the CO$_{2}$-rich phase of the binary system H$_{2}$O--CO$_{2}$.} \end{figure} Looking initially at CO$_{2}$ alone ({Figure~\ref{fig4}}, dotted lines), it can be inferred that the concentration of CO$_{2}$ gas decreases when the temperature rises. This~effect is very pronounced at high pressure of 120~bar and less marked at 60 and 30 bar. In the presence of water ({Figure~\ref{fig4}}, solid line), the same effect is observed but between 160 and 220~\textdegree{}C, the concentration of CO$_{2}$ decreases further. This effect can be explained by two phenomena: as temperature increases, CO$_{2}$ dissolves in water and consequently, its concentration in the gas phase decreases and concomitantly, water is ``evaporated'' in the gas phase leading to a decrease in CO$_{2}$ concentration. Both phenomena governing the mutual solubility of water and CO$_{2}$ are consistent with data reported in the literature~\cite{19,20}. \begin{figure*} \includegraphics{fig05} \caption{\label{fig5}Infrared spectra of the binary system CO$_{2}$--H$_{2}$ at 90 bar from 40~\textdegree{}C to 220~\textdegree{}C.} \end{figure*} \subsection{CO$_2$--H$_2$ binary system} The evolution of the infrared spectra of the binary mixture CO$_{2}$/H$_{2}$ (30 bar/60 bar) with temperature is elucidated in {Figure~\ref{fig5}}. We emphasize that above the critical point of CO$_2$, the binary mixture H$_{2}$/CO$_{2}$ displays only one gas phase as previously reported in thermodynamic studies on H$_{2}$/CO$_{2}$ mixtures~\cite{24,25,26}. Interestingly, a barely detectable band at 4100 cm$^{-1}$ in neat H$_{2}$ is clearly observed after adding CO$_{2}$ in the cell at 40~\textdegree{}C. Then, its intensity decreases continuously as the temperature rises. This band is assigned to the vibrational stretching mode (vibron) of H$_{2}$ interacting with surrounding CO$_{2}$ molecules and the effect of CO$_{2}$ on this band has been discussed by our group in a recent article~\cite{23}. As the intensity of this band is related to ``induced'' effects, it is not possible to accurately calculate the concentration of H$_{2}$ in the mixture. However, in order to determine the effect of H$_{2}$ on the CO$_{2}$ concentration, we determined the evolution of the concentration of CO$_{2}$ in the H$_{2}$--CO$_{2}$ binary mixture and compared it with the concentration of neat CO$_{2}$ in the same thermodynamic range (from 40 to 220~\textdegree{}C) at constant pressures of CO$_{2}$ (30 and 60~bar) as shown in Figure~\ref{fig6}. The concentration of CO$_{2}$ appears to decrease at 60 bar of H$_{2}$ (yellow line in Figure~\ref{fig6}), while at 30 bar (of H$_{2}$) negligible effect is observed (grey line in Figure~\ref{fig6}). When the pressure of CO$_{2}$ is doubled from 30 to 60 bar while keeping the pressure of H$_{2}$ at 30 bar results in a weak decrease of the concentration of CO$_{2}$ in comparison with neat CO$_{2}$ at low temperature (below 120~\textdegree{}C). This effect could be attributed to the intermolecular interactions between H$_{2}$ and CO$_{2}$ as evidenced by ``induced'' effects on the vibrational stretching mode of H$_{2}$. \begin{figure} \includegraphics{fig06} \caption{\label{fig6}Temperature versus CO$_{2}$ concentration at constant pressure in neat CO$_{2}$ and in the CO$_{2}$-rich phase of the binary system CO$_{2}$--H$_{2}$.} \end{figure} \subsection{H$_2$O--CO$_2$--H$_2$ ternary system} The binary system comprising CO$_{2}$ and H$_{2}$ is compared to the ternary system where water is added to the high-pressure cell at a given pressure of H$_{2}$ and CO$_{2}$ ({Figure~\ref{fig7}}). At temperatures below 150~\textdegree{}C, concentration of CO$_{2}$ in the H$_{2}$/CO$_{2}$ binary mixture is similar to that of the ternary mixture with water. However, at temperatures above 150~\textdegree{}C, a significant decrease in CO$_{2}$ concentration is observed in the CO$_{2}$-rich phase of the ternary mixture when compared to CO$_{2}$-rich phase of the binary system \mbox{CO$_{2}$--H$_{2}$.} \begin{figure} \includegraphics{fig07} \caption{\label{fig7}Temperature {versus} CO$_{2}$ concentration at constant pressure in the CO$_{2}$-rich phase of the binary (CO$_{2}$--H$_{2}$) and ternary (H$_{2}$O--CO$_{2}$--H$_{2}$) systems.} \end{figure} To determine if the presence of H$_{2}$ has a significant effect on the solvation of water in the gas phase, for a given ratio H$_{2}$/CO$_{2}$ (see {Figure~\ref{fig8}}), the evolution of water concentration according to the temperature for the binary (H$_{2}$O--CO$_{2}$) system is compared with the ternary system (H$_{2}$O--CO$_{2}$--H$_{2}$). First, the increase of the CO$_{2}$ pressure from 30 bar to 60 bar slightly increases the concentration of water (dotted lines). For example, at a constant temperature of 200~\textdegree{}C, the \mbox{water} concentration in the vapor phase is 0.36~mol${\cdot}$L$^{-1}$ and 0.41 mol${\cdot}$L$^{-1}$ for 30 bar and 60 bar of CO$_{2}$, respectively. When H$_{2}$ is added to the system (full lines), negligible effect is seen when 30 bar of CO$_{2}$ mixes with 30 bar of H$_{2}$ (yellow line). However, in the system comprising 60 bar of CO$_{2}$, the addition of 30 bar of H$_{2}$ leads to a slight decrease of the solubility water in the CO$_{2}$ phase (orange lines) and is similar to that measured with 30 bar of CO$_{2}$. Thus, the lower solubility of water in the CO$_{2}$ phase in the presence of H$_{2}$ could be due to the lower CO$_{2}$ concentration in the CO$_{2}$ phase as shown for the binary system CO$_{2}$--H$_{2}$ (cf.\ {Figure~\ref{fig7}}) as well as to the fact that H$_{2}$ is a highly hydrophobic molecule that is expected to limit the solubility of water in the CO$_{2}$ phase. \begin{figure} \includegraphics{fig08} {\vspace*{-2pt}} \caption{\label{fig8}Temperature versus H$_{2}$O concentration at constant pressure in the CO$_{2}$-rich phase of the binary (H$_{2}$O--CO$_{2}$) and ternary (H$_{2}$O--CO$_{2}$--H$_{2}$) systems.} {\vspace*{-2pt}} \end{figure} \subsection{H$_2$O--sorbitol--CO$_2$ ternary system} {Figure~\ref{fig9}} displays the infrared spectra of the gas phase of a ternary system, an aqueous solution of 30 wt\% of sorbitol under CO$_{2}$ pressure. It is worth noting that the evolution of the profiles is similar to that observed when the temperature is increased in H$_{2}$O--CO$_{2}$ binary system (cf.\ {Figure~\ref{fig2}}). This suggests that sorbitol is not detected in the CO$_{2}$-rich phase (under our detection limit of 10$^{-4}$--10$^{-5}$\ $g_{\mathrm{sorbitol}}$/$g_{\mathrm{CO}_2}$) as we have not observed any new peaks related to sorbitol between 2900~cm$^{-1}$ and 1100 cm$^{-1}$. \begin{figure*} {\vspace*{-2pt}} \includegraphics{fig09} {\vspace*{-2pt}} \caption{\label{fig9}Infrared spectra of the CO$_{2}$-rich phase of the ternary system H$_{2}$O--sorbitol--CO$_{2}$ at 60 bar from 40~\textdegree{}C to 220~\textdegree{}C.} {\vspace*{-2pt}} \end{figure*} The CO$_{2}$ concentration in the CO$_{2}$-rich phase of the H$_{2}$O--sorbitol--CO$_{2}$ ternary mixture is compared to that of the H$_{2}$O--CO$_{2}$ binary system ({Figure~\ref{fig10}}). No significant difference in the CO$_{2}$ concentration was seen at 30 or 60 bar of CO$_{2}$. However, at a higher CO$_{2}$ pressure of 120 bar, the concentration of CO$_{2}$ slightly increases (green, full line) when sorbitol is added to water. It can be inferred that the presence of sorbitol in water has no effect on the CO$_{2}$ concentration in the gas phase at low CO$_{2}$ pressures and higher pressure of 120 bar, sorbitol modifies the water--CO$_{2}$ equilibrium.\looseness=-1 \begin{figure} \includegraphics{fig10} {\vspace*{-1pt}} \caption{\label{fig10}Temperature {versus} CO$_{2}$ concentration at constant pressure in the CO$_{2}$-rich phase of the binary (H$_{2}$O--CO$_{2}$) and ternary (sorbitol--H$_{2}$O--CO$_{2}$) systems.} {\vspace*{-1pt}} \end{figure} In order to assess the modification of the water--CO$_{2}$ equilibrium due to the presence of sorbitol in the aqueous phase, the evolution of the concentration of water in the CO$_{2}$-rich phase for the H$_{2}$O--sorbitol--CO$_{2}$ ternary mixture with temperature is observed (see {Figure~\ref{fig11}}) and compared with the results obtained for the H$_{2}$O--CO$_{2}$ binary system. As shown in Figure~\ref{fig10}, no effect is seen at CO$_{2}$ pressure ${<}$ 60~bar, as the concentration of water in the CO$_{2}$-rich phase is similar for the binary and ternary systems. However, at CO$_{2}$ pressure of 120 bar, the water concentration decreases from 0.3 mol${\cdot}$L$^{-1}$ to 0.24~mol${\cdot}$L$^{-1}$ at 160~\textdegree{}C. Therefore, it can be inferred that sorbitol prevents the solvation of water in the CO$_{2}$-rich phase by ``keeping'' water in the liquid phase and leads to a higher concentration of CO$_{2}$ in the CO$_{2}$-rich phase. \begin{figure} {\vspace*{2pt}} \includegraphics{fig11} {\vspace*{2pt}} \caption{\label{fig11}Temperature versus H$_{2}$O concentration at constant pressure in the CO$_{2}$-rich phase of the binary (H$_{2}$O--CO$_{2}$) and the ternary (sorbitol--H$_{2}$O--CO$_{2}$) systems.} \end{figure} \subsection{H$_{2}$O--sorbitol--CO$_{2}$--H$_{2}$ quaternary system} {Figure~\ref{fig12}} shows the evolution of the infrared spectra in the CO$_{2}$-rich phase as a function of temperature of the quaternary system comprising an aqueous solution of 30 wt\% of sorbitol and the mixture of CO$_{2}$ and H$_{2}$ gases. The ``induced'' peak of H$_{2}$ at 4150~cm$^{-1}$ is only observed at low temperatures. With increase in temperature, the band of water increases and overlaps H$_{2}$ while the bands of CO$_{2}$ decrease. As seen in the ternary system ({Figure~\ref{fig9})}, sorbitol is not detected in the CO$_{2}$-rich phase. \begin{figure*} \includegraphics{fig12} \caption{\label{fig12}Infrared spectra of the CO$_{2}$-rich phase of the quaternary system H$_{2}$O--sorbitol--CO$_{2}$--H$_{2}$ at 90~bar at temperatures from 40~\textdegree{}C to 220~\textdegree{}C.} \end{figure*} In Figure~\ref{fig13}, the concentration of CO$_{2}$ in the CO$_{2}$-rich phase for the quaternary mixture is compared with the ternary system H$_{2}$O--CO$_{2}$--H$_{2}$. It appears that at the pressure range investigated (corresponds to conditions used for the catalytic reactions reported previously~\cite{8,10}), the addition of sorbitol does not have a significant effect on the CO$_{2}$ concentration in the presence of H$_{2}$. \begin{figure} \includegraphics{fig13} \caption{\label{fig13}Temperature {versus} CO$_{2}$ concentration at constant pressure in the CO$_{2}$-rich phase of the ternary (H$_{2}$O--CO$_{2}$--H$_{2}$) and quaternary (H$_{2}$O--sorbitol--CO$_{2}$--H$_{2}$) systems.} \end{figure} By the same token, the quaternary system is compared to the ternary system H$_{2}$O--sorbitol--CO$_{2}$ to study the effect of H$_{2}$ on water concentration in the CO$_{2}$-rich phase (cf.\ {Figure~\ref{fig14}}). Almost no effect is observed, which is consistent with the results reported in {Figure~\ref{fig13}.} \begin{figure} {\vspace*{-1pt}} \includegraphics{fig14} {\vspace*{-1pt}} \caption{\label{fig14}Temperature versus H$_{2}$O concentration at constant pressure and increasing temperature in the CO$_{2}$-rich phase of the ternary (H$_{2}$O--sorbitol--CO$_{2}$) and quaternary (H$_{2}$O--sorbitol--CO$_{2}$--H$_{2}$) systems.} {\vspace*{-1pt}} \end{figure} Therefore, at the pressure and temperature range investigated where two distinct water-rich and CO$_{2}$-rich phase are observed, the presence of sorbitol in the water-rich phase and H$_{2}$ in the CO$_{2}$-rich phase have a limited impact on the mutual solubility of water and CO$_{2}$. \section{Conclusion} The aim of this paper was to investigate, using {in situ} infrared spectroscopy, the thermodynamic behavior of the H$_{2}$O--sorbitol--CO$_{2}$--H$_{2}$ system which is involved in the one-pot catalytic reaction for hydrogenation of glucose to sorbitol and the acid-catalyzed dehydration of sorbitol by CO$_{2}$~\cite{8,10}. Specifically, our study focused on the gas phase of binary, ternary and quaternary mixtures and selected vibrational modes of CO$_{2}$ and H$_{2}$O that have been analyzed in order to determine the evolution of the H$_{2}$O and CO$_{2}$ concentrations as a function of the temperature and pressure. At a given pressure of CO$_{2}$, with increasing temperature, the concentration of water in the gas phase increases with a concomitant decrease of the CO$_{2}$ concentration when compared with neat CO$_{2}$. Addition of H$_{2}$ at a pressure of 30 bar to H$_{2}$O/CO$_{2}$ binary system lowered the concentration of both CO$_{2}$ and water in the gas phase. On the other hand, the addition of sorbitol to water appears to prevent the mutual solubility of CO$_{2}$ and water, an effect that is significant only at high CO$_{2}$ pressure (120 bar) investigated in this study. Finally, the purpose of these thermodynamic measurements was to determine whether sorbitol, present in the liquid water phase at high temperature, could dissolve in the gas phase and reduce the sugar concentration in water, thus affecting the catalytic reactions mentioned earlier. However, an inverse relationship was observed, where both sorbitol and H$_{2}$ limited the water solubility in the gas phase to some extent. Therefore, we confirm that under our experimental conditions ($T< 220$~\textdegree{}C and $P< 120$ bar), the ternary and quaternary mixtures display two distinct phases, sorbitol/water-rich liquid and CO$_{2}$/H$_{2}$-rich gas phase, both reactions of hydrogenation and dehydration taking place in the liquid phase. \section*{Declaration of interests} The authors do not work for, advise, own shares in, or receive funds from any organization that could benefit from this article, and have declared no affiliations other than their research organizations. \section*{Funding} The authors acknowledge the Region Nouvelle Aquitaine and the University of Poitiers for their financial support (funding of the PhD of IB). The authors are also grateful to the program ``Instrumentation in situ en conditions extr\^{e}mes'' of the MITI of CNRS {for financial support towards infrared and Raman equipment,} the INCREASE Federation and the GDR 2035 SolvATE. \back{} \bibliographystyle{crchim} \bibliography{crchim20240110} \refinput{crchim20240110-reference.tex} \end{document}