Thermodynamics of dilute aqueous solutions up to the critical region of water;

Spring 2018 UCT-IOBC Theoretical Chemistry Seminar, May 25 2018 Thermodynamics of dilute aqueous solutions up to the critical region of water; experiments versus modelling Vladimir Majer Technical University of Liberec, and CNRS, Blaise Pascal University Clermont-Ferrand, France

Organization of the lecture • Introduction to the topic – behaviour of standard derivative properties (V, H, Cp)of solutenear thecritical point of solvent • Methodology and instrumentation for acquisition of HT/HP volumetric and calorimetric data up to the critical region of water • Examples of experimental results • Simultaneous correlation of standard thermodynamic properties over a wide range of temperature and pressure

Critical region of water 640 < T < 720 K 200 < ρ< 450 kg/m3 Variation of a diverging pure component property above the critical point Water Tc= 647 K pc= 22 MPa ρc=320 kg/m3 Critical isochore Compressibility κT Vapour pressure line at Tc , pc

PARTIAL MOLAR VOLUME OF A SOLUTE AT INF. DILUTION IN THE CRITICAL REGION OF SOLVENT Partial molar volume at infinite dilution Standard molarvolume = = standard molar volume of a solute scales in the criticalregion of solvent with compressibility which diverges at the critical point standard molar volume therefore also diverges sign of the divergence is determined by: Krichevski parameter (concentration derivativeof pressure at T and V const ); well behaved in the critical region sign positive – „repulsion“, sign negative – „attraction“

Initial slope of the critical locus and the sign of the Krichevskii parameter volatile, hydrophobic solutes Crit. point nonvolatile, hydrophilic solutes

standard molar volume standard molar enthalpie standard molar heat capacity standard derivative properties scale in the critical region with mechanical coefficients of water diverging at Tc,w, pc,w sign of the divergence is determined by the well behaved Krichevski parameter STANDARD DERIVATIVE PROPERTIES OF A SOLUTE IN THE CRITICAL REGION OF WATER standard molar volume

a / K-1.102 (A) Surface (B) Isobars a / K-1.102 p / bar T / °C a(T)p maxima T / °C ρc a(p)T maxima Mechanical coefficients versus standard derivative properties near Tc and pc pc Hs°αTstandard enthalpy of solute scales with the expansivityof solvent Vs°κpstandard volume of solute scales with the compressibility of solvent

(A) Surface / K-2 . 104 T / °C p / bar Mechanical coefficients versus standard derivative properties near Tc and pc (B) Isobars T / °C Cps° (αp /T)p standard heat capacity scales with the temperature derivative of expansivity

Changes in standard derivative properties of solute through the critical region of water Standard volume cm3/ mol Standard heat capacity kJ / (K mol) p = 28 MPa

Obtaining the standard thermodynamic properties from experimental data XΦ - apparent molar property – accessible from experimental data m molality, X propertyfor a system containing1 kg of solvent (w) Xs° - standard molar property– obtained from the apparent molar properties by extrapolation to infinite dilution Volume, Heat capacity Enthalpy

Strong points : no vapour space, risks of accident low, residence time short, alternation between solution and solvent without perturbation of T and p . Principles of calorimetric and volumetric HT/HP flow techniques • measurements made on a stream of a fluid contained in thin tubes (inox, • hastelloy, Pt+Rh, d.e.  1-2 mm) • injection using HPLC pump for water and sample loops for solutions (heat • capacity and density measurements), two piston pumps for mixing experim. • (flow rate of 0.5 – 2 cm3/min) • pressure and its stability controlled by a back pressure regulator • (p < 40 MPa, stability ≈ 0.01 MPa ) • efficient system of preheaters for attaining temperatures up to 723 K • (ΔT ≤ 400 K in 1 minute,stability ≈ 0.01 K)

A B HT/HP Calo-densimeter A+B C.C. Heat exchanger Outer lid Heaters Inner lid Heat sink C.C Heat exchanger Calorimeter Preheater Heating coil Vibrating tube Burns thermometer Inner can Outer can Vacuum can V. Hynek, S. Degrange, M. Polednicek, V. Majer J.R. Quint et J-P.E. Grolier.,J. Solution Chem., 28, 631-666 (1999)

Temperature difference bridge (4 Pt1000 thermometers) Inlet A Inlet B Heat sink A A+B B 5 Inner lid  2 RTD Outlet  3 Heat leak connection 20 RTD Reference Mixing point RTD regulation 6 Regulation Heater Mixing coil Block  1 Calorimeter  1.59 Outlet Detail of heat of mixing calorimeter

Densimeter block Pick-up and drive rods Working equations: Magnet 1 Magnet 2 Extension pole piece Vibrating tube  1.6 mm Cover Brass block Transporting tube  1.1 mm Vibrating tube unit

Heat exchanger Outer lid Pt- Ir tube 1.1 mm Inner lid Heaters Preheater T2 Circulating tube RTD (cemented) T1 Calorimetric block RTD COAX heater (silver soldered) Inner can COAX heater Pt- Ir tube 2 mm Outer can Vacuum can Liquid Flow F HP/HT Picker type calorimeter L. Hnedkovsky, V. Hynek, V. Majer, R.H. Wood, J. Chem. Thermodynamics, 34, 755 (2002)

Apparent molar volumes of aqueous electrolytesin the critical region of water VΦ of NaCl(aq) vs temperature for m = 0.025 mol.kg-1 and different pressures. Results obtained with two vibrating tube densimeters (Newark, De; Cl-Fd, Fr) VΦof NaOH(aq) vs the square root of the ionic force for p = 30 MPa and different temperatures Obsil PhD Thesis 1998, Majer et al. JCT 1991, Hynek et al. IJT 1997

Standard volumes of gasous nonelectrolytes through the critical region of water CH4 p = 28 MPa p = 28 MPa CO2 V°s cm3/mol CH4 H2S p = 35MPa T / K T / K Hnedkovsky et al. JCT (1996)

240 hexane 1600 200 ) l T o ) methane 1200 m w / 3 p m 160 d c benzene / ( r s d 800 o ( V 120 400 r ( d / dp ) w T 80 660.00 670.00 680.00 T (K) 400 C° p, methane 2E+4 300 hexane ) l p o ) m T / J d k ( / w l 200 0E+0 o r s d o ( H - D benzene 100 -2E+4 r ( d / d T ) w p 0 640.00 650.00 660.00 670.00 680.00 690.00 T(K) Standard thermodynamic properties of aqueous hydrocarbonsthrough the critical region of water (p = 28 MPa) Standard enthalpies of solution and standard heat capacities; comparaison with the isobaric expansivity Standard volumes; comparison with the isothermal compressibility Degrange PhD Thesis (1998) Hnedkovsky et al. JCT (1997)

 10  100 cm3/mol Standard enthalpy of solution and standard volume of aqueous hydrocarbons(aq) in the critical region of water  2  20 kJ/mol

140 130 225 120 Prediction Amend & Helgeson (1997) 210 Prediction Amend & Helgeson (1997) 110 195 100 180 V0 / cm3.mol-1 cp0 / J.mol-1.K-1 90 165 80 150 Experimental results Experimental results 70 135 60 120 280 440 360 480 320 400 520 320 280 440 560 360 480 400 520 T / K T / K Comparison of group contribution predictions with the experimental data a-alanine(aq) Standard molar heat capacities at 30 MPa Standard molar volumes at 20 MPa Clarke, Tremaine, J. Phys. Chem. B, 1999 Clarke, Hnedkovsky,Tremaine, Majer J. Phys. Chem. B, 2000

Standard molar volumes of weak acids at pressures below 15 MPa Ballerat Ballerat, Sedlbauer, Majer J. Phys. Chem. 2007 Perfetti, Pokrovsky, Ballerat, Majer, Geochim. Cosmochim. Acta 2007 Hnedkovsky, L.; Majer, V.; Wood, R.H. J. Chem. Thermodyn. 1995 Ganopolsky, J.G.; Bianchi H.L.; Corti H.R. J. Sol. Chem. 1996 Majer, V.; Sedlbauer, J.; Hnedkovsky, L.; Wood, R.H., Phys Chem Chem Phys, 2000

Standard molar heat capacities of weak acids at pressures close to 30 MPa Inglese, A.; Sedlbauer, J.; Wood, R.H. J. Sol. Chem. 1996, 25, 849

Main semitheoretic approaches to correlation and prediction of standard molar properties of aqueous solutes up to the critical region of water -Dielectric models making use of dielectric properties of water via the Born equation, proposed primarily for aqueous electrolytes (Helgeson, HKF model) - Density models making use of pVT properties of water; respecting the behaviour of the standard derivative properties in the critical region of water -Near critical models based on an expression, assymptotically correct near the solvent’s critical point, relating Henry’s constant to the density of solvent (Levelt-Sengers) -FST Models hydration models inspired by the fluctuation solution theory (Kirkwood-Buff) making use of the generalized Krichevskii parameter(O’Connell)

Models based on the fluctuation solution theory (FST) (O’Connell, Woodand coll. 1996-2000) Background in statistical thermodynamics : - generalized Krichevskii parameter, related to the spatial integral of the infinite dilution solute/solvent direct correlation function Virial expansion : - the cross virial coefficient Analogous relationship for pure water : - a parameter related to the spatial integral of the solvent/solvent direct correlation function Cw Solute/solvent versus solvent/solvent interactions : N adjustable scaling factor relating to the difference in size between • several models developped differing by expression of the second virial coefficients • and higher terms

Hydration modelinspired bythe fluctuation solution theory FST Semitheoretical for volume at infinite dilution Sedlbauer, O´Connell, Wood Chemical Geology(2000) , ,  general constants a, b, c, Net  adjustable parameters (4 independent) Standard thermodynamic properties of hydration by integration: - parameters can be obtained for individual molecular species or ions - possibility of a group contribution scheme for organic solutes (aq)

YSS : property of a point massN : number of functional groups : contribution of each groupni : number of occurrences of each group Group contribution scheme Number of parameters:5 x Ngr + data at ref. condition Minimised objective fonction

Thermodynamic background of hydration properties and their determination from experimental data Gibbs energy of hydration 1 - solvent, 2 - solute VLE exp. – dil. solutions VLE exp., chromatography – dil. sol. solubility measurements Experimental data exploited: - Henry’s law constants, limiting activity coefficients (R), solubilities - vapour pressures, gas nonideality corrections, densities of pure solutes

Enthalpy of hydration gaseous solutes liquid and solid solutes extrapolation to inf. dil. of the data from mixing flow calorimetry experiments Experimental data exploited: - enthalpies of solution in dilute aqueous solutions extrapolated to inf. dil. - enthalpic departure function, enthalpies of vaporization/sublimation

Heat capacity of hydration differential flow calorimetry Partial molar volume at infinite dilution vibrating tube flow densimetry Experimental data exploited: - heat capacity and density differences extrapolated to inf. dilution - heat capacities of ideal gas

Effect of approximations on thermodynamic integration SOCW hydCp=0 hydCp=const

Definition Link to Ghyd Link to standard derivative properties Pressure Temperature Henry’s constant and hydration properties

Prediction of the Henry’s law constant for C6 aromatics from a group contribution method as a function of T a p Šedlbauer, Bergin, Majer; AIChE J. 2002

Effect of pressure on hydration functions - the role of standard molar volume Majer. Sedlbauer, Bergin Fluid Phase Eq. 2008 Šedlbauer, Bergin, Majer; AIChE J. 2002

Calculation of the part. molar volume at inf. dilution toluene aniline phenol

Prediction of the Gibbs energy of hydration for polar derivatives of aromatics from a group contribution method as a function of T a p toluene aniline phenol Censky, Sedlbauer, Majer, Ruzicka Geochim. Cosmochim. Acta 2007

-4.0 -4 -5.0 -5 log Kdis log Kdis -6.0 -7.0 -6 -8.0 250 350 450 550 250 350 450 550 650 T / K T / K Dissociation constants of two acides calculated as a function of T et p from the SOCW model; comparison with experimental values 30 MPa 30 MPa 20 MPa 10 MPa 20 MPa 10 MPa psat psat Propionic acid Acetic acid Majer, Sedlbauer, Hnedkovsky, Wood, PCCP 2000

Standard molar volumes of ionic and molecular forms at saturation line of water and at p = 100 MPa Ballerat,Sedlbauer, Majer J. Phys. Chem. 2007

Standard molar heat capacity of ionic and molecular forms at the saturation line of water and at p = 100 MPa Ballerat,Sedlbauer, Majer J. Phys. Chem. 2007

Thank you for attention

Hydroxy and amino derivatives of monoaromatic hydrocarbons Hydrocarbons CH3 (part of aliphatic chain ) CH2 (part of aliphatic chain) CH (part of aliphatic chain) C (part of aliphatic chain) C=C (part of aliphatic chain) Hπ (hydrogen atoms linked with C=C) CH2(c) (cycloalkane ring) CH(c) (cycloalkane ring) CH(ar) (aromatic ring) C(ar) (aromatic ring) (OH)arphenolic group (NH2)ar aniline group Steric corrections for ortho position on an aromatic ring Group contribution method for aqueous organic solutes Individual gases CH4 CO2 H2S Ref. State Values ΔGhyd(Tr,pr), ΔShyd(Tr,pr); Tr=298 K, pr=0.1 MPa - Hydrocarbons: Plyasunov and Shock GCA (2000) - Pnenols, anilines: newly determined - CH4, CO2, H2S - selected data from the literature

Thermodynamics of dilute aqueous solutions up to the critical region of water;