Differential solution enthalpy

This amount of heat is to be removed (negative sign) on condensation and needs to be supplied (positive sign) on melting if isobaric isothermal conditions are intended. The following expression is called differential solution enthalpy or differential heat of solution of the constituent b ... 

These expressions can be used to calculate the differential solution enthalpy... 

Fig.8. Differential molar enthalpy of dilution of a micellar stock solution as a function of the relative bulk molality at 298 K.

One, called isosteric (because, for gas adsorption, it requires comparing two states with same amount adsorbed, i.e., same volume adsorbed), is the calculation of the differential adsorption enthalpy by using a set of two (or, better, three) adsorption isotherms at different temperatures. In dilute solution, the calculation of the isosteric enthalpy from adsorption isotherms at different temperatures is done by applying the following equation ... 

An example is the partial molar enthalpy Hi of a constituent of an ideal gas mixture, an ideal condensed-phase mixture, or an ideal-dilute solution. In these ideal mixtures. Hi is independent of composition at constant T and p (Secs. 9.3.3, 9.4.3, and 9.4.7). When a reaction takes place at eonstant T and p in one of these mixtures, the molar differential reaction enthalpy H is eonstant during the proeess, H is a linear function of and Af// and Ai7m(rxn) are equal. Figure 11.6(a) illustrates this linear dependence for a reaction in an ideal gas mixture. 

The amount of solute molecules preferentially adsorbed from dilute solution onto a given solid can be measured in a separate adsorption experiment, independently of the calorimetry measurement. In the case of the titration calorimetry procedure, this is even the only possibility to determine the amount adsorbed after each injection step and subsequently calculate the differential molar enthalpy of adsorption. The main difficulty here, contributing to a significant uncertainty of the experimental result, is related to the necessity of reproducing strictly the same experimental conditions in both types of experiment (i.e., the same solid surface-to-solution volume ratio, evolution of the pH and ionic strength in the equilibrium bulk solution, charging behaviour of the solid surface, etc.). 

This quantity provides information about the excess of component-adsorbent interactions averaged over all surface domains from which the solvent has been displaced by the adsorbing solute species. In consequence, it is not easy to monitor subtle changes in the adsorption mechanism based on usually small variations of the Adpih values with increasing quantity of adsorption. Compared to the differential molar enthalpy of displacement, the enthalpy Adpih is less sensitive to the energetic heterogeneity of the solid surface. 

Fig. 6.30 Dilution of aqueous solution of (dodecyldimethylammonio) butanoate (C12N3C) and its adsorption onto Spherosil XOB015 (Sbet = 25m g ) at 298 K (a) enthalpy of dilution, (b) adsorption isotherm, (c) differential molar enthalpy of displacement. In both types of titration calorimetry experiment, a 0.3 mol kg C12N3C solution in pure H2O was used...

Fig. 6.31 Variations of the differential molar enthalpy of displacement as a function of the adsorption of benzyldimethylammonium bromide (BDDAB) onto silica powder S91-16 (Rhone-Poulenc, France) from aqueous solutions at 298 K at the initial pH 8 [89]. The arrows indicate the critical micelle concentration (CMC) and the isoelectric point (lEP) at which the effective charge of the silica particles together with the specifically adsorbed surfactant cations becomes equal to zero. The region of particle flocculation (where the silica particles covered with the adsorbed species are predominantly hydrophobic) is also shown...

Fig. 6.33 Effect of phenol addition on the differential molar enthalpy of displacement upon adsorption of cationic Gemini C12C12C12 onto ordered mesoporous aluminosilicate of the MCM-41 type (Sbet = 860 m g mean pore diameter = 5 nm, Si Al = 32) from aqueous solution at 298 K and the initial pH 8 [114]. The ff enthalpy is plotted against the adsorption coverage of the sohd...

However, if the adsorbed phase can be considered as an ideal solution, in which the molecular interactions are the same as for the adsorption of single components, it is possible to calculate the molar differential coadsorption enthalpy by mean of the relation ... 

It is seen that all the points lie on the same straight line, irrespective of the operating temperature and, thus, the enthalpy term is close to zero and the solutes are not retained by differential molecular forces. Thus, the curve shows the effect of... 

Solution In this example, it is assumed that we add a solute to a large enough volume of solution so that the composition of the mixture does not change. The enthalpy change for this process is referred to as a differential enthalpy of solution. We can represent this process by... 

When one polymorph can be thermally converted to another, differential scanning calorimetry (DSC) analysis cannot be used to deduce the heat of transition between the two forms, and so solution calorimetry represents an alternative methodology. This situation was encountered when evaluating the polymorphs of losartan [140], Enthalpies of transition were obtained in water (A(A//sol) = 1.723 kcal/mol) and in A A-dimethylformarnide (A(A//S0 ) = 1.757 kcal/mol), with the equivalence in results demonstrating the quality of the results. Although enthalpy does not indicate stability, the authors deduced from solution calorimetry that form I was more stable than form II at ambient temperature. 

Apart from the qualitative observations made previously about suitable solvents for study, the subject of solvates has two important bearings on the topics of thermochemistry which form the main body of this review. The first is that measured solubilities relate to the appropriate hydrate in equilibrium with the saturated solution, rather than to the anhydrous halide. Obviously, therefore, any estimate of enthalpy of solution from temperature dependence of solubility will refer to the appropriate solvate. The second area of relevance is to halide-solvent bonding strengths. These may be gauged to some extent from differential thermal analysis (DTA), thermogravimetric analysis (TGA), and differential scanning calorimetry (DSC) solvates of "aprotic solvents such as pyridine, tetrahydrofuran, and acetonitrile will give clearer pictures here than solvates of "protic solvents such as water or alcohols. 

The enthalpies of phase transition, such as fusion (Aa,s/f), vaporization (AvapH), sublimation (Asut,//), and solution (As n//), are usually regarded as thermophysical properties, because they referto processes where no intramolecular bonds are cleaved or formed. As such, a detailed discussion of the experimental methods (or the estimation procedures) to determine them is outside the scope of the present book. Nevertheless, some of the techniques addressed in part II can be used for that purpose. For instance, differential scanning calorimetry is often applied to measure A us// and, less frequently, AmpH and AsubH. Many of the reported Asu, // data have been determined with Calvet microcalorimeters (see chapter 9) and from vapor pressure against temperature data obtained with Knudsen cells [35-38]. Reaction-solution calorimetry is the main source of AsinH values. All these auxiliary values are very important because they are frequently required to calculate gas-phase reaction enthalpies and to derive information on the strengths of chemical bonds (see chapter 5)—one of the main goals of molecular energetics. It is thus appropriate to make a brief review of the subject in this introduction. 

The molar enthalpy for the transition from a solid to a supercooled liquid is not a constant with respect to temperature. The molar heat capacities of the solid and supercooled liquid forms of the solute inLuence its magnitude at temperatures below the melting point. It is frequently assumed that either the molar heat capacity of the solid at constant prestiiiippnd the molar heat capacity of its liquid form at constant pressure,pi, are nearly constant or that they change at the same rate with a change in temperature. In either case, the molar differential heat capacity, deLned as... 

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