Crystallization specific enthalpy

If appropriate enthalpy data are unavailable, estimates can be obtained by first defining reference states for both solute and solvent. Often the most convenient reference states are crystalline solute and pure solvent at an arbitrarily chosen reference temperature. The reference temperature selected usually corresponds to that at which the heat of crystallization A/ of the solute is known. The heat of crystallization is approximately equal to the negative of the heat of solution. For example, if the heat of crystallization is known at then reasonable reference conditions would be the solute as a soUd and the solvent as a Uquid, both at The specific enthalpies then could be evaluated as... 

The specific enthalpies ia equation 9 can be determined as described earUer, provided the temperatures of the product streams are known. Evaporative cooling crystallizers operate at reduced pressure and may be considered adiabatic (Q = 0). As with of many problems involving equiUbrium relationships and mass and energy balances, trial-and-error computations are often iavolved ia solving equations 7 through 9. 

Fig. 4. Dependence of the specific enthalpy of crystallization on the heat of fusion already released (after Ref. 12).

A convenient way to represent enthalpy data for binary solutions is via an enthalpy-concentration diagram. Enthalpy-concentration diagrams (H-x) are plots of specific enthalpy versus concentration (usually weight or mole fraction) with temperature as a parameter. Figure 4.21 illustrates one such plot. If available, such charts are useful in making combined material and energy balances calculations in distillation, crystallization, and all sorts of mixing and separation problems. You will find a few examples of enthalpy-concentration charts in Appendix I. 

The heat of crystallization is the heat that has to be supplied or removed during crystallization at constant temperature. It is equal to the negative value of the heat of solution during the dissolution of crystals in an almost saturated solution. The heat of crystallization is accounted for in the enthalpy values. Processes in crystallizers can easily be tracked, if an enthalpy concentration diagram is available for the respective system. The pure component s enthalpy is zero at reference temperature, not the enthalpy of real mixtures however. In such diagrams, the lever rule is applicable. This is shown for the system calcium chloride/water in Fig. 8.3-5, where the specific enthalpy is plotted vs. the mass fractions. 

Since the specific enthalpy for the crystal-liquid transition is known, it is possible to deduce that our sample had a crystallinity of 12.4% (similar to what Samuels obtained). 

Here Pc is the crystal density, is the specific enthalpy of fusion and a is the specific surface free energy. Alternatively, the Thompson-Gibbs equation can be rearranged to provide estimates of crystal thicknesses from measurements of the melting temperature. 

Physical properties of the acid and its anhydride are summarized in Table 1. Other references for more data on specific physical properties of succinic acid are as follows solubiUty in water at 278.15—338.15 K (12) water-enhanced solubiUty in organic solvents (13) dissociation constants in water—acetone (10 vol %) at 30—60°C (14), water—methanol mixtures (10—50 vol %) at 25°C (15,16), water—dioxane mixtures (10—50 vol %) at 25°C (15), and water—dioxane—methanol mixtures at 25°C (17) nucleation and crystal growth (18—20) calculation of the enthalpy of formation using semiempitical methods (21) enthalpy of solution (22,23) and enthalpy of dilution (23). For succinic anhydride, the enthalpies of combustion and sublimation have been reported (24). 

The members of Class II in Table 1 present very small enthalpies of the mesophase-liquid transition [ AHml < 0.5 kJ/(mol of chain bonds)], suggesting that their mesophase is hardly stabilized by specific interatomic interactions. By contrast, we point out that in all cases the crystal-mesophase transition has a significant enthalpy value, mostly AHqm > 1 kJ/(mol of chain bonds). Consistent with their relatively flexible character, the polymers listed in the Tables have their glass transition below ambient temperature. 

The crystal arrangement is hence important for the lattice enthalpy and Teiectrostatic can be extracted for a specific crystal structure as... 

A sample of the polymer to be studied and an inert reference material are heated and cooled in an inert environment (nitrogen) according to a defined schedule of temperatures (scanning or isothermal). The heat-flow measurements allow the determination of the temperature profile of the polymer, including melting, crystallization and glass transition temperatures, heat (enthalpy) of fusion and crystallization. DSC can also evaluate thermal stability, heat capacity, specific heat, crosslinking and reaction kinetics. 

When the free energies F of the two crystal structures are identical, the system is at a critical point. The identity of F does not imply identical fimctions (otherwise the two phases would be indistinguishable). Therefore, at the critical point first derivatives of F might differ and therefore enthalpy, volume, and entropy of the two phases would be different. These transformations are first-order phase transitions, according to Ehrenfest [105]. A discontinuous enthalpy imphes heat exchange at the transition temperature, which can easily be measured with DSC experiments. A discontinuous volume is evident under the microscope or, more precisely, with diffraction experiments on single crystals or powders. Some phase transitions are however characterized by continuous first derivatives of the free energy, whereas the second derivatives (specific heat, compressibility, or thermal expansivity, etc.) are discontinuous. These transformations are second-order transitions and are clearly softer. 

The enthalpy difference befween the AA and the GA conformers in the [C4CiIm][BFJ is much smaller than the corresponding enthalpy difference befween the conformers of a free butane chain. This indicates that the 1-butyl-3-methylimidazolium cations most likely form local liquid structures specific fo each rofafional isomers [50]. Coexistence of these local structures, incorporating different rotational isomers, seems to hinder crystallization. This is probably the reason for fhe low melting points of such ILs. 

Figure 1. Schematic presentation of volume and enthalpy as functions of temperature in the liquid, crystalline, and glassy state. Tg, melting temperature, TQf glass temperature, IIs, heat of melting, V8, specific volume difference between crystal and melt.

Below T0 the material is in the glassy state. Compared with the crystal the glass shows a larger specific volume and heat content, but both quantities have a smaller temperature coefficient than in the melt (< ). The transition from melt to glass is often called a transition of the second order (2, 3) since it is not accompanied by finite changes of volume and enthalpy, but only by changes of their temperature coefficients. 

In Fig. 3 c the schematic volume-temperature curve of a non crystallizing polymer is shown. The bend in the V(T) curve at the glass transition indicates, that the extensive thermodynamic functions, like volume V, enthalpy H and entropy S show (in an idealized representation) a break. Consequently the first derivatives of these functions, i.e. the isobaric specific volume expansion coefficient a, the isothermal specific compressibility X, and the specific heat at constant pressure c, have a jump at this point, if the curves are drawn in an idealized form. This observation of breaks for the thermodynamic functions V, H and S in past led to the conclusion that there must be an internal phase transition, which could be a true thermodynamic transformation of the second or higher order. In contrast to this statement, most authors... 

Equation (16-2) allows the calculations of changes in the entropy of a substance, specifically by measuring the heat capacities at different temperatures and the enthalpies of phase changes. If the absolute value of the entropy were known at any one temperature, the measurements of changes in entropy in going from that temperature to another temperature would allow the determination of the absolute value of the entropy at the other temperature. The third law of thermodynamics provides the basis for establishing absolute entropies. The law states that the entropy of any perfect crystal is zero (0) at the temperature of absolute zero (OK or -273.15°C). This is understandable in terms of the molecular interpretation of entropy. In a perfect crystal, every atom is fixed in position, and, at absolute zero, every form of internal energy (such as atomic vibrations) has its lowest possible value. 

It should be emphasized that none of the methods in categories (ii) and (iii) that have been used to obtain the absolute enthalpies of hydration of ions is theoretically rigorous. For example, Conway and Salomon (54) have made a detailed critique of the Halliwell—Nyburg type of treatment. If the water dipole orientation is not exactly opposite at cations and anions, as seems to be indicated by various previous calculations (55, 56), then the assumption that the difference between heats of hydration of cations and anions of the same radius originates from the ion-quadrupole interaction could be inaccurate. However, the results given in Table 7 are probably reliable to within a few kcal mole-1, despite the fact that it is impossible to assess their accuracy specifically. They indicate that an anion has a more negative absolute heat of hydration than a cation of the same crystal radius. 

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