Freezing enthalpy

The properties of the solids most commonly encountered are tabulated. An important problem arises for petroleum fractions because data for the freezing point and enthalpy of fusion are very scarce. The MEK (methyl ethyl ketone) process utilizes the solvent s property that increases the partial fugacity of the paraffins in the liquid phase and thus favors their crystallization. The calculations for crystallization are sensitive and it is usually necessary to revert to experimental measurement. 

Many materials are suitable for refrigerant purposes, and each usually has some special characteristics that allow it to serve a particular application better than some of the others. Before selecting a refrigerant, it is important to evaluate its flammability and toxicity data, pressure-temperature-volume relationships, enthalpy, density, molecular weight, boiling and freezing points, and various effects on gaskets, metals, oils, etc. ... 

The specific enthalpy (or total heat) of the mixture can be taken from 0 K (- 273.15°C) or from any convenient arbitrary zero. Since most air-conditioning processes take place above the freezing point of water, and we are concerned mostly with differences rather than absolute values, this is commonly taken as 0°C, dry air. For conditions of 25°C, saturated, the specific enthalpy of the mixture, per kilogram of dry air, is... 

For a detailed discussion of the calculation of activities (and excess Gibbs free energies) from freezing point measurements, see R. L. Snow. J. B. Ott. J. R. Goates. K. N. Marsh, S. O Shea, and R. N. Stokes. "(Solid + Liquid) and (Vapor + Liquid) Phase Equilibria and Excess Enthalpies for (Benzene + //-Tetradecane), (Benzene + //-Hexadecane). (Cyclohexane + //-Tetradecane), and (Cyclohexane +//-Hexadecane) at 293.15, 298.15, and... 

It should be noted that the curves of humidity plotted against either temperature or enthalpy have a discontinuity at the point corresponding to the freezing point of the humidifying material. Above the temperature 90 the lines are determined by the vapour liquid equilibrium and below it by the vapour-solid equilibrium. 

TABLE 6.3 Substance Standard Enthalpies pf Physical Change Freezing Formula point (I<) (kj-rnpl ) Boiling point (K) AHV P° (kj-mol )... 

An informative IR spectrum of the t-butyl radical, containing 18 bands, has been recorded after freezing of the products of vacuum pyrolysis of azoisobutane [110] and 2-nitrosoisobutane [111] in an argon matrix at 10 K (Pacansky and Chang, 1981). This spectrum is in agreement with a pyramidal structure of the radical (CH3)3C (symmetry C3v) which has elongated CH bonds in positions trans to the radical centre. On the basis of experimental vibrational frequencies and ab initio calculations of the radical geometry the enthalpy value [// (300)] of its formation has been calculated as 44 kJ moP. ... 

Assuming that we start at 298 K, the final T will be around 270 K or —3°C or 25°F. Brrr Our calculation has also involved a number of other assumptions, including that we have assumed a temperature-independent enthalpy of reaction and a temperature-independent heat capacity for the water. We have also assumed that the water does not freeze (would release some heat). Nevertheless, the calculation gives a fairly reasonable estimate of the temperature drop that provides the cooling therapy of an instant ice pack. 

The freezing point depression of a solvent is proportional to the concentration of solute particles and may be used to measure the extent of ionization once the new particles have been identified qualitatively as ions. The method has the obvious disadvantage of not allowing measurements over a range of temperatures in a single solvent. It is almost certainly not worth while to compute an enthalpy of ionization from ionization constants at two different temperatures in two different solvents. Usable solvents are limited not only by the requirement that the melting point be at a convenient temperature but also by the requirement that the solvent be capable of producing ions yet not be sufficiently nucleophilic to react irreversibly with them once they are formed. For this reason most cryoscopic work has been done in sulfuric acid or methanesulfonic acid.170... 

AJ = enthalpy difference between the the initial freezing point and the final temperature AT = difference of temperature between the freezing point and the cooling medium d = thickness of the product parallel to direction of prevailing heat transfer pg = density of the frozen product Ag = thermal conductivity of the frozen product and... 

When we compared the viscosities of solutions of natural rubber and of guttapercha and of other elastomers and later of polyethylene vs.(poly)cis-butadiene, with such bulk properties as moduli, densities, X-ray structures, and adhesiveness, we were greatly helped in understanding these behavioral differences by the studies of Wood (6) on the temperature and stress dependent, melting and freezing,hysteresis of natural rubber, and by the work of Treloar (7) and of Flory (8) on the elasticity and crystallinity of elastomers on stretching. Molecular symmetry and stiffness among closely similar chemical structures, as they affect the enthalpy, the entropy, and phase transitions (perhaps best expressed by AHm and by Clapeyron s... 

Vaporization and condensation are opposite processes. Thus, the enthalpy changes for these processes have the same value but opposite signs. For example, 6.02 kJ is needed to vaporize one mole of water. Therefore, 6.02 kJ of energy is released when one mole of water freezes. 

Several enthalpies of melting and vaporization are shown in Table 5.1. Notice that the same units (kj/mol) are used for the enthalpies of melting, vaporization, condensation, and freezing. Also notice that energy changes associated with phase changes can vary widely. 

Based on the change in enthalpy, you would expect that water would always freeze. Use the concepts of entropy and free energy to explain why this phase change is favourable only below 0°C. 

A second procedure, which is fundamentally equivalent to the analytic method, involves adding suitable equations to get the desired equation and makes use explicitly of the property that A// i is a state function. For example, if we consider the freezing of water, the enthalpy of the reaction is known at 0°C (T ), but it may be required at — 10°C (T2). We can obtain the desired A//m by adding the following equations (assuming that Cp, is constant over the temperature range) ... 

With this model, it is necessary to assume fast inversion of the two corannulene units within the dimer (or planarity) otherwise the top and bottom bowls would not be equivalent in the NMR spectra. MNDO calculations predict an activation enthalpy of approximately 13 kcal/mol for the concerted inversion process, and this value is inconsistent with the NMR behavior that shows no evidence of freezing out such a dynamic process. These calculations, however, do not take solvation of the exterior lithiums into account, and so the exterior lithiums were removed, and the system was calculated under conditions that would roughly model solvent separation of the lithium cations. Accordingly, the approximate barrier for inversion was lowered to approximately 1 kcal/mol, suggesting that solvation of the exterior lithium cations can indeed greatly reduce the inversion barrier. ... 

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