Temperatures of Pure Substances

Critical Temperature of Pure Substances.— The determination of the critical temperature of a substance is often a relatively simple experiment provided an accuracy of 0.1 K is sufficient. The most commonly used method is the observation of the appearance or disappearance of the meniscus when a sealed tube containing some of the substance is slowly cooled or heated. The tube must be filled so that the overall density of contents of the tube is approximately equal to the critical density. 

When a sealed tube containing a liquid and its vapour is slowly heated uniformly, one of three things may happen. If the overall density is less than the critical, the meniscus will fall and eventually all the liquid will evaporate. If the overall density is greater than the critical, the meniscus will rise and eventually all the vapour will condense. If the overall density is equal to the critical the meniscus will rise or fall slowly until it is near the centre of the tube, where it will become flat, fainter, and will eventually vanish at the critical temperature. For measurements of moderate precision (0.1 K) there is no great need for the overall density to be exactly the critical density. Owing to the large compressibility of both liquid and gaseous phases near the critical point, T, Andrews, Phil. Trans., 1869,159, 1876. 

The major requirement for measuring critical temperature by this technique is a suitable furnace (or cryostat) in which (a) the experimental tube can be heated or cooled without the introduction of significant temperature gradients, and (b) accidental breakage of the tube does not constitute a major safety hazard. Basically, there are three different types of furnace or cryostat which have been used, vapour baths, liquid baths, and solid block-type furnaces. 

Simple water or oil baths may be used between 280 and 480 K, provided that the bath is adequately stirred. At higher temperatures the operation can become hazardous if an experimental tube breaks unless suitable precautions are taken. For measurements below room temperature, some form of Dewar vessel is needed. Suitable coolant liquids are the non-flammable freons or hydrocarbons. Liquid hydrocarbons have often been used as coolants in critical temperature study, but their flammable nature is a major drawback. 

Vapour baths may be used at temperatures up to about 600 K. They consist of a boiler flask connected to a vapour condenser in which the sample tube is suspended. The temperature is controlled by regulating the pressure at which the vapour condenses. If a pure liquid is used in the boiler this type of equipment gives good temperature control but is fairly complex to operate and can be hazardous if a sample tube breaks. 

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J. B. Ott and J. R. Goates. "Summary of Melting and Transition Temperatures of Pure Substances and Congruent and Incongruent Melting Temperatures of Molecular Addition Compounds," J. Chem. Eng. Data. 41. 669-677 (1996). 

The ITS 90 was adopted by the Comite International des Poids et Mesures in September 1989 [14-16], The ITS 90 extends from 0.65 K to the highest temperatures, practicably measurable in terms of the Planck radiation law using monochromatic radiation. The defining fixed points of the ITS 90 are mostly phase transition temperatures of pure substances given in Table 8.2. 

Effect of bubble size on the boiling temperature of pure substances... 

In Fig. 9.26, the thermodynamic equilibrium, solid-liquid phase diagram of a binary (species A and B) system is shown for a nonideal solid solution (i.e., miscible liquid but immiscible solid phase). The melting temperatures of pure substances are shown with Tm A and Tm B. At the eutectic-point mole fraction, designated by the subscript e, both solid and liquid can coexist at equilibrium. In this diagram the liquidus and solidus lines are approximated as straight lines. A dendritic temperature T and the dendritic mass fractions of species (p)7(p)s and (p)equilibrium partition ratio kp is used to relate the solid- and liquid-phase mass fractions of species (p)7(p)J and (p)f/(p)f on the liquidus and solidus lines at a given temperature and pressure, that is,... 

Because of laborious measurement with a gas thermometer, the International Temperature Scale (containing, e.g., melting or boiling temperatures of pure substances and obtained in principle on their basis) is used for practical calibrations. 

Liquid crystals may be divided into two broad categories, thermotropic and lyotropic, according to the principal means of breaking down the complete order of the soHd state. Thermotropic Hquid crystals result from the melting of mesogenic soHds due to an increase in temperature. Both pure substances and mixtures form thermotropic Hquid crystals. In order for a mixture to be a thermotropic Hquid crystal, the different components must be completely miscible. Table 1 contains a few examples of the many Hquid crystal forming compounds (2). Much more is known about calamitic (rod-Hke) Hquid crystals then discotic (disk-like) Hquid crystals, since the latter were discovered only recendy. Therefore, most of this section deals exclusively with calamities, with brief coverage of discotics at the end. 

The state of a system containing a constant amount of material depends upon a few variables, e.g. pressure p, volume V, temperature T. For a given mass of pure substance the volume can be expressed solely as a function of pressure and temperature... 

Chapters 7 to 9 apply the thermodynamic relationships to mixtures, to phase equilibria, and to chemical equilibrium. In Chapter 7, both nonelectrolyte and electrolyte solutions are described, including the properties of ideal mixtures. The Debye-Hiickel theory is developed and applied to the electrolyte solutions. Thermal properties and osmotic pressure are also described. In Chapter 8, the principles of phase equilibria of pure substances and of mixtures are presented. The phase rule, Clapeyron equation, and phase diagrams are used extensively in the description of representative systems. Chapter 9 uses thermodynamics to describe chemical equilibrium. The equilibrium constant and its relationship to pressure, temperature, and activity is developed, as are the basic equations that apply to electrochemical cells. Examples are given that demonstrate the use of thermodynamics in predicting equilibrium conditions and cell voltages. 

In addition to chemical reactions, the isokinetic relationship can be applied to various physical processes accompanied by enthalpy change. Correlations of this kind were found between enthalpies and entropies of solution (20, 83-92), vaporization (86, 91), sublimation (93, 94), desorption (95), and diffusion (96, 97) and between the two parameters characterizing the temperature dependence of thermochromic transitions (98). A kind of isokinetic relationship was claimed even for enthalpy and entropy of pure substances when relative values referred to those at 298° K are used (99). Enthalpies and entropies of intermolecular interaction were correlated for solutions, pure liquids, and crystals (6). Quite generally, for any temperature-dependent physical quantity, the activation parameters can be computed in a formal way, and correlations between them have been observed for dielectric absorption (100) and resistance of semiconductors (101-105) or fluidity (40, 106). On the other hand, the isokinetic relationship seems to hold in reactions of widely different kinds, starting from elementary processes in the gas phase (107) and including recombination reactions in the solid phase (108), polymerization reactions (109), and inorganic complex formation (110-112), up to such biochemical reactions as denaturation of proteins (113) and even such biological processes as hemolysis of erythrocytes (114). 

In 1968, an international agreement was reached about the definition of an official (practical) scale of temperature for T> 14 K. This temperature scale IPTS-68, corrected in 1975 [11], was defined by reference fixed points given by transitions of pure substances. To extend the low-temperature range of IPTS-68, the EPT 76 [12-13] gave nine reference temperatures defined by phase transition of pure substances in particular the superconductive transition (between 0.5 and 9K) of five pure metals was introduced. Moreover,... 

The notion of standard enthalpy of formation of pure substances (AfH°) as well as the use of these quantities to evaluate reaction enthalpies are covered in general physical chemistry courses [1]. Nevertheless, for sake of clarity, let us review this matter by using the example under discussion. The standard enthalpies of formation of C2H5OH(l), CH3COOH(l), and H20(1) at 298.15 K are, by definition, the enthalpies of reactions 2.3,2.4, and 2.5, respectively, where all reactants and products are in their standard states at 298.15 K and the elements are in their most stable physical states at that conventional temperature—the so-called reference states at 298.15 K. 

Boublik T, Fried V, Hala E. 1984. The vapor pressures of pure substances Selected values of the temperature dependence of the vapor pressures of some pure substances in the normal and low-pressure region. Volume 17. Amsterdam, Netherlands Elsevier Scientific Publications. 

Although theoretical considerations are helpful to an understanding of the principles involved and may be useful for studying and predicting simple extractions of pure substances, an empirical approach ultimately must be resorted to for cases involving such complex and undefinable mixtures as kerosenes and lubricating oils. The ideal distribution law which states that the ratio of concentrations of a component distributed between two mutually insoluble phases is a constant dependent only on the temperature (K = C1/C2), is analogous to Henry s law for absorption and is rarely valid for commercial extraction problems. 

Partial Miscibility in the Solid State So far, we have described (solid + liquid) phase equilibrium systems in which the solid phase that crystallizes is a pure compound, either as one of the original components or as a molecular addition compound. Sometimes solid solutions crystallize from solution instead of pure substances, and, depending on the system, the solubility can vary from small to complete miscibility over the entire range of concentration. Figure 14.26 shows the phase diagram for the (silver + copper) system.22 It is one in which limited solubility occurs in the solid state. Line AE is the (solid -I- liquid) equilibrium line for Ag, but the solid that crystallizes from solution is not pure Ag. Instead it is a solid solution with composition given by line AC. If a liquid with composition and temperature given by point a is... 

Phase rule studies and describes the occurence of modifications and states of aggregation of pure substances or in mixtures in closed systems as well as the changes which occur in those systems when the pressure, temperature and composition of these substances in the system change. The behaviour of many pure substances and mixtures has thus been studied and recorded in diagrams. These diagrams constitute a vital aid for any scientist studying the development of materials, e.g. ceramics. 

Two cases must be considered one in which the state of aggregation is the same in the initial and final state, and the other in which the state of aggregation is different in the two states. In the first case the enthalpy is a continuous function of the temperature and pressure in the interval between (Th P,) and (T, Pj). Equation (4.86) can be used for a closed system and the integration of this equation is discussed in Section 8.1, where the emphasis is on standard states of pure substances. The result of the integration is valid in the present instance with change of the limits of integration and limitation to molar quantities. Equations (8.10) and (8.11) then become... 

Figure 3.6 shows schematically the molar entropy of a pure substance as a function of temperature. If a structural transformation occurs in the solid state, an additional increase in the molar entropy comes from the heat of the transformations. As shown in the figure, the molar entropy of a pure substance increases with increasing temperature. In chemical handbooks we see the tabulated numerical values of the molar entropy calculated for a number of pure substances in the standard state at temperature 298 K and pressure 101.3 kPa. A few of them will be listed as the standard molar entropy, s , in Table 5.1. Note that the molar entropy thus calculated based on the third law of thermodynamics is occasionally called absolute entropy. 

It is clear that temperature oscillations during heating-cooling cycles depend on the fixed-bed heat capacity. Figure 1.10 shows a simplified picture of the effect of phase change on the effective heat capacity of pure substances. Considerable amounts of... 

In practice it is the International Practical Temperature Scale of1968 (IPTS-68) which is used for calibration of scientific and industrial instruments-t This scale has been so chosen that temperatures measured on it closely approximate ideal-gas temperatures the differences are within the limits of present accuracy of measurement. The IPTS-68 is based on assigned values of temperature for a number of reproducible equilibrium states (defining fixed points) and on standard instruments calibrated at these temperatures. Interpolation between the fixed-point temperatures is provided by formulas that establish the relation between readings of the standard instruments and values of the international practical temperature. The defining fixed points are specified phase-equilibrium states of pure substances, t a given in Table 1.2. 

The original equation for the evaporation of a droplet as a function of time was first derived by James Maxwell in 1877. Although his derivation contains a number of simplifying approximations, Maxwell s equation gives reasonable results for fairly large droplets of pure substances. For this equation, it is assumed that the vapor pressure at the droplet temperature is equal to the partial pressure at the surface of the drop, that is, psurfoce = p,(Teurface) = ps. In terms of concentrations of molecules, this means that the vapor concentration at the surface just equals the concentration of saturated vapor, the saturation determined at the droplet temperature. This assumption is valid when the droplet size is not too small compared to the mean free path of the vapor molecules. 

Considering that dissociation occurs upon volatilization, the temperatures can be correlated extremely well on a In P vs (1/rd.voi) plot, where P is the total system pressure and T a.voi decomposition temperature, as the case dictates. Such a plot is shown in Fig. 11. Since the Clausius-Clapeyron relation for vapor pressure of pure substances shows an exponential dependence on temperature, TVoi was considered a pseudo-boiling point at the respective system pressure. For a substance that vaporizes congruently to its gaseous state, the slope of lines on a In P vs (l/Tvoi) plot represents the enthalpy of vaporization. Indeed, the enthalpy of vaporization calculated from the slope on a In P vs (l/TVoi) plot for the B-O2 system (360 kJ/mol) agrees exactly with the value calculated by using... 

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