Pure substances, phase transitions

Clausius-Clapeyron Equation. This equation was originally derived to describe the vaporization process of a pure liquid, but it can be also applied to other two-phase transitions of a pure substance. The Clausius-Clapeyron equation relates the variation of vapor pressure (P ) with absolute temperature (T) to the molar latent heat of vaporization, i.e., the thermal energy required to vajxirize one mole of the pure liquid ... 

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 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. 

Where applications to industrial combustion systems involve a relatively limited set of fuels, fire seeks anything that can bum. With the exception of industrial incineration, the fuels for fire are nearly boundless. Let us first consider fire as combustion in the gas phase, excluding surface oxidation in the following. For liquids, we must first require evaporation to the gas phase and for solids we must have a similar phase transition. In the former, pure evaporation is the change of phase of the substance without changing its composition. Evaporation follows local thermodynamics equilibrium between the gas... 

We have already illustrated equation 2.32 for a solution enthalpy (of liquid ethanol see section 2.5). We now apply it to another phase transition the vaporization of a pure substance. 

The physical-chemical properties of a supercritical fluid are between those of liquids and gases supercritical fluids (SCFs) indicate the fluid state of a compound in pure substance or as the main component above its critical pressure (pc) and its critical temperature (Tc), but below the pressure for phase transition to the solid state, and in terms of SCF processing, a density close to or higher than its critical density. 

Surprising behavior of liquid and ice phases is found if we follow various 7, P paths in this extended phase diagram. Sidebar 7.4 illustrates how to determine the expected phase transitions and properties of H20 for various temperatures and pressures far outside the realm of ordinary experience. It is remarkable that such multiplicity of forms and properties can result from a pure substance composed of only a single type of molecule. 

If we want to calculate the entropy of a liquid, a gas, or a solid phase other than the most stable phase at T =0, we have to add in the entropy of all phase transitions between T = 0 and the temperature of interest (Fig. 7.11). Those entropies of transition are calculated from Eq. 5 or 6. For instance, if we wanted the entropy of water at 25°C, we would measure the heat capacity of ice from T = 0 (or as close to it as we can get), up to T = 273.15 K, determine the entropy of fusion at that temperature from the enthalpy of fusion, then measure the heat capacity of liquid water from T = 273.15 K up to T = 298.15 K. Table 7.3 gives selected values of the standard molar entropy, 5m°, the molar entropy of the pure substance at 1 bar. Note that all the values in the table refer to 298 K. They are all positive, which is consistent with all substances being more disordered at 298 K than at T = 0. 

As we saw in Section 5.1, a single substance can exist in a variety of different phases, or different physical forms. The phases of matter include the solid, liquid, and gaseous forms and the different solid forms, such as the diamond and graphite forms of carbon. In one unique case— helium—there are two liquid forms of the same substance. There are several different forms of ice, which differ in the way the water molecules pack together when high pressures are applied. The conversion of a substance from one phase to another, such as the melting of ice, the vaporization of water, or the conversion of graphite into diamond, is called a phase transition. Phase transitions take place at specific temperatures and pressures that depend on the purity of the substance. Seawater, for instance, freezes at a lower temperature than pure water does. 

FIGURE 17.8 The entropy of a pure substance, equal to zero at 0 K, shows a steady increase with rising temperature, punctuated by discontinuous jumps in entropy at the temperatures of the phase transitions. 

In this volume, we will apply the principles developed in Principles and Applications to the description of topics of interest to chemists, such as effects of surfaces and gravitational and centrifugal fields phase equilibria of pure substances (first order and continuous transitions) (vapor + liquid), (liquid 4-liquid), (solid + liquid), and (fluid -f fluid) phase equilibria of mixtures chemical equilibria and properties of both nonelectrolyte and electrolyte mixtures. But do not expect a detailed survey of these topics. This, of course, would require a volume of immense breadth and depth. Instead, representative examples are presented to develop general principles that can then be applied to a wide variety of systems. 

For a phase transition between two phases A and B of a pure substance represented by... 

Chapters 13 and 14 use thermodynamics to describe and predict phase equilibria. Chapter 13 limits the discussion to pure substances. Distinctions are made between first-order and continuous phase transitions, and examples are given of different types of continuous transitions, including the (liquid + gas) critical phase transition, order-disorder transitions involving position disorder, rotational disorder, and magnetic effects the helium normal-superfluid transition and conductor-superconductor transitions. Modem theories of phase transitions are described that show the parallel properties of the different types of continuous transitions, and demonstrate how these properties can be described with a general set of critical exponents. This discussion is an attempt to present to chemists the exciting advances made in the area of theories of phase transitions that is often relegated to physics tests. 

Stilbenoid dendrimers are able to undergo aggregation. Depending upon the generation number, some of the pure substances form liquid-crystalline phases (Dha discotic hexagonal disordered phase Dra discotic rectangular disordered phase Dob discotic distorted phase). Differential scanning calorimetry (DSC) revealed phase transitions between 99°C and 0°C. 

In the first discussion of equilibrium (Ch. 5) we recognized that there may be states of a system that are actually metastable with respect to other states of the system but which appear to be stable and in equilibrium over a time period. Let us consider, then, a pure substance that can exist in two crystalline states, a and p, and let the a phase be metastable with respect to the p phase at normal temperatures and pressures. We assume that, on cooling the a. phase to the lowest experimental temperature, equilibrium can be maintained within the sample, so that on extrapolation the value of the entropy function becomes zero. If, now, it is possible to cool the p phase under the conditions of maintaining equilibrium with no conversion to the a phase, such that all molecules of the phase attain the same quantum state excluding the lattice vibrations, then the value of the entropy function of the p phase also becomes zero on the extrapolation. The molar absolute entropy of the a phase and of the p phase at the equilibrium transition temperature, Tlr, for the chosen... 

Hence we predict, from our simple thermodynamic arguments, there is a sharp rise in the entropy at phase transitions undergone by pure substances and that ... 

The FT diagram of Fig. 3.1 shows curves representing phase boundaries for a pure substance. A phase transition at constant temperature and pressure occurs... 

Over the last 30 years the recombination mechanism has become extremely widespread [16, 17]. It has been used to interpret extensive data on Ps chemistry, and explain variations of Ps yields from 0 to 0.7 in very different chemical substances where parameters of the Ore gap are practically the same. Variations of Ps formation probability under phase transitions have also received natural explanation. Experimentally observable monotonic inhibition of Ps yields (practically down to zero) in solutions of electron acceptors contradicts the Ore model, but is well incorporated in the recombination mechanism. It explains the anti-inhibition effect, including experiments on Ps formation in moderate electric fields in pure liquids and mixtures. 

From the ratio AHyu/AHcai, the cooperative unit size (CUS) (in molecules) can be determined. The CUS is a measure of the degree of intermolecular cooperation between phospholipid molecules in a bilayer for a completely cooperative, first-order phase transition of an absolutely pure substance, this ratio should approach infinity, whereas for a completely noncooperative process, this ratio should approach unity. Although the... 

The simplest applications of thermodynamics to chemically significant systems involve the phase transitions that pure substances undergo. The phase of a substance is a form of matter that is uniform throughout in chemical compoation and phyacal state. The word phase comes from the Gredc word for )pearance. Thus, we speak of the solid, liquid, and gas phases of a substance, and of different solid phases distingui ed by thdr ciystal structures (such as white and black phosphorus), h phase transition, spontaneous conversion of one phase to another, occurs at a characteristic temperature for a ven pressure. Thus, at 1 atm, ice is the stable phase of water below 0 C, but above 0°C the liquid is more stable. The difference indicates that, below 0°C, the chemical potential of ice is lower than that of liquid water, //(solid) < //(liquid) (Fig. 1), and that above OX, //(liquid) < //(solid). The transition temperature is the temperature at which the chemical potentials coincide and //(solid) = //(liquid). 

The third law of thermodynamics states that the entropy of any pure substance in equilibrium approaches zero at the absolute zero of temperature. Consequently, the entropy of every pure substance has a fixed value at each temperature and pressure, which can be calculated by starting with the low-temperature values and adding the results of all phase transitions that occur at intervening temperatures. This leads to tabulations of standard molar entropy S° at 298.15 K and 1 atm pressure, which can be used to calculate entropy changes for chemical reactions in which the reactants and products are in these standard states. 

Addition of n-octadecanol to n-nonadecane (on condition that one molecule occupies 0.21 nm in a monolayer) shifts the maximum on log Vs vs 1/T to higher temperature (curve b). The retention volumes of the test substances in pure n-nonadecane and for the column packing containing 17% mass, of n-octadecanol are almost equal. It means that the threedimensional phase above the phase transition temperature contains n-nonadecane only, thus first of all the n-octadecanol molecules remains in the oriented monolayer. 

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