Substance, pure entropy

Table 3.1 displays the entropy changes of melting and vaporization for some pure substances. The entropy of vaporization is proportional to the ratio of the degree of randomness in the vapor and liquid phases. For a pure component, A.S. consists of translational, rotational, and conformational motion of molecules. The translational effect is the largest contribution to the entropy of vaporization. 

Table 7.2, for halite (NaCl) is more complicated and more typical of natural compounds. As with 02(g) and all other substances, the entropy S°t here is the absolute value for the forms of NaCl listed at the top of the Table—pure crystals for temperatures up to 1073.8 K, and liquid NaCl at higher temperatures. Now, however, the free energy, enthalpy, and log Kf for formation of NaCl from its elements are all non-zero because they refer to the reaction... 

This can be explained on mixing phenomena. Two pure and unmixed substances have small entropy values. But with time, the substances tend to mix and the entropy of the system reaches its highest value at complete mixing of all contributing substances. Thus, entropy is a measurement of the disorder of a system or the measurement of the amount of energy in a system that cannot do work. 

For pure substances, the entropy has a fixed value that is a function of temperature as all other thermochemical properties. The standard definition of entropy is... 

If you scan the values for 5° in Appendix E, you will see that several aqueous ions have values that are less than zero. The third law of thermodynamics states that for a pure substance the entropy goes to zero only at 0 K. Use your understanding of the solvation of ions in water to explain how a negative value of S° can arise for aqueous species. 

Deals with the concept of entropy, which serves as a means of determining whether or not a process is possible. Defines the zero entropy state for any substance in a single, pure quantum state as the absolute zero of temperature. 

Equation (4.2) can be used to determine the entropy of a substance. A pure crystalline sample is placed in a cryogenic calorimeter and cooled to low temperatures. Increments of heat, q, are added and the temperature change, AT, is measured, from which the heat capacity can be calculated from the relationship... 

The most common states of a pure substance are solid, liquid, or gas (vapor), state property See state function. state symbol A symbol (abbreviation) denoting the state of a species. Examples s (solid) I (liquid) g (gas) aq (aqueous solution), statistical entropy The entropy calculated from statistical thermodynamics S = k In W. statistical thermodynamics The interpretation of the laws of thermodynamics in terms of the behavior of large numbers of atoms and molecules, steady-state approximation The assumption that the net rate of formation of reaction intermediates is 0. Stefan-Boltzmann law The total intensity of radiation emitted by a heated black body is proportional to the fourth power of the absolute temperature, stereoisomers Isomers in which atoms have the same partners arranged differently in space, stereoregular polymer A polymer in which each unit or pair of repeating units has the same relative orientation, steric factor (P) An empirical factor that takes into account the steric requirement of a reaction, steric requirement A constraint on an elementary reaction in which the successful collision of two molecules depends on their relative orientation. 

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). 

The third law of thermodynamics makes it possible to measure the absolute entropy of any substance at any temperature. Figure 14-12 shows the stages of a pure substance, in this case argon, as the temperature is raised from 7 =0,S = 0toJ = 298 K. As temperature increases, entropy increases steadily. 

The third law of thermodynamics establishes a starting point for entropies. At 0 K, any pure perfect crystal is completely constrained and has S = 0 J / K. At any higher temperature, the substance has a positive entropy that depends on the conditions. The molar entropies of many pure substances have been measured at standard thermodynamic conditions, P ° = 1 bar. The same thermodynamic tables that list standard enthalpies of formation usually also list standard molar entropies, designated S °, fbr T — 298 K. Table 14-2 lists representative values of S to give you an idea of the magnitudes of absolute entropies. Appendix D contains a more extensive list. 

This is an expression of Nernst s postulate which may be stated as the entropy change in a reaction at absolute zero is zero. The above relationships were established on the basis of measurements on reactions involving completely ordered crystalline substances only. Extending Nernst s result, Planck stated that the entropy, S0, of any perfectly ordered crystalline substance at absolute zero should be zero. This is the statement of the third law of thermodynamics. The third law, therefore, provides a means of calculating the absolute value of the entropy of a substance at any temperature. The statement of the third law is confined to pure crystalline solids simply because it has been observed that entropies of solutions and supercooled liquids do not approach a value of zero on being cooled. 

At a constant pressure, the entropy of any pure substance can be calculated for any temperature through the use of the procedure that is herein being described. The entropy change taking place during an isothermal reversible process, it may be recalled, is equal to the heat change involved divided by the absolute temperature ... 

The Third Law of Thermodynamics states that the entropy of a pure, perfect crystalline substance is zero at 0 K. 

This means that all substances have some entropy (dispersal of energy and/or matter, i.e. disorder) except when the substance is a pure, perfect, motionless, vibrationless crystal at absolute zero Kelvin. This also implies that the entropy of a substance can be expressed on an absolute basis. 

According to this second law, the entropy of the universe is continually increasing. The third law of thermodynamics states that for a pure crystalline substance at 0 K the entropy is zero. 

An ordered arrangement of particles (atoms, ions, or molecules) has lower entropy (smaller disorder) than the same number of particles in random arrangements. Thus, the entropy of a pure substance depends on its state. The entropy of a system increases (becomes more disordered) with temperature, because the motion of particles becomes more chaotic at higher temperatures. See Figure 7.6 on the next page. 

In Nemst s statement of the third law, no comment is made on the value of the entropy of a substance at 0 K, although it follows from his hypothesis that all pure crystalline substances must have the same entropy at OK. Planck [2] extended Nemst s assumption by adding the postulate that the value of the entropy of a pure solid or a pure liquid approaches zero at 0 K ... 

The assumption of any hnite constant for the entropy of all pure solids and liquids at OK leads to Nernst s theorem [Equation (11.3)] for these substances. 

Third Law of Thermodynamics. Also referred to as the Nernst heat theorem, this law states that it is impossible to reduce the temperature of any system, via a finite set of operations, to absolute zero. For any changes involving perfectly crystalline solids at absolute zero, the change in total entropy is zero (thus, A5qk = 0). A corollary to this statement is that every substance, at T > 0 K, must have a positive and finite entropy value. The entropy of that substance is zero only at absolute zero when that substance is in pure, perfect crystalline form. See Entropy... 

It is more problematical to define the third law of thermodynamics compared to the first and second laws. Experimental work by Richards (1902) and Nemst (1906) led Nemst to postulate that, as the temperature approached absolute zero, the entropy of the system would also approach zero. This led to a definition for the third law of thermodynamics that at a temperature of absolute zero the entropy of a condensed system would also be zero. This was further refined by Planck (1911) who suggested this be reworded as the entropy of a pure element or substance in a perfect crystalline form is zero at absolute zero. 

The third law of thermodynamics says that the entropy of pure, perfect crystalline substance is zero at absolute zero. But, in actual practice, it has been found that certain chemical reactions between crystalline substance, do not have DS = 0 at 0°K, which indicates that exceptions to third law exist. Such exceptional reactions involve either ice, CO, N2O or H2. It means that in the crystalline state these substances do not have some definite value of entropy even at absolute zero. This entropy is known as Residual Entropy. At 0°K the residual entropies of some crystalline substances are... 

A pure substance A exists in three modifications Ai A2 and Ag. At the triple point S j > a2 > o3 and Val>Va2>Vo3,S and V are entropy and volume respectively are there. A suitable P-T diagram on the basis of informations given above and also label the region, line and points constructed ... 

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