Solid entropy, total

Molar entropy of an adsorbed layer perturbed by the solid surface Total enthalpy change for the immersion of an evacuated solid in a solution at a concentration at which monolayer adsorption occurs Heat of dilution of a solute from a solution Enthalpy change for the formation of an interface between an adsorbed mono-layer and solution Integral heat of adsorption of a monolayer of adsorbate vapor onto the solid surface... 

This equation represents the formation of an aqueous solution of the salt ammonium nitrate, NH4N03, a widely used fertilizer. The product ions have much more freedom of movement when dissolved in water than they do when bound together within the pure solid. With this greater freedom of movement they are able to absorb more dispersed energy. The products, therefore, have larger entropy totals than the reactants. According to these ideas, this reaction should be favorable. 

This is the entropy of each mode of Irequency to. We need to consider all the modes. In a solid, the total number of modes of vibration consisting of N atoms is 3N 6, giving rise to an energy spectrum. The total harmonic entropy of the solid is obtained by integration of Eq. (19.6) over this spectrum. 

Figure 7.3 Change in total entropy caused by spontaneous workfree heat transfer in the isolated system shown in Figure 7.2. No matter whether the gas is heated or cooled by the solid, the total entropy increases, in agreement with (7.1.18).

In electrochemistry it is customary to multiply each of those quantities by Avogadro s constant and, when a few additional ions enter the already saturated solution, to speak of the entropy of solution per mole. Let the entropy of one mole of the crystalline solid be denoted by Scr and let Si and S2 denote, respectively, the entropy of the solution before, and after, the entry of the additional solute, both expressed in calories per mole. The total initial entropy is obviously (S + Si) and the final entropy is St. The difference between the final and the initial entropy is by definition AS,at. 

When solid AgCl is in contact with its saturated aqueous solution, we have found that, if additional ion pairs are transferred from the surface of the crystal to the solution, the total change of entropy is equivalent to 52.8 e.u Since the entropy of the solid is 23.0 e.u., we find that the partial molal entropy of AgCl in its saturated aqueous solution at 25°C is... 

Lead, excess entropy of solution of noble metals in, 133 Lead-thalium, solid solution, 126 Lead-tin, system, energy of solution, 143 solution, enthalpy of formation, 143 Lead-zinc, alloy (Pb8Zn2), calculation of thermodynamic quantities, 136 Legendre expansion in total ground state wave function of helium, 294 Lennard-Jones 6-12 potential, in analy-... 

The solid product, BaO, was apparently amorphous and porous. Decomposition rate measurements were made between the phase transformation at 1422 K and 1550 K (the salt melts at 1620 K). The enthalpy and entropy of activation at 1500 K (575 13 kJ mole-1 and 200 8 J K"1 mole-1) are very similar to the standard enthalpy and entropy of decomposition at the same temperature (588 7 kJ and 257 5 J K-1, respectively, referred to 1 mole of BaS04). The simplest mechanistic explanation of the observations is that all steps in the reaction are in equilibrium except for desorption of the gaseous products, S02 and 02. Desorption occurs over an area equivalent to about 1.4% of the total exposed crystal surface. Other possible models are discussed. 

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. 

For an atom in a solid, vibratory motion involves potential energy as well as kinetic ener, and both modes will contribute a term l/2kT, resulting in an average total energy of 3kT. Thus, it is the entropy of mixing that forces the creation of a certain number of vacant lattice positions above 0.0 °K. Hence, vacancies are the natural resultof thermod5mamic equilibrium md not the result of accidental growth or sample preparation. 

The melting temperature depression or enhancement may now be expressed in terms of the melting temperature and the entropy of fusion of component A, the activity coefficients of impurity B in the liquid and solid solutions at infinite dilution, and the total concentration of the impurity B, xb [12] ... 

The change in state from liquid to solid as a material crystallizes, is driven by thermodynamics and the principle of free energy minimization, in turn this results from a trade between the total enthalpy and entropy of a system. 

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... 

However, most of the examples quoted in these earlier papers do not include the higher melting-point elements such as W, where a detailed treatment shows that the total entropy (at least of the solid phases) must include many other components such as the electronic specific heat, anharmonicity terms and the temperature dependence of 9d (Grimwall et al. 1987, Moroni et al. 1996). An estimate for the Debye temperature of the high-temperature 0 phase was included in the seminal... 

The total entropy of a substance in a state defined as standard. Thus, the standard states of a solid or a liquid are regarded as those of the pure solid or Ihe pure liquid, respectively, and at a stated temperature. The standard state of a gas is at 1 atmosphere pressure and specified temperature, and its standard entropy is the change of entropy accompanying its expansion to zero pressure, or its compression from zero pressure to 1 atmosphere. The standard entropy of an ion is defined in a solution of unit activity, by assuming that the standard entropy of the hydrogen ion is zero. 

Let s calculate the entropy of a tiny solid made up of four diatomic molecules of a binary compound such as carbon monoxide, CO. Suppose the four molecules have formed a perfectly ordered crystal in which all molecules are aligned with their C atoms on the left. Because T = 0, all motion has ceased (Fig. 7.5). We expect the sample to have zero entropy, because there is no disorder in either location or energy. This value is confirmed by the Boltzmann formula because there is only one way of arranging the molecules in the perfect crystal, W = l and S = k In 1 =0. Now suppose thar the molecules can lie with their C atoms on either side yet still have the same total energy (Fig. 7.6). The total number of ways of arranging the four molecules is... 

Note that this change in entropy is greater than the decrease in entropy of the system, —22.0 J-K 1, which we calculated from the difference in entropy of the solid and liquid states of water in Table 7.2. Therefore, the total change in entropy is positive at — 10°C, and the freezing of water is spontaneous at that temperature. 

Because ASPEN is to be used with coal conversion processes, its streams can be designated to carry an arbitrary number of solids or solid phases. This is done by specifying any number of substreams. In fact, the conventional vapor/liquid stream is normally assumed as a substream and solids can comprise other substreams. For the conventional vapor/liquid substream, process data is carried on component molar flows, total molar flow, temperature pressure, specific enthalpy, specific entropy, density, molar vapor fraction, molar liquid fraction, and molecular weight. For solid substreams, which are called "non-conventional substreams," the characterizing data is not as deterministic. The information associated with these substreams is called "attributes". Such attributes may be particle size distribution, ultimate and proximate analyses, or other material specific information. Another type of substream is an "informa-... 

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