Entropy change pure components

Consider the entropy change in forming one mole of solution at constant T from 4>m moles of 1 (of molar volume V ) and ni2 moles of 2 (of molar volume V2). In the pure state, the 0m 1 moles of 1 occupy (or have available) the volume 0mIF], and the 0m2 moles of 2 have available the volume 0m2 2- However, when the solution is formed, both the 0m 1 moles of 1 and the 0m2 moles of 2 have available to them the entire volume of the solution 0mi V +0m2 2- The entropy change experienced by component 1 due to this available volume change is... 

The entropy change to form an ideal mixture from the pure components is obtained by differentiating equation (7.7) with respect to T. Since x, is independent of T, the result is... 

Ethylene hydroformylation was treated as a separate case, as difSculties arise from dramatic changes in the IR spectrum of dissolved ethylene as a function of its partial pressure. This was overcome using the method of band-target entropy minimisation (BTEM, see Chapter 4) to recover the pure component spectra of all observable species and their concentrations [72]. As well as the conventional acyl tetra-carbonyl, [Rh(C(0)Et)(C0)4], evidence was obtained for [Rh(C(0)Et)(C0)3(C2H4)], containing coordinated ethylene. The presence of this species indicates that ethylene can compete with H2 for the unsaturated [Rh(C(0)Et)(C0)3]. The ketone and polyketone side products of Rh-catalysed ethylene hydroformylation arise from insertion of coordinated ethylene into the Rh-acyl bond in [Rh(C(0)Et)(C0)3(C2H4) ... 

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. 

Note that these entropies are with respect to the entropy equal to zero for the pure component and 0 K. Also, the entropy change of reaction at 0 K is zero for all reactions. Therefore... 

A so-called regular solution is obtained when the enthalpy change (AHmix) is nonideal (i.e., non-zero, either positive or negative) but the entropy change (A mix) is still ideal. So on the molecular level, while an ideal solution is one in which the different types of molecules (A and B, for example) behave exactly as if they are surrounded by molecules of their own kind (that is, all intermolecular interactions are equivalent), a regular solution can form only if the random distribution of molecules persists even in the presence of A-B interactions that differ from the purely A-A and B-B interactions of the original components A and B. This concept has proved to be very useful in the development of an understanding of miscibility criteria. 

Be able to use the rate-of-change form of the pure component entropy balance in problem solving... 

This is the entropy change involved in mixing the two pure end-member components (FeMiFeM2)Si206 and (MgMiMgM2)Si20g to make a pyroxene solution of some intermediate composition. We will use equations (15.3) for non-ideal entropy and (15.7) for activities of the individual ions on each site, thus... 

The first step is to calculate K. The method involving the standard heat of reaction and the standard entropy change is usually used because these data are available for most substances. In the tables giving standard heats of formation (or standard heats of combustion) and absolute ejn-tropies, the standard state is usually specified as unit fugacity for all ga es and is usually stated as th pure gas at 1 atm pressure. The calculation must be based upon the standard state specified by these tables and is not arbitrary, as many people are led to believe. If the standard state for each component is that of unit fugacity, the equilibrium equation becomes... 

The reaction enthalpy A// is negative in exothermic processes, and positive in endothermic processes. The reaction entropy AS, which is a measure of the change in the state of disorder of the system, is always positive since the entropy of the solution (mixture) is always greater than that of the pure components. 

To obtain the entropy of the mixture, we imagine a component going from the pure state at P, T, into the mixture at same pressure and temperature (see Figure.222). This process increases the volume available to this component, from Vi (the molar volume of the pure component) to V (the molar volume of the mixture). This amounts to expanding this component isothermally from volume V = x. V to volume V. The entropy change for this process is... 

Figure 5.7. Thermoelasticity experiments to estimate the entropic component of elastic force in pure water (curves B) and in the solvent mixture of 30% ethylene glycol 70% water (curves A). On increasing ethylene to 30%, the heat of the transition approaches zero, which means that the solvent entropy change approaches zero. The purpose of the experiment is to see if solvent entropy change contributes to the force developed on raising the temperature. Interestingly, the 90% entropic elastic force...

First-Order Transitions. The principal transitions in macromolecules are those concerned with enthalpy (latent heat) and entropy changes. They are called first-order transitions according to a classification requiring the first derivative of the change in free enthalpy with respect to temperature not to be zero (92). For a single-component system (pure compound), thermodynamic equilibrium states... 

There is another process in which mixing is involved and in which both the Helmholtz energy and the entropy do change. Consider process II in Fig. 2.2. We start with two pure components A and B as in the previous experiment. We let the two components mix in a volume 2 F, instead of F as in the previous experiment. This can be achieved by removing a partition separating the two compartments. 

Entropy of fusion data of pure, one-component systems of different molecular structures are collected in Tables 5.2-5.5. These will be discussed in connection with Fig. 1.9, progressing from spherical molecules to asymmetric molecules with conformational mobility. Naturally, as discussed in the previous section, the equilibrium data on linear macromolecules are often derived by extrapolation, to both the equilibrium melting temperature and crystallinity = 1.0). In Fig. 3.7 the equilibrium melting temperature is shown to be AHf/AS [Eq. (6)]. Heat of fusion measurements are thus able also to provide data on the entropy of fusion. This allows the development of quantitative lists of entropies of fusion. In this section an attempt is made to find the connection between the entropy of fusion and molecular structure. A typical example of experimental data on entropy changes with fusion is shown in Fig. 5.26. 

Properties of mixing for ideal mixtures The change of entropy upon mixing is the difference between the entropy of the mixture and file sum of entropies of pure, individual components, that is... 

The entropy change upon mixing the pure components 1 and 2 is given by... 

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