Entropy transition increase

We can expect the entropy to increase when a solid melts and its molecules become more disordered. Similarly, we can expect an even greater increase in entropy when a liquid vaporizes, because its molecules then occupy a much greater volume and their motion is highly chaotic. In this section, we develop expressions for the change in entropy at the transition temperature for the prevailing pressure. For instance, if the pressure is 1 atm, then these expressions are applicable only at the normal melting point, Tf (the f stands for fusion), the temperature at which a solid melts when the pressure is 1 atm, or the normal boiling point, Th, the temperature at which a liquid boils when the pressure is 1 atm. 

A correct understanding of the ice-water transition came when it was recognized that when ice melts not only does H increase by 6.008 kj mol-1, as the molecules acquire additional internal energy of translation, vibration, and rotation, but also the molecules become more disordered. Although historically entropy was introduced in a different context, it is now recognized to be a measure of "microscopic disorder." When ice melts, the entropy S increases because the structure becomes less ordered. 

The effect of adding homopolymer to ordered block copolymer melts was interpreted by considering how homopolymer is distributed within the microstructure (Matsen 19956). Within the A-rich domains of a microslructure, the A blocks tend to segregate to the interfaces, whereas homopolymer A is preferentially located in the domain centre due to tension in the A blocks. This is countered by the entropy of mixing which favours a more uniform distribution of homopolymer. To allow homopolymer near the interface, a phase transition may occur to a microstructure where the interface is less curved towards the A-rich domains (this is the reverse of the process shown in Fig. 6.9). Even without such a phase transition, increasing homopolymer content leads to an increasing... 

To predict the sign of A S, look to see if the process involves a phase change, a change in the number of gaseous molecules, or the dissolution (or precipitation) of a solid. Entropy generally increases for phase transitions that convert a solid to a liquid or a liquid to a gas, reactions that increase the number of gaseous molecules, and dissolution of molecular solids or salts with +1 cations and —1 anions. 

For a constant polysaccharide mass, an extended (random) coil exposes more surface area than does a helix, and a single helix exposes more than a double helix. The energy content of a polymer molecule is a property of its surface area. Thus, one consequence of a coil-to-helix transition is a diminution of the macromolecular exposed surface area and energy in compliance with the law of entropy. An increase in viscosity coincides with an increase in surface, inasmuch as the resistance to motion covers a wider area. 

As a general guide, it will be found that entropy values increase during the transitions solid to liquid to gas, as demonstrated by the values for solid... 

One would like to ignore the entropy contribution S, but the existence of polymorphs and of polymorphUc transitions is an effective demonstration that this cannot be done. As the temperature is increased past some transition point, the polymorph stable at 0 K may become metastable and then transform to a different polymorph. The entropy always increases with temperature faster in the polymorphic form that becomes stable at higher temperature. 

For a sohd to liquid phase transition (melting) the entropy always increases (AS > 0) and the reaction is always endothermic (AH > 0). 

In accordance with the conclusion (Eq. 62) the activated complex has not only the same number, but also the same freedom degree as the particles into the main state. That is why in the presented case it cannot be obtain the AS > 0 at the expense of the freedom degrees redistribution at the transfer of particle from the main state into the activated one. Since at given P and T the activation is accompanied by the energy increasing, also the entropy should be increased like to the fact that the entropy is increased at the phases transition by the first kind at AH > 0. 

Entropy measures the change in order a positive change in entropy measures increased disorder, and a negative change in entropy measures increased order. For the transition where ice melts to form water at 0°C (273°K on the absolute scale where motion ceases at 0°K), the increase in entropy is the experimentally determined heat absorbed during the transition divided by the temperature for the transition, that is, 273°K (see Chapter 5 for a more complete discussion). 

In these last two equations, the c index after T denotes ceiling conditions corresponding to the monomer concentration at equilibrium [Mequ]. Indeed, in most of polymerizations, the variation of entropy is negative since the transition from the monomer to the polymer state corresponds to a decrease in the degrees of freedom of the system thus, the entropy term is unfavorable to the polymerization process. For the latter to occur, it should be compensated by a negative value of the polymerization enthalpy, which implies that chain polymerization reactions are exothermic processes. When the temperature is raised, the entropy term increases as well until becoming equal, in absolute value, to the enthalpy term. The polymerization can then no longer proceed. 

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