Entropy qualitative predictions

It is possible to derive an expression equivalent to Eq. (4.67) starting from entropy rather than free volume concepts. We have emphasized the latter approach, since it is easier to visualize and hence to use for qualitative predictions about Tg. 

We can usually make qualitative predictions about entropy changes by focusing on these factors. For example, when water vaporizes, the molecules spread out into a larger volume. Because they occupy a larger volume, there is an increase in their freedom of motion, giving rise to a greater number of possible microstates, and hence an increase in entropy. 

As we said earlier, entropy often is described as a measure of randomness or disorder. Although this can be a useful description, it should be used with caution and not taken too literally. It is generally preferable to view the change in entropy of a system in terms of the change in the number of microstates of the system. Nevertheless, we can use the concept of disorder to make some qualitative predictions about the entropy changes that accompany certain processes. 

Sample Problem 18.1 lets you practice the qualitative prediction of entropy change for a process. 

Equation 18.5 enables us to calculate for a process when the standard entropies of the products and reactants are known. However, sometimes it s useful just to know the sign of AA. Although multiple factors can influence the sign of AS, the outcome is often dominated by a single factor, which can be used to make a qualitative prediction. Several processes that lead to an... 

In this case AS is nearly zero, since the moles of gas-phase species of reactants and products are equivalent. In this case, the entropy may be slightly positive or negative depending on the difference between the molecular structures of the products and reactants, but we can qualitatively predict from Eq. (3.105) that the maximum thermodynamic efficiency will be nearly invariant with temperature, which would correspond to the sdaight line shown in Figure 3.13. 

Making Qualitative Predictions of Entropy Changes in Physical and Chemical Processes... 

By analogy to AfFT and AfG° how would you define standard entropy of formation Which would have the largest standard entropy of formation CH4(g), CH3CH20H(1), or CS2(1) First make a qualitative prediction then test your prediction with data from Appendix D. 

Fig. 5. Qualitative comparison between the experimental excess entropies and the APM predictions. White circles sE > 0, black circles sE < 0 (x = 0.5).

Perhaps more valuable over time than the quantitative predictions of spectra, structural parameters, and relative enthalpies and entropies of RIs, which can be obtained from electronic structure calculations, are the qualitative models of the electronic structures and reactivities of RIs that emerge from the computational results. Any model, to be successful, must do two things. 

To decide whether we need to worry about AS0 with regard to any particular reaction, we have to have some idea what physical meaning entropy has. To be very detailed about this subject is beyond the scope of this book, but you should try to understand the physical basis of entropy, because if you do, then you will be able to predict at least qualitatively whether AH° will be about the same or very different from AG°. Essentially, the entropy of a chemical system is a measure of its molecular disorder or randomness. Other things being the same, the more random the system is, the more favorable the system is. 

This simple collision theory thus predicts preexponential factors of about 10 cc/mole-sec, since we expect P < 1. Values of P < 1 are interpreted kinetically as due to improperly oriented collisions ( steric hindrance) or thermodynamically as a negative entropy of activation, i.e., a loss of freedom of A and B in forming the collision complex. As we shall see, these results are in good qualitative agreement with observations and Zab does indeed seem to be an upper limit for bimolecular frequency factors. ... 

The Adam-Gibbs equation (4-10) can be tested directly by using the calorimetrically measured entropy difference AS to compute the temperature-dependence of the relaxation time, with B then being a fitting parameter. This has been done, for example, with the data for o-terphenyl shown in Fig. 4-11, and the predicted temperature-dependence of the viscosity is found to be in qualitative, but not quantitative, agreement with the measured viscosity (see, for example. Fig 4-12). The main reason for the failure in Fig. 4-12 is that the temperature Tj at which the entropy extrapolates to zero for o-terphenyl lies below the VFTH temperature Tq required to fit the viscosity data hence the predicted viscosity does not vary as rapidly with temperature as it should. 

In addition, since it is a lattice model, the bond fluctuation model can be used to assess the validity of the Gibbs-DiMarzio theory described in Section 4.4.1. Baschnagel et al. (1997) show that the curve of entropy versus inverse temperatures (Sc versus l/T) does not cross zero when the temperature is lowered, but instead levels out at large 1/7, in disagreement with the Gibbs-DiMarzio theory but qualitatively similar to the prediction of Miller s theory in Fig. 4-13. 

Stated as an abstraction and generalization of engineering observations on the efficiency of heat engines. We start the discussion by presenting a nonmathematical qualitative summary of the arguments on efficiency. Then we define entropy and state the second law. Section 13.5 applies the definition to calculate entropy changes and to predict spontaneity of processes. 

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