Entropy change due

EXAMPLE 7.2 Calculating the entropy change due to an increase in temperature... 

If a model is inadequate and/or experimental data are insufficiently accurate, the minimization methods might show up a tendency to simultaneously decrease or increase both coefficients outside the range of physical meaning. In this case fixation of AS, is can be a sufficient remedy. For evaluation of the entropy change due to adsorption, books and papers of Adamson (1982), Barrow (1973), Cerny (1983), Waugh (1994), and Zhdanov et al. (1988) are recommended. 

A certain ambiguity arises in the proper choice of the thermodynamic parameter p, since entropy changes due to solvent orientation are neglected. The available experimental data (cf. Sect. 4) indicate, however, that the free energy of reaction for systems showing a spin change is close to zero. The numerical analysis has been therefore performed for the specific case p = 0, for which value the rate constant in Fig. 15 has been computed as a function of S and h lkgT. 

The configurational entropy on the b lattice is given by an identical equation. For the perfect long-range ordered modification the configurational entropy is zero, and the entropy change due to disorder is thus... 

Volume change and phase transition There is another formulation of the binomial number that is used for the entropy change due to volume expansion. From equation (40), we obtain in the limit that when m n... 

Each of the two gases will suffer entropy change due to the volume change. Thus... 

Following this, the thermodynamic arguments needed for determining CMC are discussed (Section 8.5). Here, we describe two approaches, namely, the mass action model (based on treating micellization as a chemical reaction ) and the phase equilibrium model (which treats micellization as a phase separation phenomenon). The entropy change due to micellization and the concept of hydrophobic effect are also described, along with the definition of thermodynamic standard states. 

Now, neglecting entropy changes due to the adsorption and desorption of physically adsorbed particles, and assuming that the empty adsorption traps are physically adsorbed particles present in surface concentration No (which is assumed independent of E2), the number of these will be, by the Boltzmann distribution... 

Fig. 3.1. Entropy change due to a reversible transfer of heat into a closed system at constant volume and temperature dQm = reversible heat transfer.

The principal structures into which organolithium compounds assemble are unsolvated octahedral hexamers 6, and cubic tetramers, and solvated cubic tetramers 7, bridged dimers 8 and monomers, 9. In common among the solvated species, lithium is always tetracoor-dinate so that the dissociating direction is exothermic with negative entropy change due to the increase in coordination of lithium to a ligand ether or a tertiary amine. 

Compute the entropy change due to phase transformation. In this case,... 

The general entropy balance relations for a control volume are given in terms of the rate of entropy change due to the heat transfer, mass flow, and entropy production... 

Equations (12.30) and (12.14) show that the contributions to the entropy change due to fluctuations in the equilibrium state are of second order, expressed by i rS/2... 

The entropy of activation would amount to about 10 cal/mole-°C, which is quite reasonable when compared with the over-all entropy change in the reaction of about 45 cal/mole- C (standard state 25 C, 1 atm pressure). The standard entropy change due to translation is 32.4 cal/mole-°C, which leaves 12.6 cal/mole-°C for rotation and vibrational changes, a figure that shoidd be compared with the 10 cal/molc- C entropy of activation. This would indicate that the transition-state complex is much more like two loosely bound NO2 molecules than it is like N2O4. 

Calculate the entropy change due to ion-solvent interaction for the ions in Exercise 13 using the relation c/ 7 = 0.356/K for water. (Kim)... 

Because of the leverage due to the presence of an axial methyl group, one might expect some evidence of an effect of boat conformations on the equilibria in Table XXVII. Since the equilibria were determined at two temperatures, assuming for the trans isomers that the log K vb I jT plots are linear, one can calculate the intercept and subtract the entropy changes due to creation of axes of symmetry or dl pairs. The residual entropies did indeed have a negative bias, rms A/S = — 0.4 0.5, but the scatter was too large for any reliable estimate of the populations of boat conformations. 

Hence, the entropy,change due solely to heat interaction with the environment is given by... 

Equation (2-34) gives the standard entropy of polymerization AS°. The overall entropy change due to polymerization is equal to ASp = AS + RT ln[M]. 

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