Entropy temperature effects

Allowable stress at test temperature Resultant bending stress Basic allowable stress at minimum metal temperature expected Basic allowable stress at maximum metal temperature expected Torsional stress Specific gravity Specific entropy Temperature Effective branch-wall thickness... 

Rate coefficients have also been measured at a range of temperatures for some aromatics in aqueous perchloric acid-trifluoroacetic acid (Table 168)468, and, surprisingly, the lower reactivity of benzene relative to toluene and /-butylbenzene appears to arise from a more negative activation entropy. This effect if real is... 

The entropy of any chemical substance increases as temperature increases. These changes in entropy as a function of temperature can be calculated, but the techniques require calculus. Fortunately, temperature affects the entropies of reactants and products similarly. The absolute entropy of every substance increases with temperature, but the entropy of the reactants often changes with temperature by almost the same amount as the entropy of the products. This means that the temperature effect on the entropy change for a reaction is usually small enough that we can consider A Sj-eaction he independent of temperature. 

The increase in the length of the side chain results normally in an internal plasticization effect caused by a lower polarity of the main chain and an increase in the configurational entropy. Both effects result in a lower activation energy of segmental motion and consequently a lower glass transition temperature. The modification of PPO with myristoyl chloride offers the best example. No side chain crystallization was detected by DSC for these polymers. 

This temperature effect is the usual one for a regular or enthalpy-entropy compensated chromatographic separation, suggesting that the retention of each... 

It is tacitly assumed in the Hughes-Ingold rules that the entropy of activation is small relative to the enthalpy of activation, i.e., AG AH, and that the temperature effect on the rate follows Eq. (2.22) with an assumed temperature independent value of AH. If the number of solvent molecules solvating the activated complex is very different from that solvating the reactants, then this assumption is no longer valid. This is the case in the solvolysis of t-butyl chloride in water (AH = 97 kJ mol 1, TAS = 15 kJ mol 1) compared to, say, ethanol (AH = 109 kJ mol 1, TAS = -4 kJ mol 1). 

The classical (or semiclassical) equation for the rate constant of e.t. in the Marcus-Hush theory is fundamentally an Arrhenius-Eyring transition state equation, which leads to two quite different temperature effects. The preexponential factor implies only the usual square-root dependence related to the activation entropy so that the major temperature effect resides in the exponential term. The quadratic relationship of the activation energy and the reaction free energy then leads to the prediction that the influence of the temperature on the rate constant should go through a minimum when AG is zero, and then should increase as AG° becomes either more negative, or more positive (Fig. 12). In a quantitative formulation, the derivative dk/dT is expected to follow a bell-shaped function [83]. 

Temperature effects and pressure effects made it possible to determine the entropies and volumes of activation for hydronium-catalysed enolisation. The large negative values observed LdS = —16.5 cal mol-1 K-1 for acetone (Dubois and Toullec, 1973) see also some data relative to cycloalkanones listed below, Table 2 AV = —2.1 cm3 mol-1 for acetone (Baliga and Whalley, 1964)] are also in agreement with a transition state in which molecules of water are incorporated. 

A similar slow evolution from energy to entropy with a final synthesis of both concepts can also be observed in the historical development of chemical kinetics. The energy factor was first pointed out by Arrhenius (1889) when he explained the temperature effect on reaction rates. But in spite of the early work of Kohnstamm and Scheffer (1911) who introduced the idea of activation entropy, the importance of entropy was generally recognized only after Eyring (1935) formulated clearly the thermodynamic treatment of the transition state method. 

The effect of the addition of water and the presence of Li on the disproportionation equilibria was also examined (Ammar and Saveant, 1973). The effect of water was observed to be a decrease in AS with little change in the entropy term. On the other hand, Li also brought about a decrease in A but the entropy increased and became positive. The latter brought about an inverse temperature effect instead of AE increasing with temperature a decrease was observed. 

Clarke and Glew did not give the entropy coefficient, but this is discussed in Chapter 15 and in papers on temperature effects (12,13),... 

Equation 41 shows that the chemical potential is a partial molar property. We will need other partial molar quantities (e.g., those for volume, enthalpy, and entropy) in dealing with pressure and temperature effects on energetics of reactions. 

This chapter has shown how the zero-temperature analyses presented earlier in the book may be extended to incorporate finite-temperature effects. By advancing the harmonic approximation we have been able to construct classical and quantum mechanical models of thermal vibrations that are tractable. These models have been used in the present chapter to examine simple models of both the specific heat and thermal expansion. In later chapters we will see how these same concepts emerge in the setting of diffusion in solids and the description of the vibrational entropies that lead to an important class of structural phase transformations. 

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