Entropy components

System Potential energy components Energy-entropy components ... 

The temperature dependence of reaction rates permits evaluation of the enthalpy and entropy components of the free energy of activation. The terms in Eq. (4.4) corresponding to can be expressed as... 

Since AG and AG are combinations of enthalpy and entropy terms, a linear free-energy relationship between two reaction series can result from one of three circumstances (1) AH is constant and the AS terms are proportional for the series, (2) AS is constant and the AH terms are proportional, or (3) AH and AS are linearly related. Dissection of the free-energy changes into enthalpy and entropy components has often shown the third case to be true. °... 

Table 9 shows that the value of AGn of the cooperative interaction between bonding centers is within the error in the determination of integral AG values. This fact can either indicate the slight mutual influence of the centers or be caused by the compensation between the enthalpy and entropy components of Gibbs free energy. 

The relationship of thermodynamic functions of selective bonding of Hb to a series of carboxylic CP in the variation of the degree of ionization of carboxylic groups is expressed by the effect of enthalpy-entropy compensation (Fig. 18). The compensation effect of enthalpy and entropy components is the most wide-spread characteristic of many reactions in aqueous solutions for systems with a cooperative change in structure [78],... 

The chemical potential difference —ju may be resolved into its heat and entropy components in either of two ways the partial molar heat of dilution may be measured directly by calorimetric methods and the entropy of dilution calculated from the relationship A i = (AHi —AFi)/T where AFi=/xi —/x or the temperature coefficient of the activity (hence the temperature coefficient of the chemical potential) may be determined, and from it the heat and entropy of dilution can be calculated using the standard relationships... 

Expanding on this example, some general criteria for predicting chemical reactions are possible. From the example, one can see that the enthalpy component in the calculation is much larger than the entropy component. This is usually (but not always) true. With... 

Equation (50) uses the fact that the a-bond energies and the entropy components may be assumed constant. However, this formula does not allow for the fact that several isomeric proton addition complexes may be present in the solution. In that case one obtains the more general relation ... 

The emphasis in the previous sections has been on the accuracy with which the Gibbs energy, particularly the entropy component above T , can be calculated. However, as the number of components, C, and the number of atoms in the chosen cluster, n, increases, the number of simultaneous equations that have to be solved is of the order of C". This number is not materially reduced by redefining the equations in terms of multi-site correlation functions (Kikuchi and Sato 1974). The position may be eased as extra computing power becomes available, but a choice will inevitably have to be made between supporting a more complex model or extending a simpler model to a greater number of components. 

Molecular structure enters into the rotational entropy component, and vibrational frequencies into the vibrational entropy component. The translational entropy component cancels in a (mass) balanced reaction, and the electronic component is most commonly zero. Note that the vibrational contribution to the entropy goes to oo as v goes to 0. This is a consequence of the linear harmonic oscillator approximation used to derive equation 7, and is inappropriate. Vibrational entropy contributions from frequencies below 300 cm should be treated with caution. 

Also the reaction temperature has been shown to have a remarkable effect on the extent of diastereoselectivity. Low temperatures seem to favor the formation of (S) diastereoisomers. This may be explained supposing that mechanisms A and C are more entropically disfavored than mechanism B. Therefore the entropy component in AG is higher and the decrease of rate on lowering the temperature is less pronounced. 

The issue of isotope effects is further complicated by the recently reported unusual temperature dependences such that either a normal or an inverse isotope effect may be observed for the same reaction depending on the temperature.96 Calculations suggest that significant contributions to the zero-point energy can come from vibrations that do not involve the bonds being made or broken. The transition between the normal and inverse isotope effects occurs because of the inverse enthalpy and normal entropy components that oppose each other and exhibit different temperature dependences. 

A relative free energy for clusters of a given size is obtained by employing the potential function and calculating the entropy (S) of the cluster. To compare various geometries, only the entropy component from vibration needs to be cal-... 

It should be noted that the entropy component of the polychelate effect is largely controlled by the same contributions as for LMWM, i.e., translation, rotation, symmetry, isomerism, oscillation, internal rotation and solvation contributions [41]. Besides both the chelate and polychelate effects depend greatly on the size of the chelate cycle. In this case the PCMU obey the known Chugaev rule by... 

Thus the force consists of an internal energy component and an entropy component [compare (iii) of Table 4-1 for the pressure of a gas]. 

To evaluate Eq. (4-32) experimentally, we proceed in an analogous fashion to the method used to estimate the entropy component of the pressure of a gas (Table 4-1). From Eq. (4-26), for any change. 

Samsonov [15] studied the direct sorption of ALA and other dipolar ions by SDV-3 ion exchanger resin at pH = 7. The enthalpy and entropy components of these sorptions were obtained from the isotherm dependence on temperature. It was found that the transformation of the resin from the hydrogen to the amino acid form was accompanied by a rise in the system s entropy. The thermodynamic-based description of the exchange of a-amino acids with hydrogen on three ion-exchange resins at pH < pK .co2 were determined as well. However, precise descriptions of the experimental measurements and the calculations program used were not given. 

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