Enthalpy and entropy terms

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. °... 

Given the partition functions, the enthalpy and entropy terms may be calculated by carrying out the required differentiations in eq. (12.8). For one mole of molecules, the results for a non-linear system are (R being the gas constant)... 

Table 6.1 summarizes the thermodynamic parameters relating to the macrocyclic effect for the high-spin Ni(n) complexes of four tetraaza-macrocyclic ligands and their open-chain analogues (the open-chain derivative which yields the most stable nickel complex was used in each case) (Micheloni, Paoletti Sabatini, 1983). Clearly, the enthalpy and entropy terms make substantially different contributions to complex stability along the series. Thus, the small macrocyclic effect which occurs for the first complex results from a favourable entropy term which overrides an unfavourable enthalpy term. Similar trends are apparent for the next two systems but, for these, entropy terms are larger and a more pronounced macrocyclic effect is evident. For the fourth (cyclam) system, the considerable macrocyclic effect is a reflection of both a favourable entropy term and a favourable enthalpy term. 

More subtle arguments have been invoked to rationalize the dichotomous behavior of so-called second-generation Mn-salen catalysts of type 7 toward unfunctionalized and nucleophilic olefins. For example, higher yields and ee s are obtained with the (i ,S)-complex for the epoxidation of indene (8). However, JV-toluenesulfonyl-l,2,3,4-tetrahydropyridine (10) gave better results using the (R,/ -configuration. An analysis of the transition-state enthalpy and entropy terms indicates that the selectivity in the former reaction is enthalpy driven, while the latter result reflects a combination of enthalpy and entropy factors <00TL7053>. 

Table 5 lists equilibrium data for a new hypothetical gas-phase cyclisation series, for which the required thermodynamic quantities are available from either direct calorimetric measurements or statistical mechanical calculations. Compounds whose tabulated data were obtained by means of methods involving group contributions were not considered. Calculations were carried out by using S%g8 values based on a 1 M standard state. These were obtained by subtracting 6.35 e.u. from tabulated S g-values, which are based on a 1 Atm standard state. Equilibrium constants and thermodynamic parameters for these hypothetical reactions are not meaningful as such. More significant are the EM-values, and the corresponding contributions from the enthalpy and entropy terms. 

In summary, the enthalpy and entropy terms do not vary independently but compensate each other in nature as far as the weak interactions are concerned, while the extent of AH-AS compensation appears to depend significantly on the host s... 

If we express EM in terms of free energies we obtain Equation 10.13 and we can recognise that RTIn (EM) is an empirical correction factor when an intermolecular process is replaced by an intramolecular one. If we substitute into Equation 10.13 the separate enthalpy and entropy terms and recognise that in a strain free ring AE/ nter = AHintm we get Equation 10.14. 

The value of AG° = -108.7 kJ/mol is divided into enthalpy and entropy terms ... 

The equilibrium constant Kcan be divided into enthalpy and entropy terms but it is the enthalpy term that determines how K varies with temperature. Plotting In K against 1/T would give us a straight line with slope - AtPIR and intercept AS0. Since T (the temperature in Kelvin) is always positive, whether the slope is positive or negative depends on the sign of AH° if it is positive then, as temperature increases, InK" (and hence K) increases. In other words, for an endothermic reaction (AHpositive), as Tincreases, K([products]/[reactants]) increases which in turn means that more products must be formed. 

The proton complex of the sulphide is stabilized by about equal contributions from the enthalpy and entropy terms, that of the phosphine mainly by the enthalpy loss. 

Positive enthalpy and entropy terms were calculated meaning that, contrary to self-organisation processes in apolar solvents, the enthalpic gain and entropic cost are completely overriden by solvation effects. Attempted inclusion of even small diatomic guests leads to a widening and thus a destabilisation of the cap-... 

We can determine the specific enthalpies and the specific entropies from the temperature, pressure, and composition of the environment. Once we specify the environmental conditions, all enthalpy and entropy terms are fully defined regardless of the process within the control volume. The term 7 0Chemical exergy, Exch, is... 

Only the enthalpy term directly reflects the change in bond energies caused by internal cis and trans effects, but the enthalpy and entropy terms have been separated in very few cases and one must therefore fall back on using formation constants. As will be seen from the discussion in Section III, A, however, the major changes in formation constant do appear to reflect changes caused by cis and trans effects. 

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