Entropy upper limit

Molecular Nature of Steam. The molecular stmcture of steam is not as weU known as that of ice or water. During the water—steam phase change, rotation of molecules and vibration of atoms within the water molecules do not change considerably, but translation movement increases, accounting for the volume increase when water is evaporated at subcritical pressures. There are indications that even in the steam phase some H2O molecules are associated in small clusters of two or more molecules (4). Values for the dimerization enthalpy and entropy of water have been deterrnined from measurements of the pressure dependence of the thermal conductivity of water vapor at 358—386 K (85—112°C) and 13.3—133.3 kPa (100—1000 torr). These measurements yield the estimated upper limits of equiUbrium constants, for cluster formation in steam, where n is the number of molecules in a cluster. 

The integral does not furnish the absolute value of, the entropy, because the lower limit is undetermined. If this is regarded as fixed, the integral with various upper limits gives the values of the entropies referred to this arbitrary standard state, and the differences between these values and any one of them referred to this arbitrary standard state will be the values of the entropies referred to the new standard state (cf. 42). 

With application of reasonable values for trapping parameters and AS2, it was possible to bracket the enthalpy and entropy of activation for isomerization of cyclobutadiene. Hence, A/Zj was estimated to fall between 1.6 and lOkcal/mol, where the upper limit was consistent with theoretical predictions for square-planar cyclobutadiene. Most surprising, though, was the conclusion that AS for automeriza-tion must lie between -17 and -32cal/(molK), based on the AS values normally observed for Diels-Alder reactions as a model for AS2. ... 

This confirms the earlier interpretation that the exponent reflects the entropy of the reservoirs only, and that the contribution from internal changes of the subsystem has been correctly removed. During the adiabatic transition the reservoirs do not change, and so the probability density must be constant. Obviously there is an upper limit on the time interval over which this result holds since the assumption that X Xs implies that A( (x)x -C XS. ... 

An early treatment of the problem of calculating effective concentrations was to consider the concentration of an intramolecular group to be approximately the same as that of water in aqueous solution, since a molecule in solution is completely surrounded by water.22 This gives an upper limit of 55 M for effective concentration, equivalent to 34 J/deg/mol (8 cal/deg/mol) of entropy. That figure does represent the probability of two molecules being next to each other in solution. But, as soon as the two molecules are tightly linked, there is a large loss of entropy. A loose transition state may, perhaps, be interpreted as two molecules that are in close juxtaposition but that retain considerable entropic freedom. 

J. D. Dunitz19 has estimated the cost in entropy of tying up solvent water. The entropy of a water molecule of hydration in. a crystal or mineral is 42 J/mol/K (10 cal/mol/K), which represents the lower limit for a tightly bound molecule. The entropy of water in liquid water is 67-71 J/mol/K (16-17 cal/mol/K), which represents the upper limit for the least constrained water molecule in solution. Thus, the energetic cost of immobilizing a water molecule is between 0 and 8.3 kJ/mol (0 and 2 kcal/mol) at 25°C (298 K). 

The specific enthalpy and entropy of the conformation transition of proteins from the native to denatured state has an upper limit that is reached above 140°C and seems to be universal for all compact globular proteins (Figs. 4 and S). By enthalpy and entropy of conformational tran-... 

If the total entropy change vanishes, as in a reversible process, exergy defines an upper limit to the work that is extractable from any process. 

It is quite difficult to analyze the data obtained in real systems, because the scattering of the results given by different authors is significant moreover, in many cases the nonideality of the system has not been considered. The analysis of the collected experimental data [53] indicates, however, that the upper limit for 45 values is not very far from this predicted on the assumption that the magnitude of the entropy of polymerization is governed mainly by the loss of translational entropy of monomer. 

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. ... 

This could result in an apparently low frequency factor. Thus if fc is in the region of being a bimolecular reaction and has the form At(M), we can compute an upper limit for A from the estimated entropy change in the reaction (Table XIII, 13) and the... 

AG, Free Energy of Activation Rate Constant Upper Limit on Concentration Diffusion-Controlled Limit Dropping the AG by 1.36 kcal/mol (5.73 kJ/mol) Increases the Rate of Reaction Tenfold at Room Temperature Reasonable Rate at 25°C Half-Life Lifetime of an intermediate Rate-Determining Step Transition State Position Reactivity vs. Selectivity Thermodynamic vs. Kinetic AG = AH -TAS, Enthalpy of Transition Entropy of Transition Stabilization of Intermediates Stabilization of Reactants... 

We now specify the equation of state used to model detonation products. For the ideal gas portion of the Helmholtz free energy, we use a polyatomic model including electronic, vibrational, and rotational states. Such a model can be conveniently expressed in terms of the heat of formation, standard entropy, and constant pressure heat capacity of each species. The heat capacities of many product species have been calculated by a direct sum over experimental electronic, vibrational, and rotational states. These calculations were performed to extend the heat capacity model beyond the 6000K upper limit used in the JANAF thermochemical tables (J. Phys. Chem. Ref. Data, Vol. 14, Suppl. 1, 1985). Chebyshev polynomials, which accurately reproduce heat capacities, were generated. 

Since most elementary unimolecular reactions require that die molecule must be in an appropriate configuration while breaking a bold, the actual frequency factor is usually lower than the universal value. The factor reducing the upper limit is by agreement thought of as the stearic factor and represents an entropy requirement for achieving the transition state. When the stearic feet or is expressed, not by a simple number (P), but by an entropy of activation (AS) it can be written as ... 

The upper limit for the enthalpy of activation is somewhat harder to set. An attempt can be made by noting that the partial molal entropy of e m is estimated to be positive. It is unprecedented for solution of a charged species to cause an increase in entropy of the surrounding medium, and the effect, if real, must be associated with the very dispersed charge of the hydrated electron. If the enthalpy of activation for the reverse of Reaction 1 is greater than the value estimated in Table II, then the partial molal entropy of the hydrated electron in Table I must... 

It is quite easy to set an upper limit to the rate enhancement, in the absence of strain, that may be brought about by covalently binding the reactants together, as in an intramolecular reaction, or by binding them to the active site of an enzyme. This may be done by considering the different entropy changes that occur in bimolecular and unimolecular reactions [14,16]. 

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