Entropy lowering

A reaction at steady state is not in equilibrium. Nor is it a closed system, as it is continuously fed by fresh reactants, which keep the entropy lower than it would be at equilibrium. In this case the deviation from equilibrium is described by the rate of entropy increase, dS/dt, also referred to as entropy production. It can be shown that a reaction at steady state possesses a minimum rate of entropy production, and, when perturbed, it will return to this state, which is dictated by the rate at which reactants are fed to the system [R.A. van Santen and J.W. Niemantsverdriet, Chemical Kinetics and Catalysis (1995), Plenum, New York]. Hence, steady states settle for the smallest deviation from equilibrium possible under the given conditions. Steady state reactions in industry satisfy these conditions and are operated in a regime where linear non-equilibrium thermodynamics holds. Nonlinear non-equilibrium thermodynamics, however, represents a regime where explosions and uncontrolled oscillations may arise. Obviously, industry wants to avoid such situations ... 

Chemical reactions can behave in this manner, too. At equilibrium the molecules will distribute themselves between products and reactants in a manner that allows them to minimize their energy and maximize their entropy. But it is always a trade-off. So if there is little to be gained either way for entropy, lower energy will carry the day. But if there is a lot of... 

Figure 6. Helix—coil transition, (top) The initiation and propagation steps and their attendant changes in enthalpy and entropy, (lower left) The free energy of folding as a function of chain length, and (lower right) the sharpness of the transition as a function of chain length.

The bonded alkyl chains density, pb, is the density of the bonded alkyl chain layer. It is often assumed to be the density of liquid octadecane in the case of Cis columns. Strictly speaking, however, the bonded layer is not a liquid since all the octadecyl chains are bonded, so their average distance is higher than in a liquid, and their entropy lower. This density (and the volume occupied by the layer) depends also on the mobile phase composition, depending on whether these chains are poorly soluble in the mobile phase and collapse on the surface or whether they are soluble and are swollen by the mobile phase or by the organic modifier in the case of the aqueous solutions most often used in RPLC. 

A system with fewer microstates (smaller IV) among which to spread its energy has lower entropy (lower S). 

The reasoning developed above shows that the biosphere is a system, which is subject to a flow of energy. The energy enters the system at a low entropy level and leaves it at a substantially higher entropy level. As such the biosphere can maintain a state with an entropy lower than the maximum corresponding to thermodynamic equilibrium and processes known as "life" result (J ). 

This reduction in the tension is due to the fact that as the interfacial area is increased, the translational entropy of the surface active component is increased (for a fixed number of the surface active molecules). This increase in entropy lowers the system free energy and thus reduces y frotit its bare value. This expression is correct for small area fractions of the surface active species, since we considered only the ideal-gas entropy. 

The ability of the surfactant to increase its translational entropy lowers the surface tension. However, we note that this expression is only valid for insoluble surfactants at low concentrations, so the tendency for y to become negative at large a is just an indication that these approximations are breaking down. For soluble surfactants, one cannot consider fixed Ng. Rather, one has to equate the chemical potentials of the surfactants on the surface and in the bulk. For small concentrations, the surface tension is still reduced in a linear manner, but at large concentrations, the reduction in surface tension saturates due to the formation of micelles in the bulk this is discussed in Chapter 8. 

The principle of tire unattainability of absolute zero in no way limits one s ingenuity in trying to obtain lower and lower thennodynamic temperatures. The third law, in its statistical interpretation, essentially asserts that the ground quantum level of a system is ultimately non-degenerate, that some energy difference As must exist between states, so that at equilibrium at 0 K the system is certainly in that non-degenerate ground state with zero entropy. However, the As may be very small and temperatures of the order of As/Zr (where k is the Boltzmaim constant, the gas constant per molecule) may be obtainable. 

Conformational Adjustments The conformations of protein and ligand in the free state may differ from those in the complex. The conformation in the complex may be different from the most stable conformation in solution, and/or a broader range of conformations may be sampled in solution than in the complex. In the former case, the required adjustment raises the energy, in the latter it lowers the entropy in either case this effect favors the dissociated state (although exceptional instances in which the flexibility increases as a result of complex formation seem possible). With current models based on two-body potentials (but not with force fields based on polarizable atoms, currently under development), separate intra-molecular energies of protein and ligand in the complex are, in fact, definable. However, it is impossible to assign separate entropies to the two parts of the complex. 

Polyamides. The next two compounds are the amide counterparts of the esters listed under item (4). Although the values of AH j are less for the amides than for the esters, the values of T j, are considerably higher. This is a consequence of the very much lower values of AS j for the amides. These, in turn, are attributed to the low entropies of the amide in the liquid state owing to the effects of hydrogen bonding and chain stiffness arising from the contribution of the resonance form... 

A heat engine is a device operating in cycles that takes in heat, from a heat reservoir at temperature Tp, discards heat, to another heat reservoir at a lower temperature T, and produces work. A heat reservoir is a body that can absorb or reject unlimited amounts of heat without change in temperature. Entropy changes of a heat reservoir depend only on the absolute temperature and on the quantity of heat transferred, and are always given by the integrated form of equation 4 ... 

The actual amount and stmcture of this "bound" water has been the subject of debate (83), but the key factor is that in water, PVP and related polymers are water stmcture organi2ers, which is a lower entropy situation (84). Therefore, it is not unexpected that water would play a significant role in the homopolymeri2ation of VP, because the polymer and its reactive terminus are more rigidly constrained in this solvent and termination k is reduced... 

Ion-Dipole Forces. Ion-dipole forces bring about solubihty resulting from the interaction of the dye ion with polar water molecules. The ions, in both dye and fiber, are therefore surrounded by bound water molecules that behave differently from the rest of the water molecules. If when the dye and fiber come together some of these bound water molecules are released, there is an increase in the entropy of the system. This lowers the free energy and chemical potential and thus acts as a driving force to dye absorption. 

A number of groups have criticized the ideas of Dauben and Noyce, especially the concept of PDC. Kamernitzsky and Akhrem, " in a thorough survey of the stereochemistry of addition reactions to carbonyl groups, accepted the existence of SAC but not of PDC. They point out that the reactions involve low energies of activation (10-13 kcal/mole) and suggest that differences in stereochemistry involve differences in entropies of activation. The effect favoring the equatorial alcohols is attributed to an electrostatic or polar factor (see also ref. 189) which may be determined by a difference in the electrostatic fields on the upper and lower sides of the carbonyl double bond, connected, for example, with the uncompensated dipole moments of the C—H bonds. The way this polar effect is supposed to influence the attack of the hydride is not made clear. 

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