Reactions entropy

For example, the expansion of a gas requires the release of a pm holding a piston in place or the opening of a stopcock, while a chemical reaction can be initiated by mixing the reactants or by adding a catalyst. One often finds statements that at equilibrium in an isolated system (constant U, V, n), the entropy is maximized . Wliat does this mean ... 

Figure A2.1.9. Chemically reacting systems, (a) The entropy. S as a fiinction of the degree of advancement of the reaction at constant U and V. (b) The affinity Aas a fiinction of for the same reacting system. Equilibrium is reached at 0.623 where tiis a maxuniim and A= 0.

The enthalpy, entropy and free energy changes for an isothennal reaction near 0 K caimot be measured directly because of the impossibility of carrying out the reaction reversibly in a reasonable time. One can, however, by a suitable combination of measured values, calculate them indirectly. In particular, if the value of... 

As seen in previous sections, the standard entropy AS of a chemical reaction can be detemiined from the equilibrium constant K and its temperature derivative, or equivalently from the temperature derivative of the standard emf of a reversible electrochemical cell. As in the previous case, calorimetric measurements on the separate reactants and products, plus the usual extrapolation, will... 

Chemical reactions may be added to the situation giving an entropy production of... 

The are many ways to define the rate of a chemical reaction. The most general definition uses the rate of change of a themiodynamic state function. Following the second law of themiodynamics, for example, the change of entropy S with time t would be an appropriate definition under reaction conditions at constant energy U and volume V ... 

Figure A3.4.1 shows as an example the time dependent concentrations and entropy for the simple decomposition reaction of chloroethane ...

Figure A3.4.1. Concentration and entropy as fiinctions of time for reaction equation (A3.4.8). S is the...

The most important themiodynamic property of a substance is the standard Gibbs energy of fomiation as a fimetion of temperature as this infomiation allows equilibrium constants for chemical reactions to be calculated. The standard Gibbs energy of fomiation A G° at 298.15 K can be derived from the enthalpy of fomiation AfT° at 298.15 K and the standard entropy AS° at 298.15 K from... 

B2.4.2). The slope of the line gives AH, and the intercept at 1/J= 0 is related to A imimolecular reaction, such as many cases of exchange, might be expected to have a very small entropy change on gomg to the transition state. However, several systems have shown significant entropy contributions—entropy can make up more than 10% of the barrier. It is therefore important to measure the rates over as wide a range of temperatures as possible to obtain reliable thennodynamic data on the transition state. 

The successful preparation of polymers is achieved only if tire macromolecules are stable. Polymers are often prepared in solution where entropy destabilizes large molecular assemblies. Therefore, monomers have to be strongly bonded togetlier. These links are best realized by covalent bonds. Moreover, reaction kinetics favourable to polymeric materials must be fast, so tliat high-molecular-weight materials can be produced in a reasonable time. The polymerization reaction must also be fast compared to side reactions tliat often hinder or preclude tire fonnation of the desired product. 

Transient, or time-resolved, techniques measure tire response of a substance after a rapid perturbation. A swift kick can be provided by any means tliat suddenly moves tire system away from equilibrium—a change in reactant concentration, for instance, or tire photodissociation of a chemical bond. Kinetic properties such as rate constants and amplitudes of chemical reactions or transfonnations of physical state taking place in a material are tlien detennined by measuring tire time course of relaxation to some, possibly new, equilibrium state. Detennining how tire kinetic rate constants vary witli temperature can further yield infonnation about tire tliennodynamic properties (activation entlialpies and entropies) of transition states, tire exceedingly ephemeral species tliat he between reactants, intennediates and products in a chemical reaction. 

The Arrhenius relation given above for Are temperature dependence of air elementary reaction rate is used to find Are activation energy, E, aird Are pre-exponential factor. A, from the slope aird intercept, respectively, of a (linear) plot of n(l((T)) against 7 The stairdard enAralpv aird entropy chairges of Are trairsition state (at constairt... 

Free energy is related to two other energy quantities, the enthalpy (the heat of reaction measured at constant pressure) and the entropy. S. an energy term most simply visualised as a measure of the disorder of the system, the relationship for a reaction taking place under standard conditions being... 

Steinberg, I. Z., Scheraga, H. A. Entropy changes accompanying association reactions of proteins. J. Biol. Chem. 238 (1963)172-181. 

Unfortunately, the number of mechanistic studies in this field stands in no proportion to its versatility" . Thermodynamic analysis revealed that the beneficial effect of Lewis-acids on the rate of the Diels-Alder reaction can be primarily ascribed to a reduction of the enthalpy of activation ( AAH = 30-50 kJ/mole) leaving the activation entropy essentially unchanged (TAAS = 0-10 kJ/mol)" . Solvent effects on Lewis-acid catalysed Diels-Alder reactions have received very little attention. A change in solvent affects mainly the coordination step rather than the actual Diels-Alder reaction. Donating solvents severely impede catalysis . This observation justifies the widespread use of inert solvents such as dichloromethane and chloroform for synthetic applications of Lewis-acid catalysed Diels-Alder reactions. 

Here we have the formation of the activated complex from five molecules of nitric acid, previously free, with a high negative entropy change. The concentration of molecular aggregates needed might increase with a fall in temperature in agreement with the characteristics of the reaction already described. It should be noticed that nitration in nitromethane shows the more common type of temperature-dependence (fig. 3.1). 

In principle the use of the entropy of activation as a criterion is straightforward. The electrostatic contribution to this quantity, A5 i, for a reaction between two cations is predicted from simple electrostatic theory to be less than that for a reaction between an ion and a neutral molecule. If the reactions are otherwise similar, the overall entropies of activation can be expected to differ in the same way ... 

An alternative approach is to assume, in the light of the experimental evidence just mentioned, that the reactions of cations and neutral molecules have similar values of (or, equivalently, of log ( /l mol and to try to calculate the difference which would arise from the fact that the observed entropy of activation for a minority free base includes a contribution from the acidic dissociation of the conjugate acid in the medium in question (see (5) above). Consider the two following reaction schemes one (primed symbols) represents nitration via the free base, the other the normal nitration of a non-basic majority species (unprimed symbols) ... 

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