Free energy equation

The quantitative treatment of solubiUty is based on the familiar free energy equation governing mutual miscibility ... 

This is the so-called free energy equation where AF (equal to AA H- FAT) is known as the free energy. 

The free energy equation is very useful and has already been mentioned in the previous chapter in connection with melting points. If applied to the mixing of molecules the equation indicates that mixing will occur if FAS is greater than A//. Therefore... 

The equilibrium constant can be derived from the free energy equation... 

NaOMe solutions, no correlation was found between reaction rates and either or stoichiometric base concentration but where the rates were successfully correlated by a linear free energy equation similar to those given above. 

A treatment partially based on the Bunnett-Olsen one is that of Bagno, Scorrano, and More OTerrall, which formulates medium effects (changes in acidity of solvent) on acid-base equilibria. An appropriate equilibrium is chosen as reference, and the acidity dependence of other reaetions compared with it, by use of the linear free energy equation... 

The following overall nucleophilicity order for Sn2 mechanisms (in protic solvents) was given by Edwards and Pearson RS > ArS >1 >CN > OH > Nj > Br > ArO > Cl > pyridine > AcO > H2O. A quantitative relationship (the Swain-Scott equation) has been worked out similar to the linear free energy equations considered in Chapter 9 ... 

The most important results of the linear free energy equations in this study (Table IV) are the applications to which they can be used. For a new free radical initiator, belonging to any of the four radical forming reactions of this study, equation 6 should be useful to predict the rate of decomposition with reasonable accuracy. All that is needed is an HMD calculation to obtain the pi-delocalization energy for the radical formed in the reaction (R ) and an estimate of the steric A values for groups bonded to the central carbon of R. ... 

The linear free energy equations generated in this study are useful for reasonably accurate predictions of rates of radical forming decompositions of Irons-symmetric bisalkyl diazenes (1),... 

Other authors found that the enthalpies for the hydrogen bonding also give a good correlation against Hammett values. The linear free energy equations between Avq , Av q and AH obtained in their investigations were as follows ... 

Now, let s return to the Gibbs free energy equation to determine if hydrogen will react spontaneously with oxygen to form water. The equation for the reaction may be written as... 

Which of the following is NOT a variable in the Gibbs free energy equation, which determines reaction spontaneity ... 

The equilibrium dissociation constant Ks has units of molarity and its value is inversely proportional to the affinity of the substrate for the enzyme (i.e., the lower the value of Ks, the higher the affinity). The value of Ks can be readily converted to a thermodynamic free energy value by the use of the familiar Gibbs free energy equation ... 

The elastic free energy of the constrained-junction model, similar to that of the slip-link model, is the sum of the phantom network free energy and that due to the constraints. Both the slip-link and the constrained-junction model free energies reduce to that of the phantom network model when the effect of entanglements diminishes to zero. One important difference between the two models, however, is that the constrained-junction model free energy equates to that of the affine network model in the limit of infinitely strong constraints, whereas the slip-link model free energy may exceed that for an affine deformation, as may be observed from Equation (41). 

As with the Marcus-Hush model of outer-sphere electron transfers, the activation free energy, AG, is a quadratic function of the free energy of the reaction, AG°, as depicted by equation (7), where the intrinsic barrier free energy (equation 8) is the sum of two contributions. One involves the solvent reorganization free energy, 2q, as in the Marcus-Hush model of outer-sphere electron transfer. The other, which represents the contribution of bond breaking, is one-fourth of the bond dissociation energy (BDE). This approach is... 

The general equation for a straight line is given below with the slightly modified Gibbs Free-Energy equation as a reference AG° = - AS°T + AH° (here AH° is assumed to be constant)... 

You get 1 point for the prediction that the reaction is spontaneous. The setup (plugging into the equation) is worth 1 point if you remember to change the temperature to kelvin and convert joules to kilojoules. An additional 1 point comes from the answer. If you got the wrong value in either part (a) or (b), but used it correctly, you will still get the point for the answer. The free-energy equation is part of the material supplied in the exam booklet. Subtract one point if all your answers do not have the correct number of significant figures. 

Coupling-in-series Reactions are said to be coupled-inseries when the product of one reaction is the substrate for the next reaction the principle underlying this coupling is explained by reference to the Gibbs free energy equation. In the reaction A B, in the hypothetical pathway S —> P, reaction A to B is catalysed by enzyme E2 as follows ... 

The Gibbs free energy equation explains why glucose 6-phosphate cannot be formed, in vivo, from glucose and phosphate, as follows ... 

A linear free energy equation for reaction between nucleophiles and certain large organic cations (e.g., tri-aryhnethyl cations, aryltropyhum cations, etc.). Thus, log /cn = log ko + N+ where is the rate constant for the reaction of a particular cation with a given nucleophile in a given solvent, ko is the corresponding rate constant for the same cation with water in water (i.e., the solvent is water), and N+ is the cation-independent parameter that is characteristic for that nucleophile system. 

At room temperature, entropy effects are so small that they have little effect on the direction of a chemical reaction unless the difference in AG or 2s.H between reactants and products is correspondingly small. But at the high temperature encountered in pyrotechnic reactions such as the combustion of gunpowder, the relative importance of the change in entropy increases until it becomes a dominant factor. Hence, the importance of the temperature term in the free energy equation. 

Define the change in entropy in the Gibbs free energy equation. 

The final step of the convolution analysis is the determination of the transfer coefficient a. This coefficient, sometimes called the symmetry factor, describes how variations in the reaction free energy affect the activation free energy (equation 26). The value of a does not depend on whether the reaction is a heterogeneous or a homogeneous ET (or even a different type of reaction such as a proton transfer, where a is better known as the Bronsted coefficient). Since the ET rate constant may be described by equation (4), the experimental determination of a is carried out by derivatization of the ln/Chet-AG° and thus of the experimental Inkhei- plots (AG° = F E — E°)) (equation 27). 

The process by which a polymer is dissolved may be described by the T3ibbs free energy equation for constant temperature ... 

For the present a, is expressed in mole fraction units. We see, therefore, that /x, approaches as a, approaches unity. Furthermore, since fi, is the partial molal Gibbs free energy, Equation (5) also applies to fx, provided we replace V with V the partial molal volume of component i ... 

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