Chemically reaction free energy

The energy factor (enthalpy) and the probability factor (entropy) in chemical reactions. The driving force of chemical reactions—free energy. Oxidation-reduction potentials and their uses. 

Figure 1 shows such a profile for an uncatalyzed and enzyme-catalyzed uni-molecular chemical reaction. Free energy profiles are commonly shown as points representing the relative free energy ch ges, connected by a smooth curve. However, it should be pointed out that experimental observations typically can only provide information forthe maxima and minima ofthese profiles and not on points in between (Thornton Thornton, 1978 Puiich Allison, 2(XX)). 

Chemical changes are not irreversible unless tliere is some fonn of dissipation in tire system. That is, tire reaction free energy must be dispersed to a number of degrees of freedom distinct from tire reaction coordinate. Models tliat include... 

As a result of the combination of Eqs. (20) and (21), the reaction free energy, AG, and the equilibrium cell voltage, A< 00, under standard conditions are related to the sum of the chemical potentials //,. of the substances involved ... 

The thermodynamic function used as the criterion of spontaneity for a chemical reaction is the Gibbs free energy of reaction, AG (which is commonly referred to as the reaction free energy ). This quantity is defined as the difference in molar Gibbs free energies, Gm, of the products and the reactants ... 

GH Theory was originally developed to describe chemical reactions in solution involving a classical nuclear solute reactive coordinate x. The identity of x will depend of course on the reaction type, i.e., it will be a separation coordinate in an SnI unimolecular ionization and an asymmetric stretch in anSN2 displacement reaction. To begin our considerations, we can picture a reaction free energy profile in the solute reactive coordinate x calculated via the potential of mean force Geq(x) -the system free energy when the system is equilibrated at each fixed value of x, which would be the output of e.g. equilibrium Monte Carlo or Molecular Dynamics calculations [25] or equilibrium integral equation methods [26], Attention then focusses on the barrier top in this profile, located at x. ... 

In a similar manner to that employed for thermochemical AH° of chemical reactions [cf. (3.106)], the reaction free energy AG° can be expressed in terms of the standard Gibbs free energy of formation AGf [AJ for each species A, namely,... 

STRATEGY First, we write the chemical equation for the formation of HI(g) and calculate the standard reaction free energy from AGr° = AH° — TASr°. It is best to write the equation with a stoichiometric coefficient of 1 for the compound of interest, for then AGr° = AGf°. The standard reaction enthalpy is found from the standard enthalpies of formation by using data from Appendix 2A. The standard reaction entropy is found as shown in Example 7.7, by using the data from Table 7.3 or Appendix 2A. If necessary, convert the units of ASr° from joules to kilojoules. 

A catalyst speeds up both the forward and reverse reactions by the same amount. Therefore, the dynamic equilibrium is unaffected. The thermodynamic justification of this observation is based on the fact that the equilibrium constant depends only on the temperature and the value of AGr°. A standard reaction free energy depends only on the identities of the reactants and products, and is independent of its rate or the presence of any substances that do not appear in the overall chemical equation for the reaction. 

One application of Eq. 2 is the determination of a reaction free energy—a thermodynamic quantity—from a cell potential, an electrical quantity. Consider the chemical equation for the reaction in the Daniel cell (reaction A) again. For this reaction, n = 2 because 2 mol of electrons migrate from Zn to Cu and we measure E = 1.1 V. It follows that... 

Cell potential and reaction free energy are related by Eq. 2 (AGr = -nFE) and their standard values by Eq. 3 (AGr° = —nFE°). The magnitude of the cell potential is independent of how the chemical equation is written. 

As the reactants in a chemical reaction are used up and the concentrations of products increase, AGr changes until it reaches 0 at equilibrium. Because the cell potential is proportional to the reaction free energy (Eq. 2), it follows that E also changes as the reaction proceeds. We already know how A Gr varies with composition ... 

Redox reactions that have a positive reaction free energy are not spontaneous, but electricity can be used to make them occur. For example, there is no common spontaneous chemical reaction in which fluorine is a product, so the element cannot be isolated by any common chemical reaction. It was not until 1886 that the French chemist Henri Moissan found a way to force the formation of fluorine by passing an electric current through an anhydrous molten mixture of potassium fluoride and hydrogen fluoride. Fluorine is still prepared commercially by the same process. 

The Equilibrium Constant. The relationship between the reaction free energy or the affinity for each chemical reaction and the composition of a closed system is readily obtained by applying Equation 14 for AG to the relationships between chemical potential, and the activity, af ... 

There are two major concepts involved in the physico-chemical description of a chemical reaction the energetics, which determines the feasibility of the reaction, and the kinetics which determines its rate. In general these two concepts are independent and the rate of a chemical reaction can be varied according to the mechanism (e.g. catalysis) but within certain assumptions there is a mathematical relationship between the rate constant and the reaction free energy difference. These relationships are either linear (linear free energy relationship, LFE) or quadratic (QFE), the latter being often referred to as the Marcus model — a description which should not hide the important contributions of other workers in this field [1],... 

One of the main advantages of the MD over the static quantum chemical approaches is that it can be utilized to directly determine the reaction free energy barriers, as it explicitly includes entropic effects. An estimation of the free energy via a normal (static) DFT approach requires frequency calculations that are relatively expensive for large molecular systems. Such an approach assumes in addition the harmonic (normal mode) approximation, which breaks down for processes where weak intermolecular forces dominate.10... 

The free energy change SGaq for the chemical reaction in solution can be described in terms of the reaction free energy SGgas in gas phase and the solvation free energies of the solutes at the initial and the final state of the reaction, thus,... 

Heat of reaction, free-energy changes, and reaction equilibrium constants are discussed in more detail in Section 4 in the context of chemical-reaction equilibrium. 

In the case of chemical processes, one also has to linearize exponentials, i.e., to assume I ArG/RT 1 I. This is, however, now a very severe approximation owing to the large values of reaction free energies (difference in // -values now important), unless we slightly perturb an already existing equilibrium. Thus, for a pure chemical process but also for the general electrochemical reaction we are advised to use the full description. 

In the equilibrium of Eq. 30, electrons are exchanged between the reduced species Fe + (aq) and the oxidized species Fe + (aq), and vice versa. Exchange occurs under conditions of chemical equilibrium the reaction free energy AGr is zero. In the second case, a mixture of Fe + (aq) and Ce" + (aq) will spontaneously evolve to an equilibrium mixture of the oxidized and reduced species of both redox systems. The driving force, that is, the reaction free energy at any time is given by... 

It may be noted that we define AG such that it equals the chemical potential of the substrate minus the chemical potential of the product. We noted above that the possibility of free-energy dissipation drives a reaction. Free-energy differences like ACr and A/tg in the above equation embody such a possibility they act as forces that drive the reaction. Other examples are the contractile force on a muscle the voltage drop across an electrical resistance the osmotic pressure on a semipermeable membrane. The dissipation function consists of the sum of the products of fluxes (currents) and the (thermodynamic) forces that drive them [4]. 

This equation has the same form as that obtained for ideal solubility but AHfvs has been replaced by the enthalpy of solution AHmjx. In non-ideal solutions of solids in liquids which do not follow either Henry s or Raoult s Laws, AHmix is the differential enthalpy of solution of the solute in the saturated solution. Both AGmix and AHmix are for non-ideal solutions similar to the reaction free energy we introduced when studying equilibrium in chemical reactions. They are all differential quantities AHmix is the enthalpy change when one mole of solute is added to an infinite volume of nearly... 

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