Free energy change reaction direction

SECTIONS 19.6 AND 19.7 The values of AH and AS generally do not vary much with temperature. Therefore, the dependence of AG with temperature is governed mainly by the value of T in the expression AG = AH — TAS. The entropy term —TAS has the greater effect on the temperature dependence of AG and, hence, on the spontaneity of the process. For example, a process for which AH > 0 and As > 0, such as the melting of ice, can be nonspontaneous (AG > 0) at low temperatures and spontaneous (AG < 0) at higher temperatures. Under nonstandard conditions AG is related to AG° and the value of the reaction quotient, Q AG = AG" + RT In Q. At equilibrium (AG = 0, Q = K), AG = —RT InkT. Thus, the standard free-energy change is directly related to the equilibrium constant for the reaction. This relationship expresses the temperature dependence of equilibrium constants. 

Under nonstandard conditicxis, AG is related to AG and the value of the reaction quotient, Q AG = AG — RT In Q. At equilibrium (AG = 0,Q = K ), AG° = —RTlnKfy. Thus, the standard free-energy change is directly related to the equilibrium constant for the reaction. This rdationship can be used to explain the temperature dependence of equilibrium constants. 

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... 

Direct, One-Step Thermal Water Splitting. The water decomposition reaction has a very positive free energy change, and therefore the equihbrium for the reaction is highly unfavorable for hydrogen production. 

But spontaneity depends on the concentrations of reactants and products. If the ratio [Bl YCA] is less than a certain value, the reaction is spontaneous in the forward direction if [Bl YCA] exceeds this value, the reaction is spontaneous in the reverse direction. Therefore, it is useful to define a standard free-energy change (AG°) which applies to a standard state where [A] = [B] = 1 M. 

What we have not yet seen is how these two points are related. Why does the stability of the carbocation intermediate affect the rate at which it s formed and thereby determine the structure of the final product After all, carbocation stability is determined by the free-energy change AG°, but reaction rate is determined by the activation energy AG. The twro quantities aren t directly related. 

Equations (9.7) and (9.8) define K, the equilibrium constant for the reaction.b It is sometimes referred to as the thermodynamic equilibrium constant. As we shall see, this ratio of activities can be related to ratios of pressure or concentration which, themselves, are sometimes called equilibrium constants. But K, as defined in equations (9.7) and (9.8), is the fundamental form that is directly related to the free energy change of the reaction. 

The free energies of activation for the one reaction series are directly proportional to the standard free energy changes for another. This form is emphasized by Eq. (10-3), and is what gives rise to the designation of this approach as an LFER. 

CHANGES IN FREE ENERGY DETERMINE THE DIRECTION EQUILIBRIUM STATE OF CHEMICAL REACTIONS... 

The relationship between Q and signals the direction of a chemical reaction. The free energy change, A G, also signals the direction of a chemical reaction. These two criteria can be compared ... 

In order to determine in which direction the reaction is spontaneous, we need to calculate the non-standard free energy change for the reaction. To accomplish this, we will employ the equation AG = AG° + RTlnQc, where... 

Our knowledge of enzymes also tells us that under usual physiological conditions (i.e. at typical cellular concentrations of substrate) most metabolic reactions are reversible. Energetically irreversible reactions, i.e. those with a large positive free energy change, effectively act as one-way valves allowing substrate flow in the forward direction only. 

Intuitively, one knows that this equilibrium reaction will proceed to the right to form A1203 and release heat. What largely determines the direction is the free energy change of the reacting system ... 

Electron-transfer reactions are normally performed in polar solvents such as acetonitrile (MeCN), in which the product ions of the electron transfer are stabilized by the strong solvation [6,7]. When a cationic electron acceptor (A ) is employed in electron-transfer reactions with a neutral electron donor (D), the electron transfer from D to A+ produces a radical cation (D +) and a neutral radical (A ). In such a case, the solvation before and after the electron transfer may be largely canceled out when the free-energy change of electron transfer is expected to be rather independent of the solvent polarity. The solvent independent value is confirmed by determination of the Eqx values of alkylbenzene derivatives (electron donors) and Ered values of acridinium cations (electron acceptors) in solvents with different polarities [79]. The E°ox values of alkylbenzene derivatives in a less polar solvent (CH2CI2) are shifted to the positive direction by about 0.1 V... 

A fuel cell is a device that converts the free energy change of a chemical reaction directly into electrical energy. This conversion occurs by two electrochemical half cell reactions. 

The equilibrium constant is fixed and characteristic for any given chemical reaction at a specified temperature. It defines the composition of the final equilibrium mixture, regardless of the starting amounts of reactants and products. Conversely, we can calculate the equilibrium constant for a given reaction at a given temperature if the equilibrium concentrations of all its reactants and products are known. As we will show in Chapter 13, the standard free-energy change (A(3°) is directly related to Ke[Pg.61]

---