Free-energy change temperature independence

The standard free energy change is a function only of temperature. That is, it is independent of pressure and concentration for a specified standard state. Thus, at a given temperature, the term a1 1 is constant and we can write... 

Plan Evaluate A7/KI1 and AS. To assess the temperature range over which the reaction is spontaneous, use the signs of AH and AS and the Gibbs free energy change equation, AG = AH - TAS. Assume that AH and AS are independent of temperature. 

Equation (16-7) is a remarkable statement. It implies that Qeq, the value of the reaction quotient under equilibrium conditions, depends only on thermodynamic quantities that are constant in the reaction (the temperature, and the standard free-energy change for the reaction at that temperature), and is independent of the actual starting concentrations of reactants or products. For this reason, Qeq is usually denoted the equilibrium constant, K, and (16-7) is rewritten as... 

Calculate AG° and Kfor each independent reaction. This may be done as in the relevant examples earlier in this section, with determination of AG° as a function of temperature. An easier route, however, is to use the standard Gibbs free-energy change of formation A Gy for each compound at the temperature of interest in the relationship... 

In contrast, electron transfers from unhindered (or partially hindered) donors such as hexamethylbenzene, mesitylene, di-ferr-butyltoluene, etc. to photoactivated quinones exhibit temperature-independent rate constants that are up to 100 times faster than predicted by Marcus theory, poorly correlated with the accompanying free-energy changes (see Figure 20A), and only weakly affected by solvent polarity and salt effects. Most importantly, there is unambiguous (NIR) spectroscopic and kinetic evidence for the pre-equilibrium formation K c) of long-lived encounter complexes (exciplexes) between arene donor (ArH) and photoexcited quinone acceptor (Q ) prior to electron transfer (A et) [20] (Eq. 95). 

As a rule, when calculating AG at temperatures other than 298 K, we have made the assumption that AH and AS are independent of temperature. That is, we have calculated free energy changes at any temperature T as ... 

Figure 5. Temperature independence of the free-energy change, AQ° obtained from equilibrium constants measured by pulse radiolysis in MTHF,forthe electron transfer reaction B SN BSN, where B biphenyl, N naphthel and S is the steroid 3,16-androstane is measurements by intramolecular ET in BSN is measurements in mixtures of monofunctional molecules BS and NS.

Under which circumstance would the free energy change for a reaction be relatively temperature independent ... 

Because AG° is a property of pure species t in their standard state and at constant pressure, its value depends only on the temperature. In fact, AG° represents the quantity v, G°. Therefore, this function is the difference between the Gibbs ffee-energies of the products and reactants and depends on their stoichiometric coefficients. It is independent of the equilibrium composition or pressure and it is fixed for any given corrosion reaction once the temperature is established. The Gibbs free-energy change is defined according to Eqs. (2.29) and (2.31) as ... 

Practical separations with a porous column packing in SEC are performed close to equilibrium conditions. Elutions are performed at flow rates around 1 mL/min when Yr is independent of flow rate. Although many theoretical models have been proposed for polymer separations in SEC, thermodynamic treatments provide a sound representation of separation behavior. For a separation operating at equilibrium conditions, the standard free-energy change AG° for the transfer of solute molecules from the mobile phase to the stationary phase at constant temperature T is related to Ksec by... 

Assuming that the entropy of fusion, Sf, and heat of fusion, Hf, are independent of temperature, the free energy change of the reaction (6.G.1) at 1800°C is given by... 

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