Variation with temperature Gibbs energy

Variation of Gibbs Energy, G with Temperature, T at Constant Pressure (dP = 0)... 

The most useful expression for describing the variation of standard Gibbs free energy changes with temperature is ... 

Thermodynamics is used to predict whether reactants have a spontaneous tendency to change into products. This tendency is associated with a decrease in the free energy or Gibbs energy of the system (G) to a minimum. As a consequence, the thermodynamic criterion for spontaneous change at constant temperature and pressure is AG < 0. Under standard conditions (concentrations = 1 M, and P = 1 atm), the standard Gibbs energy variation (AG°) is related with the equilibrium constant (A) by equation 11 ... 

Knowledge of these changes in standard Gibbs energy and enthalpy allows one to calculate the equilibrium composition and its variation with temperature. 

The variation in Gibbs-free-energy change with temperature at constant pressure is given by... 

Variation of Gibbs Energy, G With Pressure, P at Constant Temperature (dT = 0) and Variation of Entropy, S With Pressure, P at Constant Temperature (dT = 0) for an Idea Gas... 

The Gibbs-Helmholtz equation equation gives us the variation of the change in Gibbs free energy, AG, with temperature T. An important part of its derivation requires the differentiation of the quantity AG/T. It is important to reahse that AG does depend upon T, so that this is an example of differentiating a quotient. If AG did not vary with temperature, then the task would be simpler... 

Fig. 3.3 The variation of molar Gibbs energy with temperature. All molar Gibbs energies decrease with increasing temperature. The regions of temperature over which the solid, liquid, and gaseous forms of a substance have the lowest molar Gibbs energy are indicated in the band at the top of the illustration.

Using these relations the variation with temperature of the standard Gibbs energy change can be expressed in the following form... 

Figure 11.1 Variation with temperature of the Gibbs free energy per unit volume.

The enthalpy of fomiation is obtained from enthalpies of combustion, usually made at 298.15 K while the standard entropy at 298.15 K is derived by integration of the heat capacity as a function of temperature from T = 0 K to 298.15 K according to equation (B 1.27.16). The Gibbs-FIehiiholtz relation gives the variation of the Gibbs energy with temperature... 

FIGURE 7.25 The variation of the (molar) Gibbs free energy with temperature for three phases of a substance at a given pressure. The most stable phase is the phase with lowest molar Gibbs free energy. We see that, as the temperature is raised, the solid, liquid, and vapor phases in succession become the most stable. 

The local conditions of temperature and pressure, as well as the new energy source in the form of the electrochemical gradient, can all be incorporated into the Gibbs free energy by adding new terms to the chemical potential. Variation of AG and AH with temperature are all standard thermodynamics, although we will resist the temptation to explore them here. 

The transfer coefficient a has a dual role (1) It determines the dependence of the current on the electrode potential. (2) It gives the variation of the Gibbs energy of activation with potential, and hence affects the temperature dependence of the current. If an experimental value for a is obtained from current-potential curves, its value should be independent of temperature. A small temperature dependence may arise from quantum effects (not treated here), but a strong dependence is not compatible with an outer-sphere mechanism. 

Figure 7.9. Variation of (a) the Gibbs energy, (b) ttie enthalpy and (c) the entropy with temperature (scaled to the nearest-nei bour interaction energy J ) for the complex structure A15. Comparison between BWG CVM in the tetrahedron approximation ( ) and the Monte Carlo method (—) (Turchi and Finel 1992).

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