Temperature dependence of the Gibbs energy

The dependence of the Gibbs energy on temperature is expressed in several different ways for convenience in different problems. Rewriting Eq. (10.41), we have 

Frequently it is important to know how the function G/T depends on temperature. By the ordinary rule of differentiation, we obtain 

Any of Eqs. (10.52), (10.53), (10.54), (10.55) are simply different versions of the fundamental equation, Eq. (10.52). We will refer to them as the first, second, third, and fourth forms of the Gibbs-Helmholtz equation. 

1 For what sort of experimental conditions is (a) A or (b) G the appropriate indicator of spontaneity  

2 The second law states that the entropy of the universe (system and surroundings) increases in a 

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By contrast, electron energy calculations have the inherent capability of yielding accurate values for many metastable structures at 0 K but have little or no capability of predicting the temperature dependence of the Gibbs energy, especially in cases where mechanical instabilities are involved. 

However, AmicH° and TA, determined from the temperature dependence of the Gibbs energy, are less sensitive to the association number than is AmicG° itself (Yang ef al. 1995). Assuming that Am cH° is approximately constant within a certain temperature range, eqn 3.7 can be integrated to yield... 

Finally, the enthalpy of unfolding AH and melting temperature Tm are obtained from the temperature dependence of the Gibbs energy, given by the Gibbs-Helmholtz equation... 

Figure 2.4 shows the temperature dependence of the Gibbs energy of silicon. 

Figure V-9 Comparison between the temperature dependence of the Gibbs energy of formation for NiO obtained from electrochemical as well as chemical reduc-tion/oxidation equilibrium measurements and the prediction based on the present selection of thermodynamic properties for NiO.

This value was also selected by the present review. The entropy value calculated from the temperature dependence of the Gibbs energy of the reaction of nickel with silica and oxygen e.g., as estimated by [68CAM/ROE], [76MAH/PAN], was not accepted by this review. 

Inspection of Table 18.3 shows that the structures 1-2 and 1-3 of mechanism (1) have slightly lower Gibbs energy than the corresponding structures 2-2 and 2-3 of mechanism (2) at 298 K but the situation is reversed at 600 K. This reflects the temperature dependence of the Gibbs energy. The effect is small, however, and the data are not as precise that this effect should be discussed seriously. In other simations, such effects may be more pronounced. 

In the temperature range 20 to 65 °C, there is no change in either a or 5 in Eq. 6.23, This lack of temperature dependence of the solvation force is consonant with the very small temperature dependence of the Gibbs energy change for cation solvation in aqueous solutions. 

Gibbs energies have been measured and listed for a number of chemical compounds. The temperature dependence of the Gibbs energy may be expressed in different ways. Since, according to Equation 5.36 G = H - TS and according to Equation 5.43, (dG/dT)p = -S, we have... 

The temperature dependence of the Gibbs energy of formation allows one to determine the entropy of formation according to the Gibbs-Helmholtz relation AS = -(dAG/dT), i.e., the temperature dependence of the cell voltage relates to the entropy of the cell reaction, AS = nq(dE/dT). The enthalpies of formation and cell reaction follow according to AH = AG + TAS. Knowledge of these fundamental thermodynamic quantities allows the comprehensive determination of the thermodynamic properties of the system. 

How well we need to know the a-x relationships depends on the temperature dependence of the Gibbs energy of reaction. For example, consider two reactions (a and b) for which the equilibrium relations (2) are ... 

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