The Gibbs Energy Third Law Method

Besides the second law method, there is another way of extracting reaction enthalpies from gas-phase equilibrium constants. This alternative involves the determination of a single value of an equilibrium constant at a given temperature and the calculation of the reaction entropy at the same temperature. From equations 2.54 and 2.55, we obtain 

Once again we use subscript T to indicate that the reaction enthalpy and entropy may not refer to 298.15 K. The subscript p in the equilibrium constant indicates that we are accepting the perfect gas model and therefore Kp is defined in terms of partial pressures, not fugacities. 

Statistical mechanics affords an accurate method to evaluate ArSP, provided that the necessary structural and spectroscopic parameters (moments of inertia, vibrational frequencies, electronic levels, and degeneracies) are known [1], As this computation implicitly assumes that the entropy of a perfect crystal is zero at the absolute zero, and this is one of the statements of the third law of thermodynamics, the procedure is called the third law method. 

Although equation 2.71 can be directly applied to derive a reaction enthalpy at the temperature T, and the correction to 298.15 K (or to any other temperature) 

The advantage of equation 2.72, compared with 2.71, is that PP = (Gj -7/298)/T is tabulated (or readily calculated) for many common gaseous substances as a function of temperature, thus saving some computational work [53,54]. The only point to consider is that some of those compilations actually list the data for another function, t g = (GP —Hq)/T, which is useful to derive the standard reaction enthalpy at the absolute zero  

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