The Gibbs Energy First and Second Law Methods

Perhaps the two most important outcomes of the first and the second laws of thermodynamics for chemistry are representedby equation 2.54, which relates the standard Gibbs energy (ArG°) with the equilibrium constant (K) of a chemical reaction at a given temperature, and by equation 2.55, which relates ArG° with the standard reaction enthalpy (A rH°) and the standard reaction entropy (ArA°). 

For ArG° = -12 kJ mol-1, K = 126.6, and 99.2% of A is converted into B. If ArG° becomes -8 kJ mol-1, K = 25.21, and the yield is 96.2% with ArG° = -16 kJ mol-1, A =635.4, and the yield is 99.8%. Thus, although the errors in K are enormous, the yields do not vary that much—they are all near 100%. In other words, when ArG° becomes more negative, its inaccuracy leads to huge errors in the equilibrium constants, but this is not important because the conversion of A into B is almost complete. By contrast, for reactions that have Ar G° values closer to zero, the uncertainty has a dramatic influence on the yield. For ArG° = —4 4 kJ mol-1, K varies between 1 and 25.21, and the yield correspondingly ranges from 50% to 96%. 

It will be shown in several chapters of this book that equations 2.54 and 2.55 are also employed to derive ArH° and Ar.S ° from equilibrium constant data at several temperatures. The simplest procedure involves van t Hoff equation written as 

Equation 2.58 is applied to any suitable function fitted to the data. For instance, the equation 

Once Ar// is determined at a given temperature, equations 2.54 and 2.55 can be used to obtain Ar,V. at the same temperature (but that is often found in practice to be unreliable). To calculate the standard reaction enthalpy at 298.15 K, we can use the procedures described after equations 2.10 or 2.14. On the other hand, the standard reaction entropy at 298.15 K can be derived from 

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