Procedure of calculating a chemical equilibrium

The preceding sections show that there are in principle two approaches to the solution of the chemical equilibrium of a system. 

The first, up to now more conventional approach sets out from a description of the overall chemical conversion of the given system by means of a set of chemical reactions, and the corresponding standard changes of free enthalpy or equilibrium constants. Assuming R linearly independent reactions and ideal behaviour of the gas mixture, this procedure converts to the solution of a non-linear set of R equations for R unknown variables i, 2  

In the second approach, the system is considered as a whole, its thermodynamic properties being expressed by the overall free enthalpy of the system. Calculation of the chemical equilibrium is then equivalent to the problem of finding the minimum of free enthalpy of the system in dependence on the variables or maintaining validity of the balance relations (2.20) and (2.19). 

It can of course be proved easily that the two methods are equivalent. From relation (3.82) follows 

Substituting from equation (3.83) into relation (3.84) and inverting the order of addition we obtain 

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