Mathematical Derivations and Analysis

All derivations are based on a balanced chemical equation of the form 

1 Derivation of Expression for Overall F-Factor for Any Chemical Reaction 

Suppose in the balanced chemical equation that reagent A is the limiting reagent where jc moles of A are used, and that an excess of reagent B is used (z moles), where z x. Let the masses of reaction solvent, catalyst, and all auxiliary materials in the work-up and purification stages be s, c, and o), respectively. Assume that these are not recovered and are destined for waste. Let the moles and mass of target product P collected be y and yMWp, respectively. Rewrite the balanced chemical equation as 

Beginning with the definition of overall L-factor as the mass ratio of all waste material to target product collected, we have 

Define reaction yield with respect to limiting reagent A as 

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