Maximum Equilibrium Chemical Transformation As A Tool to Evolve 19 A Mathematical Inequality

For gas phase chemical reactions of the types a₁A₁ + a₂A₂ +......+ a_rA_r → b₁B₁, the conditions for maximum yield at equilibrium fit into a general mathematical inequality which in compact notation takes the form ^rπ_i=1(x_i)^a_i ≤ 1 if ^rƩ_i=1F_ix_i = 1 and F_i = a_i/^rƩ_j=1a_j for positive values of a_i and x_i. The equality sign holds if x_i= 1 for all i, and the inequality refers to all other situations. Moreover, x₁ = x₂ = …. = x_r = 1 are the coordinates of the common point of the hyperplanes ƩF_ix_i = 1, which corresponds to the point of equilibrium of stoichiometric mixturechiometric mixture.