where n₀ is an arbitrary positive number, and N₂ is the residue(or excess) of A₂, i.e., the number of moles of A₂ which cannot combine. If the reaction is assumed to proceed complete it to the left with the disappearance of the final constituent A₃ then

(3.7)

(3.8)

where  is an arbitrary positive number and N₄ is the excess number of moles of A₄ left after the reaction is complete from right to left. For a reaction that occurred completely to the left, there is a maximum possible amount of each initial constituent, and a minimum possible amount of each final constituent, so that

(3.9)

where n₀v₁ = Original number of moles of
           = Number of  moles of formed by chemical reaction

(3.10)

where (n₀v₁ + N₂) = Original number of moles of
              = Number of moles of formed bychemical reaction

The constituent A₃ completely disappears by reaction, hence

n3(min) = 0

(3.11)

The excess number of moles of  that are left after the reaction is complete to left

n4(min) = 0

(3.12)

Similarly, if the reaction is imagined to proceed completely to the right, there is a minimum amount of each initial constituent, and a maximum amount of each final constituent, so that

n1(min) = 0

(3.13)

n2 (min) = N2

(3.14)

(3.15)

 where = original amount
            n₀v₃ = amount formed by chemical reaction

(n₀v₁A₁ + n₀v₂A₂ → n₀v₃A₃ + n₀v₄A₄)

(3.16)

Let us suppose that the reaction proceeds partially either to the right or to the left to the extent that there are n₁ moles of A₁, n₂ moles of A₂, n₃ moles of A₃ and n₄ moles of A₄. The degree (or advancement) of reaction ε is defined in terms of any one of the initial constituents, say, A₁ as the fraction

(3.17)