It is seen that when n₁ = n₁(max), ε = 0, the reaction will start from left to right. When n₁ = n₁(min),ε = 1, reaction is complete from left to right.
The degree of reaction can thus be written in the form

(3.18)

Therefore

(3.19)

or,

n1 = Number of moles of A1 at start - number of moles of A1 consumed in the reaction =

(3.20)

(3.21)

(3.22)

(3.23)

The  number of moles of the constituents change during a chemical reaction, not independently but restricted by the above relations (Eqs. (3.20-3.23)). These equations are the equations of constraint. The n's are functions of ε only. In a homogeneous system, in a given reaction, the mole fraction x's is also function of ε only, as illustrated below.

Let us take the reaction

(3.24)

in which n₀ moles of NO dissociates to produce   moles of N₂ and  moles of O₂. The n's and x's as function of ε are shown in the Table-3.1 given below

Table 3.1 Values of v, n and x (Eq. (3.24))

If the reaction is imagined to advanced to an infinitesimal extent, the degree of reaction changes from ε to ε + dε, and the various n's will change by the amounts (Upon differentiation of  Eqs. (3.20-3.22) w.r.t. ε)

(3.25)

which shows that the dn's are proportional to the v's.