why is the number of equivalence of each species in a reaction always same

Hello Student
According to the law of equivalence, whenever two substances react, the equivalents of one will be equal to the equivalents of other and the equivalents of any product will also be equal to that of the reactant.

Let us suppose we have a reaction, A + B →C + D.

In this reaction, the number of moles of electrons lost by 1 mole of A are x and the number of mole of electrons gained by 1 mole of B are y. Since, the number of mole of electrons lost and gained are not sane, the molar ratio which A & B react cannot be 1 : 1.

Thus, if we take y moles of A, then the total moles of electrons lost by y moles of A would be (x × y).

Similarly, if x moles of B are taken, then the total mole of electrons gained by x moles of B would be (y × x).

Thus, the number of electrons lost by A and number of electrons gained by B becomes equal. For reactant A, its n-factor is x and the number of moles used are y.

So,The equivalents of A reacting = moles of A reacting × n-factor of A = y × x.

Similarly, for reactant B, its n-factor is y and the number of moles used are x, So,

The equivalents of B reacting = moles of B reacting × n-factor of B= x × y

Thus, the equivalents of A reacting would be equal to the equivalent of B reacting. Thus, the balancing coefficients of the reactant would be as

yA + xB → C + D

(n-factor = x) (n-factor = y)

The n-factor of A & B are in the ratio of x : y, and their molar ratio is y : x. Thus, molar ratio is inverse of the n-factor ratio.