Question

Dedonders equation concept of degree of advancement of a reaction

Answer 1

In discussions of reactions approaching an equilibrium, it is helpful to have a single
variable that measures the progress of all species as they move from their initial amounts
to their final, equilibrium amounts. This variable is called the degree of advancement or
extent of reaction variable, which we will symbolize .
Imagine a schematic reaction in which reactants A and B form products C and D
according to
A + B -
C + D
with , -
, , and the appropriate stoichiometric coefficients. We imagine mixing, at a
given temperature and pressure, arbitrary amounts of each species:
nA
o = initial amount of A
nB
o = initial amount of B
nC
o = initial amount of C
nD
o = initial amount of D
Reaction then starts, and at any later instant imagine finding nA, nB, etc., moles of A, B,
etc. These amounts are related to nA
o, nB
o, etc., and to the stoichiometric coefficients
through the equalities that define :
nA
o – nA

=
nB
o – nB
-

=
nC – nC
o

=
nD – nD
o

= . (1)
Note that has units of moles. The differential degree of advancement, d, is
d = –
dnA

= –
dnB
-

=
dnC

=
dnD

. (2)
For d > 0, dnA and dnB are negative, corresponding to the disappearance of reactants,
while dnC and dnD are positive, as more of the products appear. Thus, d > 0
corresponds to a reaction progressing from left to right as written.
The degree of advancement starts at zero, no matter what the initial composition,
since nA = nA
o, etc., at the start. As reaction ensues, can either increase (become
positive) or decrease (become negative), according to the spontaneous direction of the
reaction away from the initial composition and towards the equilibrium composition.
Note that cannot increase or decrease without limit, however; its range is governed by
the initial composition and the reaction stoichiometry.