Untitled - Aerobib - Universidad Politécnica de Madrid

30 CHAPTER 1. THERMOCHEMISTRY
This law states that the number dc i / dt of moles of A i produced within unit
volume during unit time is
dc i
dt = (ν′′ i − ν ′ i) k ∏ j
c ν′ j
j . (1.117)
Here, k is independent from the composition and pressure of the mixture and depends
only on its temperature. It is called specific rate or rate coefficient of the reaction and
its dimensions are ( cm 3 /mol ) ν−1
s −1 , where
ν = ∑ j
ν ′ j (1.118)
is called order or molecularity of the reaction.
Since the molar mass of A i is M i , we have for w i , from (1.117)
w i = M i
dc i
dt = M i (ν ′′
i − ν ′ i) k ∏ j
c ν′ j
j . (1.119)
This formula can also be expressed as a function of the mass fractions of the reacting
species, by virtue of (1.31), in the form
w i = ∏
ρ ν
M ν′ j
j
j
kM i (ν ′′
i − ν ′ i) ∏ j
Y ν′ j
j . (1.120)
For example, in the case of a bimolecular reaction between species A 1 and A 2 which
produces A 3 ,
one has, due to (1.120),
A 1 + A 2 → A 3 , (1.121)
w 1
= w 2
= − w 3
= dc 1
M 1 M 2 M 3 dt = dc 2
dt = − dc 3
dt = −
ρ2
kY 1 Y 2 . (1.122)
M 1 M 2
The way in which the specific rate k depends on temperature is given by Arrhenius’s
law
k = Ae −E/RT (1.123)
where E is called activation energy of the reaction and A is a constant or the product
of a constant by a power of the absolute temperature T
A = BT α . (1.124)
Here B is a constant called frequency factor and α is an exponent within zero and one.
Arrhenius [27] deduced his law empirically as a generalization of van’t Hoff’s
law for the variation of equilibrium constants as functions of temperature. Statistical