Chemical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 214

[ 107 ]. Second, increasing temperature accelerates the forward and reverse reaction
to a different degree. As seen in Fig. 4.40 , the process having a steeper Arrhenius
plot has a larger increase in the rate constant per the same increase in temperature.
To put it differently, the same increase in temperature would accelerate more the
process having larger activation energy. In the case of an endothermic reversible
process, it means that the forward reaction would be accelerated more than the
reverse reaction because the activation energy for the former is always larger than
for the latter (Fig. 4.39 ).
Let us assume that temperature increases from T 1 to T 2 . In accord with the Ar-
rhenius equation (Eq. 1.2), the resulting increase in the rate constant is proportional
to the activation energy as follows:

= −

E
RT T

11

∆ ln k = ln ()ln () k T − k T − .

(4.88)

2 1

2 1

Then the difference between the increases in the respective rate constants for the
forward and reverse reaction is:

= −+

EE
RTT

11

= −

∆ H

RTT

11

1 2 r

∆ ln k − ∆ ln k − − .

(4.89)

1 2

2 1 2 1

Equation 4.89 suggests that the acceleration of the forward reaction relative to the
reverse one is proportional to the process enthalpy. It means that the larger the en-
thalpy of reversible decomposition the easier it is to reach the temperature region in
which the rate of the forward reaction is significantly faster than that of the reverse
reaction.

Fig. 4.40 Arrhenius plots for
the forward (ln k 1 ) and reverse
(ln k 2 ) reactions of reversible
decomposition (Eq. 4.73).
∆ln k represents the respec-
tive acceleration of these two
reactions due to an increase
in temperature from T 1 to T 2

N

⇔ $ % + &

V V J

N

∆ OQN

∆ OQN

OQN

OQN

7 7