Lecture 29 : Temperature Dependence of Reaction Rates
ln Kc /
T =
ln k1 /
T -
ln k -1 /
T =
U0 / R T 2 = E1 / R T 2 - E -1 / R T 2
(29.5)
When U0 = E1 - E -1 and the central observation is that the forward and reverse rates are influenced by different activation energies Eq (29.5) can be split into two separate equations
d ln k1 / d T = E1 / R T 2 and d ln k2 / dt = E-1 / RT2
(29.6)
and eq (29.6) readily integrates to give the Arrhenius equation for the forward and backward reactions
k1 = A1 e - E 1/ RT , k-1 = A -1 e - E -1/ RT
(29.7)
The activation energies are graphically shown in Fig 29.1
Figure 29.1 Energy as a function of the reaction coordinate (RC).
Activation energies for the forward and reverse reactions. The reaction coordinate (RC) represents a variable or a parameter that changes as we go from reactants to the products. In a reaction like F2 2F, RC is the distance between the fluorine atoms. Before the reaction, RC = bond distance in F2 and when the reaction is over, RC =
. In a reaction, such as HA + HBHC HA HB + HC, RC = r BC - r AB.
In the course of the reaction, RC goes from large negative values to large positive values. The important region of interest is around the high values of the energy where the reaction "occurs".
ln Kc /
T =
ln k1 /
T -
ln k -1 /
T =
U0 / R T 2 = E1 / R T 2 - E -1 / R T 2
2F, RC is the distance between the fluorine atoms. Before the reaction, RC = bond distance in F2 and when the reaction is over, RC =
. In a reaction, such as HA + HBHC 
HA HB + HC, RC = r BC - r AB. 
