Using the Arrhenius equation:
k=Ae−Ea/RT
where
k is the rate constant,
A is the pre-exponential factor,
Ea is the activation energy,
R is the gas constant, and
T is the temperature in Kelvin.
The equation is used for both the uncatalyzed forward reaction and the catalyzed backward reaction. By setting the two equations equal to each other and cancelling out the pre-exponential factor, we get:
e600×R300×103=e300×R−Ea
Simplifying the equation, we get:
600×R300×103=300×REa
Solving for
Ea, we get:
Ea=2103×300=150×103 J mol−1=150 kJ mol−1
This gives us the activation energy for the uncatalyzed forward reaction.
To find the activation energy for the catalyzed backward reaction, we use the relationship:
Erev,catalysed=Efwd,uncat−ΔHforward reaction
Substituting the given values, we get:
Erev,catalysed=150 kJ mol−1−20 kJ mol−1=130 kJ mol−1
Therefore, the activation energy for the catalyzed backward reaction is
130 kJ mol−1.
