Arrhenius Equation and EA Energy of Activation
Label the graph and identify the Ea for the catalyzed and un-catalyzed reaction.
Ea = Energy of Activation
The rate constant k is affected by the temperature and this dependence may be represented by Arrhenius equation:
k = A e
where the pre-exponential factor A is assumed to be independent of temperature, R is the gas constant, and T the temperature in K. Taking the natural logarithm of this equation gives:
ln k = ln A – Ea/(RT)
ln k = –Ea/(RT) + constant
ln k = -(Ea/R)(1/T) + constant
These equations indicate that the plot of ln k vs. 1/T is a straight line, with a slope of –Ea/R. These equations provide the basis for the experimental determination of Ea.
The reaction constants k determined at 298 K and 350 K are 0.00123 /(M s) and 0.0394 /(M s) respectively.
(a) Calculate Ea.
(b) What is the rate constant at 308 K?
Let k1 and k2 be the rate constants determined at T1 and T2, respectively. Then you have two equations:
ln k1 = lnA – Ea/(R T1)
ln k2 = lnA – Ea/(R T2)
From these, you should be able to derive the following relationships,
= 57811 J/mol
= 57.8 kJ/mol
It is a good idea to manipulate the formula with symbols until you have obtained the desirable form before you substitute numerical values into it. The necessary units are included here to show you the derivation of units for Ea.
(b) To calculate k at 308 K,
= -6.70 + 0.758
k = e-5.94
k = 0.00263
An increase of 10 k doubles the rate constant in this case.
If Ea is positive, increasing temperature always leads to an increase in the rate constant.