Untitled - Kelly Walsh High School

194 CHEMISTRY FOR THE UTTERLY CONFUSED
13-4 Arrhenius and Activation Energy
A change in the reaction temperature affects the rate constant k. As the temperature
increases, the value of the rate constant increases and the reaction is faster.
The Swedish scientist, Arrhenius, derived a relationship that related the rate
k Ae E a /RT
constant and temperature. The Arrhenius equation has the form: .
In this equation, k is the rate constant and A is a term called the frequency factor
that accounts for molecular orientation. The symbol e is the natural logarithm
base and R is universal gas constant. Finally, T is the Kelvin temperature
and E a is the activation energy, the minimum amount of energy needed to initiate
or start a chemical reaction.
E
Reactants
We commonly use the Arrhenius equation to calculate the activation energy of
a reaction. One way to do this is to plot the ln of k versus 1/T. This gives a
straight line whose slope is E a/R. Knowing the value of R, we can calculate the
value of E a.
Another method for determining the activation energy involves using a modification
of the Arrhenius equation. If we try to use the Arrhenius equation
directly, we have one equation with two unknowns (the frequency factor and
the activation energy). The rate constant and the temperature are experimental
values, while R is a constant. One way to prevent this difficulty is to perform
the experiment twice. We determine experimental values of the rate constant at
two different temperatures. We then assume that the frequency factor is the
same at these two temperatures. We now have a new equation derived from the
Arrhenius equation that allows us to calculate the activation energy. This equation
is:
ln k 1
k 2
Activated complex
Reaction progress →
Ea 1
B
R T2 Products
1
R
T1 E a
∆H rxn