![]() | ||
An Arrhenius plot displays the logarithm of kinetic constants (
The Arrhenius equation can be given in the form:
or alternatively
The only difference is the energy units: the former form uses energy/mole, which is common in chemistry, while the latter form uses energy directly, which is common in physics. The different units are accounted for in using either the gas constant
The former form can be written equivalently as:
When plotted in the manner described above, the value of the true y-intercept (at
The pre-exponential factor, A, is an empirical constant of proportionality which has been estimated by various theories which take into account factors such as the frequency of collision between reacting particles, their relative orientation, and the entropy of activation.
The expression
Worked Example
Based on the red "line of best fit" plotted in the graph given above:
Let y = ln(k[10−4 cm3 mol−1 s−1])Let x = 1/T[K]Points read from graph:
y = 4.1 at x = 0.0015y = 2.2 at x = 0.00165Slope of red line = (4.1 - 2.2) / (0.0015 - 0.00165) = -12,667
Intercept [y-value at x=0] of red line = 4.1 + (0.0015 x 12667) = 23.1
Inserting these values into the form above:
yields:
as shown in the plot at the right.
for:
k in 10−4 cm3 mol−1 s−1T in KSubstituting for the quotient in the exponent of
The activation energy of this reaction from these data is then:
Ea = R x 12,667 K = 105,300 J mol−1 = 105.3 kJ mol−1.