k=rate constant of the reaction
A= Arrhenius Constant
Ea= Activation Energy
R= Universal Gas Constant
T=Temperature in absolute scale
$k = Ae^{−Ea/RT}
If we take to log on both sides of the equation, the resulting equation will be as follows:
lnk=lnA–Ea/R×1/T.... (1)
Now let’s compare this equation with the equation of a straight line that is y=mx+c, where the m= slope of the line and c= y-intercept.
So we have:
y=lnk
x=1/T
m=−Ea/R
c=lnA
So a plot of ln k on the y-axis and 1/T on x-axis will give a straight line with its slop equal to –Ea/R and y-intercept equal to ln A.
As per Arrhenius Equation, for first condition:
lnK1=lnA–Ea/R×1/T1 ……………. (2)
For second condition:
lnK2=lnA–Ea/R×1/T2……………. (3)
Subtracting Equation (2) from equation (3) we will get,
lnk2–lnk1=Ea/R×1/T1–Ea/R×1/T2
lnk2k1=Ea/R(1/T1–1/T2)
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