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Arrhenius Equation

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Quick
The Arrhenius equation relates the movement of atoms to thermal energy.


Equations

(Eq1)     Rate = c0 exp ( −Q RT )

Arrhenius equation

Nomenclature

c0	constant
R	gas constant (1.987 cal/mol K)
T	absolute temperature in Kelvins
Q	activation energy (cal/mol) required to cause the imperfection to move

Details

The ability of atoms and imperfections to diffuse increases as the temperature, or thermal energy, possessed by the atoms increases. The rate of movement is related to temperature or thermal energy by the Arrhenius equation:

Eq1	Rate = c0 exp ( −Q RT )

This equation is derived from a statistical analysis of the probability that the atoms will have the extra energy Q needed to cause movement. The rate is related to the number of atoms that move.

The equation can be rewritten by taking natural logarithms of both sides:

ln (Rate) = ln (c0) −

Q RT

If the ln (rate) of some reaction versus 1/T is plotted as shown:



the slope of the curve will be −Q/R, and consequently Q can be calculated. The constant c₀ is the intercept when 1/T is zero.