Logarithms and Arrhenius

The rate of most reactions changes with temperature because the rate constant k varies with temperature. Svante Arrhenius established experimentally the relationship between rate constant k and the temperature (T) in Kelvin shown below.

k = Ae^-E_a/RT
for a particular reaction
A, the preexponential factor, is constant
R is the ideal gas constant
E_a_, the activation energy, is constant

A form of the Arrehenius equation generated by taking the natural logarithm (The logarithm of a number is the power to which a fixed base must be raised to give that number. log is the logarithm to base 10. log 100 (10²) is 2. ln is the natural logarithm to base e (2.718). ln 100 is 4.61. Natural logarithms are larger than logarithms to the base 10 because the natural logarithm base is smaller.) of both sides is useful for determining the activation energy for a reaction, if the rate constant at several temperatures is known.

ln k	=	–	E_a	×	1	+ ln A
			R		T

The logarithm rules below were used to generate this equation.

ln(ab) = ln a + ln b
ln(e^c) = c