### Arrhenius Equation Variations

Posted:

**Thu Mar 14, 2019 9:20 pm**Is the equation ln(k2/K1)= Ea/R(1-T1-(1-T2) a variation of the Arrhenius equation?

Created by Dr. Laurence Lavelle

https://lavelle.chem.ucla.edu/forum/

https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=151&t=44608

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Posted: **Thu Mar 14, 2019 9:20 pm**

Is the equation ln(k2/K1)= Ea/R(1-T1-(1-T2) a variation of the Arrhenius equation?

Posted: **Thu Mar 14, 2019 9:30 pm**

The equation ln(k_{2}/k_{1})= Ea/R(1-T_{1}-(1-T_{2}) is derived from the Arrhenius equation for two temperatures.

ln k_{2} = -Ea/RT_{2} + ln A

ln k_{1} = -Ea/RT_{1} + ln A

By subtracting the two equations, you get ln k_{2} - ln k_{1} = -Ea/RT_{2} + Ea/RT_{1}

Then you can factor out -Ea/R to get ln k_{2} - ln k_{1} = -Ea/R (-1/T_{2} + 1/T_{1})

After rearranging the temperature variables, you get the variation:

ln k_{2}/k_{1} = -Ea/R (1/T_{1} - 1/T_{2}).

ln k

ln k

By subtracting the two equations, you get ln k

Then you can factor out -Ea/R to get ln k

After rearranging the temperature variables, you get the variation:

ln k