Arrhenius Activation Energy for Two Temperature

The Arrhenius Activation Energy for Two Temperature calculator uses the Arrhenius equation to compute activation energy based on two temperatures and two reaction rate constants.

INSTRUCTIONS: Choose units and enter the following:

• (k₁) Reaction rate constant 1
• (k₂) Reaction rate constant 2
• (T₁) Temperature 1
• (T₂) Temperature 2

Activation Energy(E_a): The calculator returns the activation energy in Joules per mole.

The Math / Science

The Arrhenius Equation is used to describe the temperature dependence of reaction rates in chemical reactions. It was developed by Swedish chemist Svante Arrhenius in the late 19th century. The Arrhenius Equation is particularly relevant in the field of chemical kinetics, which studies the speed or rate at which chemical reactions occur.

The Arrhenius Equation, `k = A*e^(-E_a/"RT")`, can be rewritten (as shown below) to show the change from k₁ to k₂ when a temperature change from T₁ to T₂ takes place.

The Activation Energy equation using the Arrhenius formula is:

  `E_a = R*(ln(k_2/k_1))/(1/T_1 -1/T_2)`

where:

• E_a is the activation energy in Joules per mole (J/mol)
• k₁ is the reaction rate constant at temperature 1
• k₂ is the reaction rate constant at temperature 2
• R is the ideal gas constant (8.314 J/mol*K)
• T₁ is temperature 1 in Kelvin (K)
• T₂ is temperature 2 in Kelvin (K)

The calculator converts both temperatures to Kelvin so they cancel out properly. 

Related Calculators

• Arrhenius Equation (for two temperatures)
• Ideal Gas Constant (R)
• Arrhenius Equation
• Temperature Coefficient Q10

References

Whitten, et al. "Chemistry" 10th Edition. Pp. 645