From Arrhenius equation, derive an expression for temperature variation

The Arrhenius equation is a simple, but remarkably accurate, formula for the temperature dependence of reaction rates. The equation is:

k = Ae^(-Ea/RT)

where:

• k is the rate constant,
• A is the pre-exponential factor,
• Ea is the activation energy,
• R is the universal gas constant, and
• T is the absolute temperature.

To derive an expression for temperature variation, we can rearrange the Arrhenius equation to solve for T:

T = -Ea / (R * ln(k/A))

This equation tells us how the temperature needs to change to achieve a certain rate constant, given the activation energy, the pre-exponential factor, and the universal gas constant.