The temperature dependence of a reaction is given by K = AT²exp(-E_o/RT).
The activation energy (E_a) of the reaction is given by -

CONCEPT:

Arrhenius Equation and Modified Temperature Dependence

• The Arrhenius equation describes how the rate constant \(K \) depends on temperature, usually in the form \(K = A \exp(-E_a/RT) \), where \(E_a \) is the activation energy.
• In the modified equation  \(K = AT^2 \exp(-E_0/RT)\), the  \(T^2\)  term accounts for an additional temperature dependency, but \(E_0\) still represents the activation energy barrier.
• The activation energy \(E_a\) is the energy required to start the reaction, which in this case is given directly by \(E_0\).

EXPLANATION:

• The form of the equation \(K = AT^2 \exp(-E_0/RT\)) suggests that despite the additional \(T^2 \) factor, the exponential term controls the temperature dependence of the reaction rate.
• The activation energy \(E_a\) is thus directly given by \(E_0\), which is the energy required for the reaction to occur.

CONCLUSION:

The correct answer is: \(E_0\)