A certain physiologically important first - order reaction has an activation energy equal to `45.0` kJ/mol at normal body temperature `(37^(@)C)` .Without a catalyst ,the rate constant for the reaction is `5.0 xx10^(-4)s^(-1)`.To be effective in the human body , where the reaction is catalysed by an enzyme , teh rate constant must be at least `2.0 xx10^(-2)s^(-1)`. If the activation energy of the reaction to achieve the desired rate ?

Explanation

To solve the problem, we will use the Arrhenius equation and the relationship between the rate constants and activation energies of the reaction. Here’s a step-by-step breakdown of the solution:

### Step 1: Write down the known values
- Activation energy without catalyst (Ea1) = 45.0 kJ/mol
- Rate constant without catalyst (k1) = 5.0 × 10^(-4) s^(-1)
- Rate constant with catalyst (k2) = 2.0 × 10^(-2) s^(-1)
- Temperature (T) = 37°C = 310 K (since T(K) = T(°C) + 273)

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