The lac operon includes the following genes and their products:
'i' gene: Produces the repressor protein (iii).
'z' gene: Produces $\beta$-galactosidase (i), which breaks down lactose.
'a' gene: Produces transacetylase (iv).
'y' gene: Produces lac permease (ii), which facilitates lactose entry into the cell.
A certain reaction is 50 complete in 20 minutes at 300 K and the same reaction is 50 complete in 5 minutes at 350 K. Calculate the activation energy if it is a first order reaction. Given: \[ R = 8.314 \, \text{J K}^{-1} \, \text{mol}^{-1}, \quad \log 4 = 0.602 \]