For the two parallel reactions `A overset(k_(1)) rarr B and A overset(k_(2)) rarr C`, show that the activation energy E' for the disappearance of A is given in terms of activation energies `E_(1) and E_(2)` for the two paths by
`E' =(k_(1)E_(1)+k_(2)K_(2))/(k_(1)+k_(2))`

Explanation

To solve the problem of finding the activation energy \( E' \) for the disappearance of \( A \) in the parallel reactions \( A \overset{k_1}{\rightarrow} B \) and \( A \overset{k_2}{\rightarrow} C \), we will derive the expression step by step.

### Step 1: Define the reactions and their rate constants
We have two parallel reactions:
1. \( A \overset{k_1}{\rightarrow} B \)
2. \( A \overset{k_2}{\rightarrow} C \)

Where \( k_1 \) and \( k_2 \) are the rate constants for the respective reactions.
...