The activation energy of the reaction, `A+BtoC+D+38` kcal is 20 kcal. What would be the activation energy pof the following reaction.
`C+DtoA+B`

Options

A. 20 kcal
B. `-20 kcal`
C. 18 kcal
D. 58 kcal

Answer

To find the activation energy for the reaction \( C + D \to A + B \), we can follow these steps:

### Step 1: Understand the Forward Reaction
The forward reaction is given as:
\[ A + B \to C + D + 38 \text{ kcal} \]
This reaction has an activation energy (\( E_a \)) of 20 kcal.

### Step 2: Determine the Enthalpy Change
The enthalpy change (\( \Delta H \)) for the forward reaction is given as:
\[ \Delta H = +38 \text{ kcal} \]
This indicates that the reaction is exothermic, meaning it releases energy.

### Step 3: Relate Activation Energies
For a reaction and its reverse, the relationship between the activation energies is given by:
\[ E_a(\text{backward}) = E_a(\text{forward}) + \Delta H \]

### Step 4: Substitute Known Values
Now, we can substitute the known values into the equation:
- \( E_a(\text{forward}) = 20 \text{ kcal} \)
- \( \Delta H = -38 \text{ kcal} \) (since it is exothermic, we take it as negative)

Thus, the activation energy for the backward reaction becomes:
\[ E_a(\text{backward}) = 20 \text{ kcal} + 38 \text{ kcal} \]

### Step 5: Calculate the Activation Energy
Now, we perform the calculation:
\[ E_a(\text{backward}) = 20 + 38 = 58 \text{ kcal} \]

### Final Answer
The activation energy for the reaction \( C + D \to A + B \) is:
\[ \boxed{58 \text{ kcal}} \]

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