For a given reaction, energy of activation for forward reaction `(E_(af)` is 80 kJ `mol^(-1).DeltaH=-40"kJ mol"^(-1)` for the reaction. A catalyst lowers `E_(af)` to 20 kJ `mol^(-1)`. The ratio of energy of activation for reverse reaction before and after addition of catalyst is :

Options

A. `1.0`
B. `0.5`
C. `1.2`
D. `2.0`

Answer

To solve the problem, we need to determine the ratio of the energy of activation for the reverse reaction before and after the addition of a catalyst. We will follow these steps:

### Step 1: Understand the Given Data
We are given:
- Energy of activation for the forward reaction (E_af) before the catalyst = 80 kJ/mol
- Enthalpy change (ΔH) = -40 kJ/mol (indicating an exothermic reaction)
- Energy of activation for the forward reaction (E_af) after the catalyst = 20 kJ/mol

### Step 2: Calculate the Energy of Activation for the Reverse Reaction Before the Catalyst
Using the relationship:
\[ E_{a \text{ (backward)}} = E_{a \text{ (forward)}} + \Delta H \]

Substituting the values:
\[ E_{a \text{ (backward)}} = 80 \text{ kJ/mol} + (-40 \text{ kJ/mol}) \]
\[ E_{a \text{ (backward)}} = 80 \text{ kJ/mol} - 40 \text{ kJ/mol} \]
\[ E_{a \text{ (backward)}} = 120 \text{ kJ/mol} \]

### Step 3: Calculate the Energy of Activation for the Reverse Reaction After the Catalyst
Again using the same relationship:
\[ E_{a \text{ (backward)}} = E_{a \text{ (forward)}} + \Delta H \]

Now substituting the new forward activation energy:
\[ E_{a \text{ (backward)}} = 20 \text{ kJ/mol} + (-40 \text{ kJ/mol}) \]
\[ E_{a \text{ (backward)}} = 20 \text{ kJ/mol} - 40 \text{ kJ/mol} \]
\[ E_{a \text{ (backward)}} = 60 \text{ kJ/mol} \]

### Step 4: Calculate the Ratio of Energy of Activation for the Reverse Reaction Before and After the Catalyst
Now we can find the ratio:
\[ \text{Ratio} = \frac{E_{a \text{ (backward, before)}}}{E_{a \text{ (backward, after)}}} \]
\[ \text{Ratio} = \frac{120 \text{ kJ/mol}}{60 \text{ kJ/mol}} \]
\[ \text{Ratio} = 2 \]

### Final Answer
The ratio of energy of activation for the reverse reaction before and after the addition of the catalyst is **2**.

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