Question

The activation energy for the reaction X \(\rightarrow\) Y is 150 kJ mol\(^{-1}\). The change in enthalpy for the above reaction is -135 kJ mol\(^{-1}\). Then the activation energy for Y \(\rightarrow\) X is _________.

• A. 280 kJ mol\(^{-1}\)
• B. 285 kJ mol\(^{-1}\)
• C. 270 kJ mol\(^{-1}\)
• D. 15 kJ mol\(^{-1}\)

Hint:

Always draw a simple reaction coordinate diagram to visualize the relationship. For an exothermic reaction ($\Delta H<0$), the products are lower in energy than reactants. The energy barrier from products to reactants ($E_{a,b}$) will always be larger than the barrier from reactants to products ($E_{a,f}$) if $\Delta H$ is negative.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks to determine the activation energy for the reverse reaction (Y \(\rightarrow\) X), given the activation energy for the forward reaction (X \(\rightarrow\) Y) and the enthalpy change for the forward reaction.
Step 2: Key Formula or Approach:
The relationship between the activation energy of the forward reaction ($E_{a,f}$), the activation energy of the reverse reaction ($E_{a,b}$), and the enthalpy change of the reaction ($\Delta H$) is:
\[ \Delta H = E_{a,f} - E_{a,b} \]
This relationship can be visualized using a reaction coordinate diagram. For an exothermic reaction ($\Delta H<0$), the products are at a lower energy level than the reactants.
Step 3: Detailed Explanation:
Given values for the forward reaction \(X \rightarrow Y\):
Activation energy for forward reaction, \( E_{a,f} = 150 \text{ kJ mol}^{-1} \)
Change in enthalpy, \( \Delta H = -135 \text{ kJ mol}^{-1} \)
We need to find the activation energy for the reverse reaction \(Y \rightarrow X\), which is \( E_{a,b} \).
Substitute the given values into the formula:
\[ -135 \text{ kJ mol}^{-1} = 150 \text{ kJ mol}^{-1} - E_{a,b} \]
Now, solve for \( E_{a,b} \):
\[ E_{a,b} = 150 \text{ kJ mol}^{-1} + 135 \text{ kJ mol}^{-1} \]
\[ E_{a,b} = 285 \text{ kJ mol}^{-1} \]
Step 4: Final Answer:
The activation energy for the reverse reaction Y \(\rightarrow\) X is 285 kJ mol\(^{-1}\).