See image — GOC and Organic Chemistry Basics Chemistry Question

💡 Solution & Explanation

Concept: Resonance energy is the difference between the theoretical (expected) heat of hydrogenation and the observed (actual) heat of hydrogenation. A more stable (resonance-stabilized) compound releases less heat upon hydrogenation than expected. Step 1: Understand the reference compound. Cyclohexa-1,4-diene has two isolated (non-conjugated) double bonds. Its observed heat of hydrogenation is x kcal/mol. Since the two double bonds are isolated (no conjugation/resonance), each double bond contributes x/2 kcal/mol upon hydrogenation. Step 2: Calculate the theoretical heat of hydrogenation for cyclohexa-1,3-diene. Cyclohexa-1,3-diene also has two double bonds. If these were isolated (non-interacting), the expected heat of hydrogenation would be the same as for cyclohexa-1,4-diene, i.e., x kcal/mol. However, the question states the theoretical value should be based on the isolated double bond reference. Since cyclohexa-1,4-diene with two isolated double bonds gives x kcal/mol, the theoretical heat of hydrogenation for cyclohexa-1,3-diene (treating its two double bonds as isolated) = x kcal/mol. Wait - re-examining: cyclohexa-1,4-diene has two isolated double bonds and gives x kcal/mol total. So per double bond = x/2. For cyclohexa-1,3-diene with two double bonds, theoretical ΔH = 2 × (x/2) = x kcal/mol. Step 3: Observed heat of hydrogenation of cyclohexa-1,3-diene = y kcal/mol. Step 4: Resonance energy = Theoretical ΔH - Observed ΔH = x - y. Now, x - y = 2x/2 - y, which matches option (b): 2x/2 - y. Step 5: Why other options fail. (a) 3x/2 - y: This would imply three double bonds worth of theoretical energy, which is incorrect for a diene. (c) 3y/2 - x and (d) 2y/2 - x: These subtract x from a multiple of y, which reverses the logic (observed minus theoretical instead of theoretical minus observed). Therefore, the correct answer is B.