See image — Hydrocarbons Chemistry Question

💡 Solution & Explanation

Concept: Cubane (C8H8) has a cubic carbon skeleton. To determine the number of bond cleavages needed to convert a cyclic (or polycyclic) structure into a non-cyclic (acyclic/tree) skeleton, we use the circuit rank (cyclomatic number) formula: μ = E - V + 1, where E is the number of edges (bonds) in the carbon skeleton and V is the number of vertices (carbon atoms), assuming a connected graph. Step 1: Identify the graph parameters of cubane's carbon skeleton. - Cubane has 8 carbon atoms (vertices, V = 8). - A cube has 12 edges (bonds, E = 12). Step 2: Apply the cyclomatic number formula. μ = E - V + 1 = 12 - 8 + 1 = 5 Step 3: Interpret the result. The cyclomatic number μ = 5 means cubane has 5 independent rings (ring systems). To convert a polycyclic structure into a non-cyclic (acyclic) skeleton, you must break exactly as many bonds as there are independent rings, i.e., 5 bond cleavages. Step 4: Why other options fail. - (a) 2: Too few; breaking only 2 bonds would leave 3 rings intact. - (b) 3: Too few; breaking 3 bonds would leave 2 rings intact. - (c) 4: Too few; breaking 4 bonds would leave 1 ring intact, still cyclic. - (d) 5: Correct; breaking 5 bonds reduces the cyclomatic number to 0, yielding a fully acyclic (non-cyclic) skeleton. Therefore, the correct answer is D.