Chlorobenzene when subjected to Fittig reaction gives a compound 'X'. The sum of \(\sigma\) and \(\pi\)-bonds in X is
Show Hint
A quick way to find the total number of bonds in a simple organic molecule is to sum all valence electrons and divide by two. Then subtract the number of \(\pi\) bonds (one for each double bond, two for each triple bond) to find the number of \(\sigma\) bonds.
Step 1: Identify the Fittig reaction and the product X. The Fittig reaction is a coupling reaction where two aryl halides react with sodium metal in dry ether to form a biaryl. It is analogous to the Wurtz reaction for alkyl halides. The reactant is chlorobenzene (C\(_6\)H\(_5\)Cl). Two molecules of chlorobenzene will react with sodium. \( 2 \text{C}_6\text{H}_5\text{Cl} + 2\text{Na} \xrightarrow{\text{dry ether}} \text{C}_6\text{H}_5\text{-}\text{C}_6\text{H}_5 + 2\text{NaCl} \). The product 'X' is biphenyl (or diphenyl), C\(_6\)H\(_5\)\(-\)C\(_6\)H\(_5\). Its molecular formula is C\(_{12}\)H\(_{10}\). Step 2: Count the number of \(\sigma\) and \(\pi\) bonds in biphenyl. Biphenyl consists of two benzene rings connected by a single bond. First, let's count the \(\pi\) bonds. Each benzene ring has 3 delocalized \(\pi\) bonds. So, in two rings, there are a total of \(3+3=6\) \(\pi\) bonds. Next, let's count the \(\sigma\) bonds. A quick way to count \(\sigma\) bonds in a non-cyclic hydrocarbon is (Number of C atoms) + (Number of H atoms) - 1. For cyclic systems, it's (Number of C atoms) + (Number of H atoms). A simpler way is to count directly from the structure. - There are 10 C-H bonds, all of which are \(\sigma\) bonds. - Within each benzene ring, there are 6 C-C bonds. So, in two rings, there are 12 C-C bonds in the rings. - There is 1 C-C single bond connecting the two rings. Total \(\sigma\) bonds = (C-H bonds) + (C-C bonds in rings) + (C-C connecting bond) = 10 + 11 = 21. Let's re-count. Each ring has 6 carbons. That's 12 carbons. Each ring has 5 hydrogens, total 10 hydrogens. Total atoms = 22. For a molecule with N atoms, the number of sigma bonds is at least N-1. Here \(22-1=21\). And since it has two rings, we add one more for each ring. No, this rule is confusing. Let's count again. In ring 1: 5 C-H bonds, 6 C-C bonds. Total 11. In ring 2: 5 C-H bonds, 6 C-C bonds. Total 11. Connecting bond: 1 C-C bond. Total = 11+11 = 22? No, one C-C bond in each ring is the connecting bond. This is confusing. Let's use a simpler method. Total atoms = 12 (C) + 10 (H) = 22 atoms. For any polycyclic molecule, the number of \(\sigma\) bonds = (Total number of atoms) + (Number of rings) - 1. This is also confusing. Let's count directly. - C-H bonds: Each ring has 5 hydrogens attached. Total = 10 \(\sigma\) bonds. - C-C bonds: Each ring has 6 carbons. The total number of vertices in the graph is 12. The number of edges is 11 (within rings) + 1 (between rings) = 12? No. Let's draw it. Two hexagons joined by a line. Each hexagon has 6 edges. Total 12 edges. Plus the joining edge. Total 13 C-C bonds. Wait, the joining carbons are part of the hexagons. So there are 6 C-C bonds in ring 1, 6 C-C bonds in ring 2, and the joining bond is shared. Let's just count from the skeleton: There are 11 C-C single bonds and 10 C-H single bonds. That's 21 sigma bonds. No, that's wrong. Total valence electrons = \(12 \times 4 + 10 \times 1 = 48 + 10 = 58\). Each bond is 2 electrons. So \(58/2=29\) total bonds. Number of pi bonds = 6. Number of sigma bonds = Total bonds - pi bonds = \(29-6=23\). So, x=23 and y=6. x+y = 23 + 6 = 29. Let's re-verify the sigma count. 12 carbons, 10 hydrogens. Total 22 atoms. Number of \(\sigma\) bonds = Number of atoms - 1 + number of rings = 22 - 1 + 2 = 23. This formula works. Step 3: Find the sum. The sum of \(\sigma\) bonds (x) and \(\pi\) bonds (y) is \( x+y = 23 + 6 = 29 \). The provided answer is D, 29. There may have been a typo in my scratchpad. Let me re-check option B. Let's assume the product is something else. Wurtz-Fittig: C6H5Cl + CH3Cl + Na → C6H5-CH3 (Toluene). In Toluene (C7H8): \(\sigma\) bonds = 7(C-C in ring and side) + 8(C-H) = 15. \(\pi\) bonds = 3. Sum = 18. This is option C. But the question says Fittig reaction. So the product must be Biphenyl. My calculation for Biphenyl gives a sum of 29. The keyed answer is 29. So my calculation is correct.
