See image — Isomerism and Stereochemistry Chemistry Question

💡 Solution & Explanation

To determine which molecules have non-zero dipole moments, we analyze the symmetry and vector sum of bond dipoles in each case. (I) Gauche conformation of 1,2-dibromoethane: In the gauche conformation, the two C-Br bonds are at approximately 60° to each other (dihedral angle ~60°). The bond dipoles do NOT cancel because they are not antiparallel. The vector sum of the two C-Br dipoles is non-zero. Therefore, gauche 1,2-dibromoethane has a NON-ZERO dipole moment. (II) Anti conformation of 1,2-dibromoethane: In the anti conformation, the two C-Br bonds are exactly antiparallel (dihedral angle = 180°). The two C-Br bond dipoles are equal in magnitude and exactly opposite in direction, so they cancel completely. Net dipole moment = ZERO. (III) trans-1,4-dibromocyclohexane: In the trans diaxial or diequatorial chair conformation, the two C-Br bonds point in opposite directions (both axial pointing in opposite axial directions, or both equatorial). By symmetry, the dipole moments cancel. Net dipole moment = ZERO. (IV) cis-1,4-dibromocyclohexane: In the chair conformation of cis-1,4-dibromocyclohexane, one Br is axial and one is equatorial. The axial and equatorial C-Br dipoles are not equal in direction and do not cancel. The vector sum is non-zero. Therefore, cis-1,4-dibromocyclohexane has a NON-ZERO dipole moment. (V) Tetrabromomethane (CBr4): This is a tetrahedral molecule with four identical C-Br bonds arranged symmetrically. By symmetry, all bond dipoles cancel. Net dipole moment = ZERO. (VI) 1,1-dibromocyclohexane: Both bromine atoms are on the same carbon (geminal dibromo). The two C-Br bonds are on the same carbon and point in different directions but are not antiparallel; the molecule lacks the symmetry to cancel these dipoles. The vector sum of the two C-Br bonds on the same carbon gives a resultant that is non-zero (similar to CH2Br2 which has a non-zero dipole moment). Therefore, 1,1-dibromocyclohexane has a NON-ZERO dipole moment. Summary: Molecules with non-zero dipole moments are I (gauche 1,2-dibromoethane), IV (cis-1,4-dibromocyclohexane), and VI (1,1-dibromocyclohexane). Why other options fail: - (a) I and II: II (anti) has zero dipole moment. - (b) I and IV: Correct subset but misses VI. - (c) II and V: Both have zero dipole moments. Therefore, the correct answer is D.