Use these gauche interaction energies (dihedral $60^{\circ }$ only, no other terms): Br/Br $4.0$, Br/$\mathrm{CH}{}_3$ $3.0$, $\mathrm{CH}{}_3$/$\mathrm{CH}{}_3$ $3.8$ kJ/mol; any interaction involving H is zero. The anti-Br staggered conformer of meso-2,3-dibromobutane has front carbon Br at 12, $\mathrm{CH}{}_3$ at 4, H at 8 o'clock, and rear carbon Br at 6, $\mathrm{CH}{}_3$ at 10, H at 2 o'clock. Rotating the rear carbon by $\pm 120^{\circ }$ gives the two gauche-Br staggered conformers. What is the energy of a gauche-Br conformer relative to the anti-Br conformer?

1. A$+10.8$ kJ/mol
2. B$+4.8$ kJ/mol
3. C$+6.0$ kJ/mol
4. D$+3.8$ kJ/mol