Hess's Law Cycle for Enthalpy of Formation Using Combustion Data Steps:

• Compute total combustion enthalpy for elements: 4 × 394 + 5 × 286 = 1576 + 1430 = 3006 kJ (magnitudes, exothermic).
• Subtract combustion enthalpy of butane: 3006 - 2877 = 129 kJ.
• The positive sign indicates endothermic formation relative to combustion energies.
• Thus, ΔH_f°(C₄H₁₀) = +129 kJ mol⁻¹.

Why B is correct:

• Hess's law states ΔH_f° = Σ(coefficients × |ΔH_c°| of elements) - |ΔH_c°| of compound, yielding +129 kJ mol⁻¹.

Why the others are wrong:

• A: Incorrect; likely misadds 4 × (-394) + 5 × (-286)/something = -3006/5 or error in stoichiometry.
• C: Incorrect; perhaps uses 4 × 286 or wrong H₂ coefficient, overestimating by 90 kJ.
• D: Incorrect; minor arithmetic error in 3006 - 2877, off by 1 kJ.

Final answer: B