Enthalpy changes from reaction diagram

Steps:

• Identify labeled enthalpy values for each transformation in the diagram.
• Calculate net enthalpy for multi-step paths using Hess's law: ΔH total = sum of individual ΔH.
• Determine endothermic/exothermic based on sign: positive ΔH is endothermic, negative is exothermic.
• Compare calculated values to given options.

Why D is correct:

• Hess's law states that enthalpy change for a reaction is the same regardless of path, so D correctly applies this to verify overall ΔH.

Why the others are wrong:

• A: Direct value from diagram shows U → T as +42 kJ/mol, not -42 kJ/mol.
• B: R → S arrow points downward, indicating exothermic (negative ΔH), not endothermic.
• C: R → T path sums to -77 kJ/mol via R → S + S → T, not -35 kJ/mol.

Final answer: D