Two separate hydrogenation reactions of unsaturated hydrocarbons have been studied at 298 K:
(I) C₂H₂(g) + 2 H₂(g) → C₂H₆(g) ΔH° = –311 kJ
(II) C₂H₄(g) + H₂(g) → C₂H₆(g) ΔH° = –137 kJ
Standard molar enthalpies of formation (298 K) for selected species are:
• H₂(g): 0 kJ·mol⁻¹
• C₂H₆(g): –84.7 kJ·mol⁻¹
• C₂H₂(g): ?
• C₂H₄(g): ?
Complete the tasks below.
(1) Write an algebraic expression for the enthalpy change of reaction (I) in terms of the unknown ΔH°ₓ(C₂H₂), the known ΔH°ₓ(C₂H₆), and any other relevant quantities.
(2) Repeat the procedure for reaction (II), expressing ΔH° in terms of the unknown ΔH°ₓ(C₂H₄) and known data.
(3) Solve simultaneously for the two unknown standard molar enthalpies of formation: ΔH°ₓ(C₂H₂) and ΔH°ₓ(C₂H₄). Show all algebraic steps and report each value to three significant figures.
(4) Compare the magnitudes of the two values you found and provide a chemical rationale, based on structural considerations, for any difference in stability indicated by the data.