Consider the following measured enthalpy changes at 298 K:
(1) 2 C2H6(g) → 2 C2H4(g) + 2 H2(g) ΔH° = +272 kJ
(2) C2H4(g) + 3 O2(g) → 2 CO2(g) + 2 H2O(l) ΔH° = –1411 kJ
(3) C2H6(g) + 3.5 O2(g) → 2 CO2(g) + 3 H2O(l) ΔH° = –1555 kJ
The enthalpy change for the hydrogenation reaction
C2H4(g) + H2(g) → C2H6(g) ΔH° = x kJ
is unknown.
(a) Using an appropriate algebraic combination of reactions (1)–(3), obtain a single equation whose net chemical change is the hydrogenation reaction given above. Show each manipulation (reversing and/or scaling) used.
(b) Derive, in symbolic form, an equation relating x to the numerical enthalpy values in reactions (1)–(3). Do not substitute numbers in this part.
(c) Solve for x numerically and report the value with units.
(d) Briefly comment on whether the sign and magnitude of x are consistent with the reaction type (addition of H2 to an alkene).