12. The standard enthalpy of formation at 298 K for methane is -74.8 kJ mol–1. What
additional information is required to determine the average energy for C–H bond
formation?
a. The dissociation energy of H2
b. The enthalpy of sublimation of carbon
c. Latent heat of vaporization of methane
d. Both (a) and (b)
Answer: d. Both (a) and (b)
The standard enthalpy of formation of methane (ΔH_f° = -74.8 kJ/mol) represents the reaction C(s, graphite) + 2H₂(g) → CH₄(g). To find the average C-H bond energy, which is the enthalpy change for CH₄(g) → C(g) + 4H(g) divided by 4, additional data must convert elements from standard states to gaseous atoms.
Option Analysis
a. Dissociation energy of H₂: This provides the energy (typically 436 kJ/mol) to break 2H₂(g) → 4H(g), essential for forming four C-H bonds in methane.
b. Enthalpy of sublimation of carbon: This gives the energy (~720 kJ/mol) for C(s) → C(g), needed since carbon starts as solid graphite, not gas atoms.
c. Latent heat of vaporization of methane: This relates to CH₄(l) → CH₄(g), but methane is already gaseous in the formation reaction, so it’s irrelevant.
d. Both (a) and (b): Correct, as the cycle requires both: ΔH = ΔH_sub(C) + 2×D(H-H) – ΔH_f(CH₄) = 719.6 + 2(435.4) – (-74.8) = 1665.2 kJ/mol; average C-H = 416.3 kJ/mol.
Calculation Cycle
Using Hess’s law:
-
C(s) → C(g): +719.6 kJ/mol
-
2H₂(g) → 4H(g): +870.8 kJ/mol
-
Reverse formation: +74.8 kJ/mol
Total for atomization: 1665.2 kJ/mol for 4 bonds.
The standard enthalpy of formation of methane at 298 K (-74.8 kJ/mol) is key for determining C-H bond formation energy in CH₄. This CSIR NET-level concept requires specific thermodynamic data to link formation from elements to gaseous atom combination.
To compute the average C-H bond energy (~416 kJ/mol), use the atomization cycle: sublimation of carbon (C(s) → C(g)) and H₂ dissociation (2H₂ → 4H(g)) provide the endothermic steps offsetting the exothermic formation. Without both, the energy balance fails.
Key Requirements:
-
H₂ dissociation energy: Breaks H-H bonds for atomic H.
-
Carbon sublimation enthalpy: Converts solid C to gas atoms.
-
Irrelevant: Methane vaporization (gas phase already).
This approach exemplifies Hess’s law applications in bond enthalpy calculations for competitive exams.
