The standard enthalpy of formation of ethane ( C₂H₆(g) ) is -84 ~kJ mol⁻¹ . The enthalpy of sublimation of graphite is 716 ~kJ mol⁻¹ and the bond dissociation enthalpy of H₂(g) is 436 ~kJ mol⁻¹ . If the average C-H bond enthalpy is 412 ~kJ mol⁻¹ , the C-C bond enthalpy in ethane is __________ kJ mol⁻¹ .

Step-by-step solution

The enthalpy of atomization of ethane ( C₂H₆(g) ) corresponds to the reaction: C₂H₆(g) 2 C(g) + 6 H(g) The standard enthalpy of formation of gaseous carbon atoms is equal to the enthalpy of sublimation of graphite: _ f H ^ ( C(g) ) = 716 ~kJ mol⁻¹ The standard enthalpy of formation of gaseous hydrogen atoms is half the bond dissociation enthalpy of H₂(g) : _ f H ^ ( H(g) ) = 436 2 = 218 ~kJ mol⁻¹ Using Hess's Law, the enthalpy of atomization of ethane is: _ atom H = 2 _ f H ^ ( C(g) ) + 6 _ f H ^ ( H(g) ) - _ f H ^