What is the difference between enthalpy of formation and bond enthalpy ?

Enthalpy of formation is the enthalpy change when a mole of a substance is formed from its elements in their standard states under standard conditions. For methane this would be #DeltaH# for :

#C_((s))+2H_(2(g))rarrCH_(4(g))#.

It is given the symbol #DeltaH_f#.

Bond enthalpy is quite different and is a measure of the strength of an individual bond.

You can work out how much energy is needed to break a mole of methane into gaseous carbon and hydrogen atoms:

#CH_(4(g))rarrC_((g))+4H_((g))#

This takes a different amount of energy for each bond since, as you break a bond, the chemical environment of those bonds left behind changes and the strength of a bond is affected by what else is around it.

In this case you can work out an average amount of energy to break each bond.

This comes to +1662 kJ and involves breaking 4 moles of C-H bonds. The average bond enthalpy is therefore +1662/4 = +415.5 kJ per mole of C-H bonds.

This means that many bond enthalpies are quoted as "mean" or "average" bond enthalpies as measured over a range of different chemical environments. These are what are quoted when you look them up in tables. In summary:

• Enthalpy of formation is a guide to how stable a substance is.
• Bond enthalpies are a measure of the strength of an individual bond and can be used in calculations to estimate #DeltaH#.