Enthalpy changes depend on the state of reactants and of products, not on the pathway between them.
Alternative pathways are often represented as thermodynamic cycles as seen above for sulfur. The Born-Haber cycle shows formation of an ionic solid by reaction of its elements by the set of reactions shown below.
The enthalpy changes for several of the reactions in the indirect pathway are known for a variety of metals and nonmetals.
The Born-Haber cycle can be used
The enthalpy change for direct reaction between substances is the same as
the enthalpy change for any set of reactions that sum to give the direct reaction.
the enthalpy change for any set of reactions that sum to give the direct reaction.
| The equations in the indirect pathway add to give the equation for the direct pathway as each proceeds from reactants to products of the direct pathway. Their enthalpy changes add to give the enthalpy change for the direct pathway. |
| Direct pathway: or Indirect pathway: | Direct pathway S(s) + 3/2 O2(g)  SO3(g)  SO2(g)  Indirect pathway |
Alternative pathways are often represented as thermodynamic cycles as seen above for sulfur. The Born-Haber cycle shows formation of an ionic solid by reaction of its elements by the set of reactions shown below.
 metal | + | nonmetal  | indirect pathway | |||||
| metallic bond breaking |  | | covalent bond breaking | |||||
 gas phase atoms  | ||||||||
| electron loss | | | electron gain | |||||
 gas phase ions  | ||||||||
| form lattice | | |||||||
| ||||||||
| M(s) | + | ½X2(g) | direct pathway | |
| | | |||
| M(g) | + | X(g) | ||
| –e– | +e– | |||
| M+(g) | + | X–(g) | ||
| | ||||
 | ||||
The enthalpy changes for several of the reactions in the indirect pathway are known for a variety of metals and nonmetals.
If known enthalpy changes are for reactions that proceed toward the products of the direct pathway, they can be simply added. The sign of any enthalpy change that proceeds toward reactants of the direct pathway must reversed.
The Born-Haber cycle can be used
to determine the magnitude of enthalpy changes that are difficult to measure directly
to give insight into the driving force for formation of an ionic solid.
such as MX(s) M+(g) + X–(g)
M+(g) + X–(g) to give insight into the driving force for formation of an ionic solid.
Is it electron transfer?? Is it formation of the lattice??