3.5.1 Thermodynamics - Born-Haber cycles
Students should:
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Hess' law
Hess' law is the fundamental basis behind the calculation of all thermodynamic quantities. The principle can be applied to ionic systems by considering the different energy changes required to get from one situation to another.
When Hess' law is applied to the standard enthalpy of formation of an ionic lattice, the different stages form a cycle, called a Born-Haber Cycle.
Born-Haber Cycles
The enthalpy of formation of a compound is defined as the energy change when 1 mole of a compound is formed from its constituent elements in their states under standard conditions.
For an ionic compound it is the formation of 1 mole of an ionic lattice from its constituent elements in their standard states:
Na(s) + ½Cl2(g) 
NaCl(s) |
Notice the difference between the equation above and that of the lattice enthalpy, which forms the lattice from gaseous ions.
The Born-Haber cycle must begin with the elements in their standard states and arrive finally at the ions in position within 1 mole of a lattice. For this, several theoretical energy transformations must take place. These processes are best considered while referring to a specific example, in this case sodium chloride.
1 - The metal (sodium) must be turned into separate gaseous atoms - atomisation. This is an endothermic process as energy is required to overcome the metallic bonding forces. This is can also be referred to as vaporisation for elements that form atomic vapours (such as a metal)
Na(s) 2 - The non-metal must be turned into separate gaseous atoms - in the case of chlorine this means breaking half a mole of bonds to give one mole of atoms. It is one half the bond enthalpy of chlorine. This can also be referred to as atomisation. However, it is important to note the difference between the definitions of atomisation enthalpy (energy quoted per mole of atoms formed) and the bond dissociation enthalpy (energy quoted per mole of bonds broken = 2 moles of atoms formed).
½Cl2(g) 3 - The gaseous metal atoms must be ionised to form gaseous ions - this is the first ionisation energy of sodium. For atoms that have double charges there are two ionisations involved, the first ionisation energy and the second ionisation energy. You may be given the two values separately, or combined together.
Na(g) 4 - The chlorine atoms must be turned into ions. For a non-metal this involves adding an electron to the atom. This is an exothermic process called the electron affinity of chlorine. For negative ions with a double charge there are two electron affinities involved, the first electron affinity and the second electron affinity. The energies may be give to you separately, or combined into one value.
Cl(g) 5 - The gaseous ions can then be brought together into the lattice. This is the opposite of the lattice enthalpy and is exothermic. Remember that the lattice enthalpy is defined by the IBO as the energy required to break the lattice. In the Born Haber cycle the step is usually shown as forming the lattice. This should not be a problem providing you understand that breaking the lattice must be an endothermic process.
Na+(g) + Cl-(g)
Hess' law tells us that the sum of the energies of all of these steps must equal the enthalpy of formation, as it also takes us from the same starting point to the same conclusion. Born-Haber presents this idea in a graphical form, with the endothermic steps on the left and the exothermic steps on the right.
To use a Born-Haber cycle your starting point and your destination are given by the question's requirements. You simply add up all of the quantities along the alternative route, taking into account whether the energy change is negative or positive in the direction you are going.