Lattice Energy: Part 1 Born-Haber Cycle
Video by Janet Gray Coonce, MS
In this video I will discuss lattice energy and how to use the Born-Haber cycle to calculate lattice energy from known enthalpies of certain reactions.
What is lattice energy? Lattice energy is the energy released when ions in the gaseous form are combined to form a solid ionic compound.
Na+ (g) + Cl– (g) —-> NaCl(s)
ΔH = –787 kJ/mol
In this symbolic expression, gaseous sodium ion and gaseous chloride ions combine to form a more stable solid sodium chloride. Whenever a reaction goes to a more stable compound, heat is released. The magnitude of the energy released is the lattice engergy expressed as a ΔH of NEGATIVE 787 kJ/mol. Since energy was lost, the ΔH is a negative number. This change in thermal energy, or change in enthalpy associated with the reaction is represented by the symbol ΔH. If the reaction were to be reversed, it would require adding heat to break the solid up into gaseous ions. That reaction would require a ΔH of POSITIVE 787 kJ/mol. So to summarize, if heat is lost, the change in enthalpy or ΔH is negative. Since heat is given off, it is an exothermic reaction. If heat is added, the change in enthalpy or ΔH is positive. When heat is used by the reaction, the reaction is an endothermic reaction. Lattice energy is released when gaseous ions come together to bond as a solid. It is an exothermic reaction. The change in enthalpy or ΔH is negative. The solid form must be heated in order to convert the solid back to the ionic gaseous form. Since heat is added, it is an endothermic reaction and the change in enthalpy or ΔH is positive.
How does the size of the anions and cations affect the magnitude of lattice energy? Smaller atoms are closer together and are held more strongly than larger atoms. Therefore the magnitude of the change in enthalpy is higher for the smaller molecules.
How does the size of the cation and anion affect the magnitude of the lattice energy? The smaller the atoms, the stronger the attraction (ionic bond) between them. So looking at the table, the absolute value of lattice energy is predictably larger for LiF (-1036) than for NaCl (-787) or at the bottom RbI (-630). The value of the lattice energy is negative or positive depending upon whether the ions are coming together as a solid compound and therefore negative or whether they are split into the gaseous ions in which case the value would be positive. The absolute value of the numeric magnitude is the same. Again, energy is required (positive lattice energy) to break a bond. Energy is released (negative lattice energy) when a bond is formed.
Repeating the definition: Lattice Energy is the energy released when gaseous ions combine to form a solid ionic compound.
We have discussed the inverse relationship between the size of the ions and the magnitude of lattice energy released when the ions form a bond. The charge also affects the lattice energy.
The higher the absolute value of the charge of the ion, the stronger the ionic bond. For example, the absolute value of the lattice energy released by the reaction of Al3+ + 3OH– ( | -5627|= 5627) is higher than when Na+ + OH– ( | -900|= 900) are combined. This is because the higher charge of the Al3+ cation when compared to the Na+ cation. The same is true for the charge of the anion. Look at the chart and compare the lattice energy of Na+ + OH– ( | -900|= 900) with Na+ + O2- ( | -2481|= 2481). The absolute value of the lattice energy released is larger associated with Na+ +O2- than with Na+ + OH– due the more negative charge of the O2– anion.
To restate this concept in other terms, the higher the absolute value of the valence of the ion ( |valence| ), the higher the lattice energy of the ionic compound. This means the compound is much more stable. It will take more energy to break the bond. The formation of the solid ionic compound from the gas is exothermic and more heat will be given off when compared to formation of compounds with ions of lower valence. Look at the chart and note the lattice energy when Al3+ + O2– are combined. This is a very exothermic reaction and the absolute value of lattice energy released is |-15916|. Since energy is released from the system it is expressed as a negative number. If heat were applied to the solid compound, 15916 kJ/mol would have to be added to break the ions back into their gaseous state. When energy is added, the reaction is endothermic and the lattice energy is expressed as a positive number. The absolute value (magnitude of energy change) is the same.
This diagram illustrates the change in lattice energy when gaseous form of the lithium cation and fluorine anion are combined to form lithium fluoride. The gaseous ions are at a higher energy state than the lithium fluoride solid compound. This difference in energy state results in heat being released with the formation of the solid compound. Since energy is release, it is an exothermic reaction. The magnitude of this change is the lattice energy.
To write this reaction symbolically:
Li+ (g) + F- (g) —————–> LiF (s) + 1036kJ/mol heat released
Looking at the known enthalpy chart, the lattice energy ( ΔH ) = –1036 kJ/mol
If the direction of the reaction were changed from solid to gaseous, then the reaction could be expressed:
Li+ (g) + F- (g) <—————– LiF (s) + 1036kJ/mol heat or
LiF (s) + 1036kJ/mol heat ————————> Li+ (g) + F- (g)
ΔH = 1036 kJ/mol
Sometimes its not so easy to directly calculate the lattice energy taking the gaseous ions that form that solid, so what we do is indirectly calculate the lattice energy using the Born-Haber cycle.
To use the Born-Haber Cycle, you have to understand a few terms.
1. Enthalpy of Sublimation:
Sublimation is when a solid is converted to a gas. When particles are released in the gaseous form from a solid substance the change in enthalpy or ΔH is going to be positive because energy will have to be added to break those bonds. In the case of elemental sodium illustrated above, the enthalpy of sublimation is 107 kJ/mol. That means that 107 kJ/mol of heat will have to be applied to the sodium metal to release the sodium as a gas. The change in enthalpy (heat required) is expressed symbolically as:
Na (s) + heat ———> Na (g)
ΔH = +107 kJ/mol
Values of the enthalpy of sublimation for known substances may be found in tables where the values have been calculated by physical chemists. For this lesson you need to know that these are calculated values, but we will look them up in a table. We will leave the “how to calculate” the values up to the physical chemists.
Another term you need to understand to use the Born-Haber Cycle to calculate lattice energy is:
2. Bond Dissociation Energy
Bond dissociation energy is the energy required to dissociate or break a bond between atoms. In the illustration above, using any of the halogens designated by the symbol X, there is a homolytic cleavage of the bond between X—X (gas) to release 2 atomic radicals of the halogen atom.
The bond dissociation energy to break a molecule of chlorine gas into 2 atoms of chlorine radicals can be expressed by the equation given in the example at the bottom of the diagram.
The same reaction can be expressed as a Lewis dot structure to illustrate what happens to the valence electrons. The bond dissociation energy for this reaction is expressed as:
ΔH = +243 kJ/mol The positive number indicates that energy is required before diatomic chlorine gas will dissociate into free radicals.
The 3rd term you will need to understand in order to use the Born-Haber Cycle to calculate lattice energy is the Ionization Energy, IE.
3. IE: Ionization Energy
The ionization energy is the energy required to remove an electron from a gaseous ion or atom. In this illustration the ionization energy required to convert Na gas to a Na+ ion by the removal of an electron is expressed by:
ΔH = +496 kJ/mol This is the amount of heat which would be required for this step.
The smaller the atom, the lower the amount of energy required to release an electron. More energy is required by atoms to the right of Na in the periodic table. More energy is also required for atoms below Na in the periodic table. Since Na is in group 1 and period 3, it is a relatively small atom and will have a lower ionization energy than elements in the other groups in period 3. It will also have a lower ionization energy than elements in periods below period 3.
Na is an alkali metal, a member of group I in the periodic table, and has only one electron in its outer shell which can be removed. What would we have to consider instead of Na, we chose Mg, an alkaline earth metal, a member of group II in the periodic table? Members of the alkaline earth metals have 2 electrons in their outer shell which can be removed. For these elements there are 2 ionization energies.
The ionization energy for the first electron, and the ionization energy to release the second electron. It will require more energy to remove the second electron than the first so the second ionization energy will be higher than the first ionization energy. So the first ionization energy is the amount of energy required to remove one electron from the outermost shell of an atom in its gaseous state.
The last consideration of terms you need to know before you can calculate lattice energy using the Born-Haber Cycle is Electron Affinity, EA.
4. EA: Electron Affinity
Electron affinity is the energy released when an electron is added to a neutral atom in its gaseous state to form an ion.
In the case of chlorine gas radicals (produced by dissociating the bonds of diatomic chlorine gas discussed above), adding an electron releases 349 kJ/mol. The fact that energy is release means that chlorine ion gas is more stable than the chlorine gas radical and the change in enthalpy is a negative number.
ΔH = -349 kJ/mol
Transcribed by James C. Gray MD FACOG
Janet Gray Coonce 