Lattice energy is the energy change connected with forming an ionic solid from separated gaseous ions, and it helps explain why ionic compounds are often hard, brittle, and have high melting points. The Born-Haber cycle is a thermochemical method for finding lattice energy using measurable energy changes. It is based on Hess's law, which says the total enthalpy change depends only on the starting and ending states.
For a compound such as NaCl(s), the cycle connects sodium metal and chlorine gas to the final ionic crystal.
Understanding Chemistry: Lattice Energy and the Born-Haber Cycle
Inside a crystal, each ion attracts many nearby ions of the opposite charge and repels ions with the same charge. The ions arrange themselves so that attraction is strong overall while repulsion is kept lower. This repeating three dimensional arrangement is called a lattice.
The energy depends on every attraction and repulsion in the structure, not just on one pair of ions. Ions with greater charges pull on each other much more strongly. Smaller ions can get closer together, which strengthens the attraction.
This is why magnesium oxide has a much stronger lattice than sodium chloride. Magnesium and oxide ions carry charges of two, while sodium and chloride ions carry charges of one.
A useful detail is that textbooks use two sign conventions for lattice energy. One convention describes making the solid from gaseous ions. This value is negative because energy is released.
Another convention describes pulling the crystal apart into gaseous ions. This value is positive because energy must be supplied. The numerical size is the same, but the sign changes.
Students should always read the definition before using a value in a calculation. A missing sign can produce an answer that looks reasonable but is physically wrong.
The Born Haber cycle works because enthalpy is a state property. It does not matter whether sodium chloride forms directly from its elements or through several imagined stages. Each stage prepares particles for the next one.
The metal must first become separate gaseous atoms. An electron must be removed from each metal atom. Chlorine molecules must be split into atoms before an electron can join an atom.
Some stages need energy, while others release it. The final crystal forming step is usually too difficult to measure directly, so it is found from the known total and the other measured steps. This method turns a hard to measure process into an energy balance.
Lattice energy helps explain more than melting point. It affects whether an ionic solid dissolves in water. Water molecules can surround ions and release hydration energy.
Dissolving is more likely when this released energy can compete with the energy needed to separate the lattice. A strong lattice does not automatically mean that a compound cannot dissolve, since hydration matters too. In problems, draw the cycle clearly and label the physical state of every substance.
Pay close attention to elements that exist as molecules, such as chlorine gas, because splitting one molecule can provide two atoms. Check whether the question asks for lattice formation or lattice dissociation. Finally, use consistent energy units throughout the calculation, usually kilojoules per mole.
Key Facts
- Lattice energy for formation: Na+(g) + Cl-(g) -> NaCl(s), ΔH_latt is usually negative.
- Born-Haber cycle for NaCl: ΔH_f = ΔH_sub + IE1 + 1/2D(Cl2) + EA + ΔH_latt.
- Hess's law: ΔH_total = sum of ΔH_steps for any path between the same initial and final states.
- Ionization energy step: Na(g) -> Na+(g) + e-, IE1 is positive.
- Electron affinity step: Cl(g) + e- -> Cl-(g), EA is usually negative for halogens.
- Lattice energy magnitude increases as ionic charge increases and ionic radius decreases.
Vocabulary
- Lattice energy
- The enthalpy change when gaseous ions combine to form one mole of an ionic solid, or the energy needed to separate the solid into gaseous ions depending on convention.
- Born-Haber cycle
- A thermochemical cycle that uses several enthalpy changes to calculate the lattice energy of an ionic compound.
- Hess's law
- The principle that the total enthalpy change of a reaction is the same no matter how many steps are used.
- Ionization energy
- The energy required to remove an electron from a gaseous atom or ion.
- Electron affinity
- The enthalpy change when a gaseous atom gains an electron to form a negative ion.
Common Mistakes to Avoid
- Using the wrong sign for lattice energy. Formation of an ionic solid from gaseous ions is exothermic, so ΔH_latt is negative, while separating the solid into ions is positive.
- Forgetting the 1/2 factor for chlorine gas in NaCl formation. The reaction uses 1/2Cl2(g) to make one mole of Cl(g), not a full mole of Cl2(g).
- Mixing up atomization, ionization, and electron affinity steps. Each step changes a different species, so writing the correct chemical equation helps prevent using the wrong value.
- Assuming lattice energy depends only on ion size. Charge has a very strong effect, so MgO has a much larger lattice energy magnitude than NaCl even though both are ionic solids.
Practice Questions
- 1 For NaCl(s), use ΔH_f = -411 kJ/mol, ΔH_sub(Na) = 108 kJ/mol, IE1(Na) = 496 kJ/mol, 1/2D(Cl2) = 121 kJ/mol, and EA(Cl) = -349 kJ/mol. Calculate ΔH_latt for NaCl(s).
- 2 Compare two ionic compounds using charge and size: NaF and NaI. Which should have the larger magnitude lattice energy, and why?
- 3 A student says the Born-Haber cycle proves that NaCl forms in one physical step from Na(g) and Cl(g). Explain why this statement is incorrect and what the cycle actually represents.