# Resolving ambiguity around Lattice Enthalpy in Born-Haber Cycle

According to my textbook,

Lattice enthalpy is the enthalpy change that occurs when one mole of a solid ionic compound is separated into gaseous ions under standard conditions.$$^1$$

According to the same textbook, this is an endothermic process, which makes sense as a lattice is generally held together by strong ionic bonds and thus would require energy to separate the atoms. The following diagram is given for the born-haber cycle in the textbook:

The diagram supports the definition as the enthalpy of the individual gaseous atoms is greater than that of the lattice, i.e. the arrow moves up. However, as I was working through past papers by the International Baccalaureate, a question asked to draw the born-haber cycle for LiF.$$^2$$ This was the answer:

In this case, the arrow is pointing down for the lattice enthalpy. To me, this does not suite the definition of lattice enthalpy as separating a lattice into its ions would require energy and not release energy. Hence, should the arrow not be pointing upwards for $$\ce{LiF_{(s)}}$$ to $$\ce{Li^+_{(g)} + Cl^-_{(g)}}$$? Am I making a fundamental error, is the case for NaCl different to LiF or is the answer wrong?

Works Cited:

1. Pearson Baccalaureate: Higher Level Chemistry 2nd Edition. By Catrin Brown and Mike Ford
2. International Baccalaureate
• The downward pointing arrow means that energy is released when the crystalline solid is formed from the gas phase separated ions. So it is the negative of lattice enthalpy. The diagram is just a schematic showing the enthalpy balance in the B-H cycle. – Ed V Mar 16 at 22:53
• Ah, that makes sense, thank you. So, just to clarify, the arrow for the first image is for lattice enthalpy (endothermic) and therefore points upwards and the arrow for the second image is negative lattice enthalpy (exothermic) and therefore points downward? – Liam Mar 17 at 8:40
• Exactly correct! – Ed V Mar 17 at 12:28
• Cheers for the help! :-) – Liam Mar 17 at 12:31