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From previous studies, I recalled in my lecture theatre today that lattice energy was the energy released when an ionic compounds is formed from individual atoms in the gaseous state. I thought this idea would follow through throughout my studies at university.

However, my lecturer this afternoon defined lattice energy as the following:

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• For an ionic solid the lattice energy is defined as the energy required to completely separate a mole of solid ionic compound into its gaseous ions

I thought this was my definition but in the reverse order.

Which one of us is correct, the lecturer or myself?

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There is not necessarily a set convention: https://en.wikipedia.org/wiki/Lattice_energy#Lattice_energy_vs_lattice_enthalpy

However, the sign must match the convention used. For example, the values in the table you provided are all positive which implies you are adding energy to break the lattice.

The definition from you prior experience would require negative values.

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