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I know that when making a bond the reaction is exothermic (positive) and breaking a bond the reaction is endothermic (negative).

Lattice enthalpy or lattice formation enthalpy is defined as the enthalpy of formation of 1 mole of an ionic compound from gaseous ions under standard conditions, which is endothermic (negative).

My question is .. Why lattice formation is negative? It should be positive when making the ionic lattice because we are releasing energy.

Is bond making/breaking different than lattice making/breaking?

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You have to consider the system. If energy is being added to the system the sign is positive, if energy leaves the system the sign is negative.

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In an endothermic process, energy enters into the system; in an exothermic process, energy leaves the system. You wrote that exothermic means a positive $\ce{\Delta H}$. I don't know if that was a mistake on your part, or if it was a result of your textbook having a different sign convention (do you have an older textbook?).

The formation of 1 mole of an ionic solid from the gaseous ions of its components is always an energy releasing process. When something is imagined to be in the ideal gas phase, it is another way of saying that there are no inter-molecular attractions between the particles. When the gaseous ions become a solid, all of the positive and negative charges interact and form a much more stable compound, thereby releasing potential energy. (Like you said, bonds release energy). Thus, this process is an exothermic reaction by the above definition, releasing energy, and $\ce{\Delta H}$ is always negative.

I think the important thing is for you to first visualize processes in terms of energy entering/leaving the system. Then, try to figure out the signs. This way you won't get confused when some textbooks use a different sign convention (if that is the case with yours), or if different sources define lattice energy (The other definition is the energy needed to break an ionic compound into the gaseous ions, which would be endothermic).

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