What is "electron-gain" enthalpy?

Electron gain enthalpy is simply another term used for electron affinity, which represents the change in enthalpy when one mole of electrons in added to one mole of atoms in the gaseous state.

This will result in the formation of one mole of anions in the gaseous state

#color(blue)(X_((g)) + "e"^(-) -> "X"_((g))^(-) + "energy")#

However, an important difference exists between the two terms. Electron gain enthalpy represents the heat given off by the ionization reaction, which means that it will carry a negative sign.

On the other hand, electron affinity is viewed as the heat absorbed by the surroundings, and will thus carry a positive sign.

Simply put, you can say that

#overbrace("electron gain enthalpy")^(color(red)("carries a negative sign")) = - overbrace("electron affinity")^(color(green)("carries a positive sign"))#

So, let's say that you have something like this

#Cl_((g)) + "e"^(-) -> Cl_((g))^(-) + "349 kJ/mol"#

Now, here's what you've got here. Since energy is being released by this reaction, i.e. it's being listed as a product, you can say that chlorine's electron gain enthalpy will be negative

#E_"ge" = -"349 kJ/mol"#

At the same time, the fact that heat is being released by the reaction implies that heat is being absorbed by the surroundings. This means that chlorine's electron affinity will be positive

#E_"a" = +"349 kJ/mol"#

This is why electron affinity values are always listed without a negative sign.