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For what electron gain enthalpy is the most negative?

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Answer
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Hint: Electron gain enthalpy is the energy released when an isolated gaseous atom gains an electron that completes its octet. As the energy is released it is an exothermic process whose energy has a negative value. So more negative value, higher is the electron gain enthalpy. It is more in the case of non – metals.

Complete answer:
Electron gain enthalpy also called electron affinity is the energy released when a neutral isolated gaseous atom accepts an electron to achieve its fully filled electronic configuration. As we know when energy is released in any reaction, the enthalpy change is negative due to the exothermic reaction. So, when an electron is being added to an isolated gaseous atom, then there is an energy release that makes the atom an anion. The reaction may be:
$Cl+1{{e}^{-}}\to C{{l}^{-}};\,-\Delta $
As we move from left to right in a period there is an electron added in the sub shells, so electron gain enthalpy increases, because the tendency to accept an electron in order to achieve noble gas configuration increases.
Due to this reason, the elements of group 17, that is the halogens that only require 1 electron to achieve noble gas configuration, have the highest electron gain enthalpy, or the most negative electron gain enthalpy.
So, for the halogen electron gain enthalpy is the most negative as it increases from left to right in a period.

Note:
Group 17 halogens have most negative electron affinity while group 18 noble gases have a positive electron gain enthalpy as they have completely filled electronic configuration. Also the 2nd electron gain enthalpy is positive as an electron is added to the anion, which experiences a repulsion that causes the 2nd electron gain enthalpy to be endothermic and positive.