Introduction:
Electron affinity and electron gain enthalpy are two related concepts in chemistry that describe the energy change that occurs when an atom gains an electron. While they are related, they have opposite signs. This can be explained by considering the underlying principles of atomic structure and energy.

Understanding Electron Affinity:
Electron affinity is defined as the energy change when an atom in the gaseous state gains an electron to form a negatively charged ion. It is a measure of the attraction between the incoming electron and the nucleus of the atom. Electron affinity is typically expressed as a negative value, indicating that energy is released during the process.

Understanding Electron Gain Enthalpy:
Electron gain enthalpy is defined as the enthalpy change when an atom in the gaseous state gains an electron to form a negatively charged ion. It is a thermodynamic property that takes into account both the energy change and the volume change associated with the process. Electron gain enthalpy can be either positive or negative, depending on whether energy is released or absorbed during the process.

The Difference in Sign:
The main reason for the opposite signs of electron affinity and electron gain enthalpy lies in the different reference states used to calculate them.

Electron Affinity:
- Electron affinity is measured relative to a neutral gaseous atom.
- The energy released when an atom gains an electron is considered negative because the process is exothermic.
- The neutral atom is in its ground state, and the energy released is due to the increased stability of the resulting negatively charged ion.

Electron Gain Enthalpy:
- Electron gain enthalpy is measured relative to a positively charged ion.
- The energy change when an atom gains an electron is considered positive if energy is absorbed during the process, as indicated by an endothermic reaction.
- The positively charged ion is in an excited state, and the energy absorbed is used to stabilize the ion and bring it back to its ground state.

Conclusion:
In conclusion, electron affinity and electron gain enthalpy have opposite signs due to the different reference states used in their calculations. Electron affinity measures the energy released when a neutral atom gains an electron, while electron gain enthalpy measures the energy change when a positively charged ion gains an electron. Understanding these concepts helps in interpreting and predicting the behavior of atoms and ions in various chemical reactions.

Sign Convention For Electron Gain Enthalpy:Negative:When energy is released while accepting an electron.Positive: When energy is supplied to an atom while adding an electron.Electron affinity means love for electron.It is the negative of the electron gain enthalpy.By using the concepts of thermodynamics, we find a relationship between electron gain enthalpy and electron affinity i.e.electron gain enthalpy = electron affinity – 5/2  RTwhere R= universal gas constantT= temperature in Kelvin scalee..?