The first ionisation potential of Na is 5.1 eV. The value of electron gain enthalpy of Na + will be :-10.2 eV+2.55 eV-2.55 eV-5.1 eV

The electron gain enthalpy of Na+ will be -5.1 eV.

Here's why:

The first ionization potential of an atom is the energy required to remove an electron from a neutral atom in its gaseous state. For Sodium (Na), this is given as 5.1 eV. This means it takes 5.1 eV of energy to remove an electron from a Na atom.

The electron gain enthalpy is the energy change when an electron is added to a neutral atom in its gaseous state to form a negative ion. In this case, we're looking at Na+.

Since Na+ is a positive ion, it means it has lost one electron (which is what the ionization potential tells us). So, to gain an electron (to become neutral Na again), it would require the same amount of energy but in the opposite direction.

Therefore, the electron gain enthalpy of Na+ is -5.1 eV. The negative sign indicates that energy is released when the electron is gained.