Why the 2nd ionization energy of an O atom is positive , it should be less negative but not because if an O atom gain two electron it attains stability /
The second ionization enthalpy of oxygen is positive it is can be explained as when we remove one electron from the outermost shell of the O atom ( 1st ionization energy ) it becomes cation of oxygen and after that the size decreases and hence as the size decreases the attraction between the outer most electron and the nucleus increases and hence we required more amount of energy to remove another electron ( 2nd ionization enthalpy ). Hence second ionization enthalpy is more positive.
On the other hand addition of second electron is opposed by electrostatic repulsion and hence the energy has to be supplied for the addition of second electron. Thus the second electron gain enthalpy of an element is positive.