We interrogate 2 processes:
(i)(i) Li(g) + Delta_1 rarr Li^(+)(g) + e^(-)
(ii) Li^(+)(g) + Delta_2 rarr Li^(2+)(g) + e^(-)
Now just from an electrostatic point of view, we would anticipate that Delta_2>Delta_1 simply on the basis that it should be harder to remove an electron from a positively charged species, Li^(+), to make a dication, Li^(2+), than from the neutral metal atom to make a cation. Why? Because the electron is more tightly bound to a formal cation.
So, as physical scientists, let us put in some numbers:
This site reports that for lithium, Delta_1=520.2*kJ*mol^-1, and Delta_2=7298.1*kJ*mol^-1.
So in fact our facile expectation was correct. However, the substantial magnitude of Delta_2, which dwarfs Delta_1, also reflects the electronic stucuture of the lithium atom. The second ionization requires the removal of a 1s^2 electron, rather than than a 2s^1, which was the one first removed. Because this second electron is inner shell, its attraction to the nucleus should be quite substantial, and our data support this expectation.
