Help! Can somebody explain the answer and how they got it? "Write the equation for the first ionization of potassium."

K°(g)* + 419 Kj/mole => K⁺(g) + e⁻

Explanation:

1st ionization step for potassium is the ionization of the 4s¹ electron. This requires 419 Kj/mole energy (endothermic). The reaction equation is ...

K°(g)* + 419 Kj/mole => K⁺(g) + e⁻

*note: Ionization of group IA metals requires they be in gas phase. That is, as shown by the Born-Haber Cycle** for formation of ionic compounds ...

K°(s) + 89.24 Kj/mole => K°(g); then ...

K°(g) + 419 Kj/mole => K⁺(g).

**Recommend review of Born-Haber cycle for formation of ionic compounds.