Answer
After the first ionization, Potassium is in a stable noble gas configuration. Thus, removing the second electron is much harder as it requires more energy to remove electrons when the ion is stable.
Work Step by Step
First ionization energy:
$1s^22s^22p^63s^23p^6$
Second ionization energy:
$1s^22s^22p^63s^23p^5$
After the first ionization, potassium is in a stable noble gas configuration. Thus, removing the second electron is much harder as it requires more energy to remove electrons when the ion is stable.
