Question

1. the first ionization energy for potassium, k, is 419 kj/mol and the second ionization energy for calcium, ca, is 1145 kj/mol. using concepts from this unit explain why they are different even though they are isoelectronic (have the same number of electrons).

k$_{(g)}$ → k$^{+}_{(g)}$ + e$^-$
ca$^{+}_{(g)}$ → ca$^{2+}_{(g)}$ + e$^-$

Explanation:

1. Ionization Process & Species:

• \( \text{K}_{(g)}

ightarrow \text{K}^+_{(g)} + e^- \): First ionization of K (removes 1 electron from neutral K).

• \( \text{Ca}^+_{(g)}

ightarrow \text{Ca}^{2+}_{(g)} + e^- \): Second ionization of Ca (removes 1 electron from \( \text{Ca}^+ \)).

1. Nuclear Charge & Electron Configuration:

• \( \text{K}^+ \) and \( \text{Ca}^{2+} \) are isoelectronic (same electron count, e.g., [Ar] noble gas configuration).
• Nuclear Charge: \( \text{Ca}^{2+} \) has \( Z = 20 \), \( \text{K}^+ \) has \( Z = 19 \). Higher \( Z \) in \( \text{Ca}^{2+} \) means stronger attraction between nucleus and valence electrons.

1. Energy Requirement:

• Removing an electron from \( \text{Ca}^+ \) (to form \( \text{Ca}^{2+} \)) requires overcoming a stronger nuclear pull than removing an electron from neutral \( \text{K} \) (to form \( \text{K}^+ \)). Thus, \( \text{Ca} \)’s second ionization energy (1145 kJ/mol) is much higher than \( \text{K} \)’s first ionization energy (419 kJ/mol).

Answer:

The first ionization of \( \boldsymbol{\text{K}} \) removes an electron from a neutral atom (\( \text{K}
ightarrow \text{K}^+ + e^- \)), while the second ionization of \( \boldsymbol{\text{Ca}} \) removes an electron from \( \text{Ca}^+ \) (to form \( \text{Ca}^{2+} \)). Although \( \text{K}^+ \) and \( \text{Ca}^{2+} \) are isoelectronic, \( \text{Ca}^{2+} \) has a higher nuclear charge (\( Z = 20 \) vs. \( Z = 19 \) for \( \text{K}^+ \)). This stronger nuclear attraction in \( \text{Ca}^{2+} \) makes it harder to remove an electron, so \( \text{Ca} \)’s second ionization energy (1145 kJ/mol) is much larger than \( \text{K} \)’s first ionization energy (419 kJ/mol).