Question

Explain why the first ionization energy of Ca is greater than that of \(\mathrm{K}\), whereas the second ionization energy of Ca is lower than the second ionization energy of \(\mathbf{K} .\)

Short answer

Ca has a higher first ionization energy due to less shielding; K's second ionization energy is higher because it disrupts a stable noble gas configuration.

Step-by-step solution

Understanding Ionization Energy

Ionization energy is the energy required to remove an electron from a neutral atom in its gaseous state. The first ionization energy refers to removing the first electron, while the second ionization energy refers to removing the second electron after the first has been removed.

Comparing First Ionization Energies of Ca and K

Calcium (Ca) and potassium (K) are both in period 4 of the periodic table. Potassium has an electronic configuration ending in 4s¹, while calcium ends in 4s². Since potassium's outer electron is in a higher energy orbital and experiences more shielding, it's easier to remove, resulting in a lower first ionization energy compared to calcium.

Analyzing the Removal of the Second Electron

For K, after the first electron is removed, the configuration becomes similar to that of argon (Ar), making the next electron removal involve breaking into a filled noble gas configuration. This requires significantly more energy. In contrast, the removal of the second electron from Ca means removing one from the 4s orbital, which is still energetically favorable compared to disrupting a noble gas configuration.

Conclusion

The lower first ionization energy of K compared to Ca is due to K's electron being easier to remove because of higher electron shielding and lesser effective nuclear charge. In the second ionization, K requires breaking into a noble gas core, whereas Ca does not, increasing K’s required energy drastically.

Key concepts

Periodic Table

The periodic table is more than just a list of elements; it's a structured map of the chemical elements, arranged by increasing atomic numbers. This arrangement highlights periodic trends and helps predict the properties of elements. For example, as you move from left to right across a period, elements generally have higher ionization energies.
Calcium (Ca) and Potassium (K) are located in the fourth period. While their chemical properties might appear similar due to their proximity in the table, significant differences arise due to their electronic configurations.

• Elements in the same period have the same number of electron shells, but different numbers of electrons in those shells.
• The behavior in electron removal, such as ionization energy, shifts because of these electronic configurations.

Understanding an element's placement within the periodic table helps us predict its reactivity and energy requirements for processes such as ionization.

Electron Configuration

Electron configuration is the distribution of electrons of an atom or molecule in atomic or molecular orbitals. The configuration helps us understand the energy level of each electron, and their interactions with other electrons.
For example, the electron configuration of Potassium (K) is \([Ar] \, 4s^1\), meaning it has one electron in the 4s orbital beyond the filled argon core. Calcium (Ca), on the other hand, has a configuration of \([Ar] \, 4s^2\), thus having two electrons in the 4s orbital.

• The outermost electrons, or valence electrons, are primarily involved in chemical reactions and determine the atom's chemical properties.
• Electrons in higher energy levels are further from the nucleus, experiencing less effective nuclear charge and more shielding by the inner electron shells.

These nuances in configuration between K and Ca account for their different ionization energies.

Atomic Structure

Atomic structure refers to the arrangement of protons, neutrons, and electrons within an atom. Central to this is the nucleus, comprised of protons and neutrons, with electrons orbiting in shells or energy levels. Each element exhibits a unique atomic structure that can strongly influence its chemical behavior.
The electron shell configuration defines the structure and dictates how electrons interact within an atom:

• Protons in the nucleus remain constant for a particular element, determining its identity and positive charge.
• Electrons are distributed in energy levels. The closer an electron is to the nucleus, the stronger the attractive force it feels and the harder it is to remove.

When we compare K and Ca, both having two well-filled energy levels before their differing valence electrons, these differences lead to their unique ionization energies as their atomic structure alters the electron's energy and position.

Noble Gas Configuration

Noble gas configuration refers to the electron configuration of an element that matches the nearest noble gas. Noble gases, found in Group 18 of the periodic table, are known for their stability and full valence electron shells, meaning they rarely engage in reactions.
In terms of ionization energy:

• When Potassium loses one electron, its configuration mirrors that of Argon (Ar), a noble gas. This stable configuration makes the energy required to remove another electron significantly high.
• Calcium, after losing one electron, does not attain a noble gas configuration until both 4s electrons are removed. Hence, the first ionization energy reflects the ease of creating a stable, noble-like configuration.

Understanding noble gas configurations provides insight into the stability of electron configurations and why certain atoms require more energy to remove additional electrons.