Question

The first and second ionization energies of \(\mathrm{K}\) are 419 and \(3052 \mathrm{~kJ} / \mathrm{mol}\), and those of \(\mathrm{Ca}\) are 590 and \(1145 \mathrm{~kJ} /\) mol, respectively. Compare their values and comment on the differences.

Short answer

Potassium has a higher second ionization energy due to breaking a stable shell, while calcium more easily removes the second electron.

Step-by-step solution

Understanding Ionization Energy

Ionization energy is the energy required to remove an electron from an atom in its gaseous state. It generally increases across a period and decreases down a group in the periodic table. The first ionization energy is for removing the first electron, and the second ionization energy is for removing the second electron.

Analyzing Potassium's Ionization Energies

For Potassium (K), the first ionization energy is 419 kJ/mol, and the second ionization energy is 3052 kJ/mol. The large increase between the first and second ionization energies indicates that removing the second electron is much more difficult, as it requires breaking into a new, more stable electron shell.

Analyzing Calcium's Ionization Energies

For Calcium (Ca), the first ionization energy is 590 kJ/mol, and the second ionization energy is 1145 kJ/mol. The increase from the first to the second ionization energy is present but not as dramatic as with K, showing it is less costly to remove the second electron due to its electronic configuration and relative stability of its ions.

Comparing the Values

When comparing K and Ca, the first ionization energy of K is lower than Ca, suggesting K loses its first electron more readily. The second ionization energy of Ca is much lower than that of K, indicating that Ca can lose the second electron more easily after the first one's removal. This reflects their atomic structures: K loses one electron to achieve a stable noble gas configuration, while Ca can lose up to two with less energy cost than K for the second.

Conclusion on Differences

The differences in ionization energies are due to their electronic structures. K has a high energy rise because the second electron removal requires penetrating a stable and complete inner shell. Ca, on the other hand, can achieve a stable noble gas-like configuration by losing two electrons, facilitating the second ionization somewhat.

Key concepts

Electron Configuration

Electron configuration defines the arrangement of electrons in an atom. Each electron occupies orbitals that have different energy levels. These orbitals are s, p, d, and f, which are further divided into sublevels depending on the principal quantum number. Electrons fill the lowest energy orbitals first, according to the Aufbau principle. Potassium (K), for instance, has the electron configuration of \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^1\]. This means it has one valence electron in the 4s orbital. Calcium (Ca), on the other hand, has a configuration \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2\], with two valence electrons in the 4s orbital.
Understanding electron configurations helps us predict how atoms interact, their bonding tendencies, and the energy required to remove an electron.

Noble Gas Configuration

Noble gas configuration is a shorthand electron configuration that simplifies the notation by using the previous noble gas. It highlights how atoms achieve stability by either filling or losing electrons to simplify to the noble gas next to them in the periodic table. For example, Potassium reaches the noble gas configuration of Argon (Ar) \[1s^2 2s^2 2p^6 3s^2 3p^6\] by losing one electron from its 4s orbital.
Calcium's path to a stable form is by losing two electrons to also mimic Argon's configuration. Once Ca loses its two 4s electrons, it achieves the Ar configuration. The stability of noble gas configurations explains why atoms tend to undergo certain chemical reactions. They strive for the reduced energy state seen in noble gases.

Periodic Table Trends

Periodic table trends provide us with a map of atomic properties. Understanding these trends helps explain why elements behave as they do in chemical reactions. One key trend is ionization energy, which generally increases across a period from left to right and decreases down a group.

• **Across a period**, elements have more protons and relatively constant shielding, which means higher ionization energy, since there's more pull on the electrons.
• **Down a group**, there's an increase in atomic size with more electron shells, which means outer electrons are farther from the nucleus and less tightly held.

For example, comparing K and Ca from the same period shows us that Ca has a higher first ionization energy due to its greater nuclear charge and smaller atomic radius compared to K. The trend ensures that analyzing these relationships is easier when predicting an element's reactivity and bonding capabilities.