Question

The following numbers are the ratios of second ionization energy to first ionization energy: Na: \(\quad 9.2\) P: \(1.8\) Mg: \(\quad 2.0\) \(\mathrm{S}: \quad 2.3\) Al: \(\quad 3.1\) \(\mathrm{Cl}: \quad 1.8\) Si: \(\quad 2.0\) Ar: \(1.8\) Explain these relative numbers.

Short answer

In short, the given ratios of second ionization energy to first ionization energy for the elements (Na, P, Mg, S, Al, Cl, Si, and Ar) can be explained by their electron configurations and the factors affecting ionization energies, which are distance from the nucleus, effective nuclear charge, and electron shielding. The large ratio for Na is due to breaking a stable noble gas configuration, while the smaller ratios for P, Mg, S, Al, Cl, and Si are because their second ionization energies involve removing an electron from a subshell with similar energy. The ratio for Ar is smaller as both first and second ionization energies involve breaking stable configurations, and the first ionization energy is already significantly high.

Step-by-step solution

Recall Ionization Energy and Factors

Ionization energy is the amount of energy required to remove an electron from a gaseous atom. There are mainly three key factors that affect ionization energies: 1. Distance of electrons from the nucleus 2. Effective nuclear charge 3. Electron shielding By considering these factors, we can analyze each element's electron configuration to explain these numbers.

Analyze Electron Configurations

Each element's electron configuration affects its ionization energies: 1. Na (Sodium): [Ne]3s^1 2. P (Phosphorus): [Ne]3s^23p^3 3. Mg (Magnesium): [Ne]3s^2 4. S (Sulfur): [Ne]3s^23p^4 5. Al (Aluminum): [Ne]3s^23p^1 6. Cl (Chlorine): [Ne]3s^23p^5 7. Si (Silicon): [Ne]3s^23p^2 8. Ar (Argon): [Ne]3s^23p^6

Explain Equations

Now, let's attempt to explain the given ratios: 1. Na: The first ionization energy of Na corresponds to removing its only 3s electron, while the second ionization energy involves breaking a much more stable [Ne] noble gas configuration. Hence, the second ionization energy is considerably higher than the first, resulting in a large ratio of 9.2. 2-7. P, Mg, S, Al, Cl, and Si: In all these cases, the second ionization energy involves removing an electron from either the same subshell (3s or 3p) or another subshell with similar energy (3s to 3p or vice versa). Thus, while there is a difference in the energies, the difference is not as large as in the case of Na. The ratios range from 1.8 to 3.1. 8. Ar: The first ionization energy corresponds to removing an electron from a full 3p subshell, while the second ionization corresponds to breaking a stable [Ne] noble gas configuration. Moreover, the loss of another electron would make the atom more positively charged, thus making it even more difficult to remove an electron in the second ionization. However, the first ionization energy is significantly high, as the stable noble gas configuration of Ar is hard to break. As a result, the second ionization energy is not too much greater than the first one, resulting in a ratio of 1.8.

Conclusion

In conclusion, the relative numbers of the second ionization energy to first ionization energy for each element are explained by their electron configurations and the factors affecting ionization energies: distance from the nucleus, effective nuclear charge, and electron shielding.

Key concepts

Electron Configuration

The concept of electron configuration is fundamental to understanding the properties of elements, including their ionization energies. Every element has a unique arrangement of electrons around its nucleus, which determines the electron configuration. This arrangement can be thought of as electrons filling up shells and subshells in a specific order. The sequence follows the increasing energy levels where the lowest energy levels are filled first.

• Sodium (Na): [Ne]3s¹
• Phosphorus (P): [Ne]3s²3p³
• Magnesium (Mg): [Ne]3s²
• Sulfur (S): [Ne]3s²3p⁴
• Aluminum (Al): [Ne]3s²3p¹
• Chlorine (Cl): [Ne]3s²3p⁵
• Silicon (Si): [Ne]3s²3p²
• Argon (Ar): [Ne]3s²3p⁶

Understanding these configurations helps explain why ionization energies vary. Removing an electron from a configuration significantly alters its stability, affecting how much energy is needed.

Noble Gas Configuration

Noble gas configuration is a term used to describe the highly stable electron arrangement seen in noble gases, which are known for their lack of reactivity.
Often, elements strive to achieve a similar configuration in reactions, as it is energetically favorable. In the original problem, both Sodium and Argon delineate significant differences in ionization energies due to their respective approaches to noble gas configurations.

• Sodium (Na) tries to achieve the [Ne] configuration by losing its 3s electron.
• Argon (Ar) already possesses the [Ne]3s²3p⁶ configuration, which is highly stable and resistant to losing electrons.

Thus, breaking into or achieving noble gas configurations is a major determinant of ionization energy. Elements closer to a filled configuration, like Argon, resist losing additional electrons, while those needing one less to reach stability, like Sodium, require relatively less energy to remove the outer electron.

Effective Nuclear Charge

Effective nuclear charge (Z_{eff}) is the net positive charge experienced by electrons in an atom. It takes into account not only the actual nuclear charge (Z), or the number of protons in the nucleus, but also the shielding effect from other electrons.
The formula to calculate the effective nuclear charge is:\[ Z_{eff} = Z - S \]where \( S \) is the shielding constant. This charge influences electron attraction and ionization energy.

• Higher Z_{eff} means electrons are held more tightly, resulting in higher ionization energy.
• Lower Z_{eff} shows electrons are less tightly held, leading to lower ionization energy.

This principle is evident in the given elements like Magnesium and Phosphorus, where variations in electron configurations result in different Z_{eff} values influencing their ionization energy ratios. As electrons are removed, especially from the same shell or subshell, the existing electrons become more strongly held due to a relatively constant shielding and reduced electron-electron repulsions.

Electron Shielding

Electron shielding refers to the phenomenon where inner shell electrons partially block the attraction between the nucleus and outer shell electrons. This effect is crucial in determining the ionization energy of an atom.

• Shielding reduces the effective nuclear charge felt by outer electrons which results in them being more easily removed.
• As the number of inner electrons increases, the shielding effect becomes stronger.

In the context of ionization energy, Sodium, with its configuration of [Ne]3s¹, experiences significant shielding from its inner electrons. Hence, its first ionization energy is quite low because the 3s electron is relatively easy to remove. However, once removed, the next electron is much more difficult to detach because it is from a filled shell with minimal shielding. This results in a stark increase in the ionization energy ratio seen in the problem.