Question

Titanium metal and \(\mathrm{Cr}^{2+}\) have the same number of electrons. However, the electron configuration of Ti is \([\mathrm{Ar}] 4 s^{2} 3 d^{2},\) but that of \(\mathrm{Cr}^{2+}\) is \([\mathrm{Ar}] 3 d^{4} .\) Explain.

Short answer

Ti and \(\text{Cr}^{2+}\) have the same number of electrons, but fill orbitals differently due to stability preferences.

Step-by-step solution

Determine the Atomic Number of Titanium and Chromium

Titanium (Ti) has an atomic number of 22, which means it has 22 electrons. Chromium (Cr) has an atomic number of 24, indicating it has 24 electrons initially.

Electron Configuration of Neutral Titanium (Ti)

The electron configuration of neutral Titanium is \([ ext{Ar}] 4s^2 3d^2\). It means after reaching the Argon state, Titanium fills the 4s orbital with 2 electrons and then begins filling the 3d orbital with 2 electrons.

Electron Configuration of Neutral Chromium

The electron configuration for neutral Chromium should follow the order to fill the \(4s\) and \(3d\) subshells. However, to get extra stability from a half-filled \(d\) subshell, its configuration is \([ ext{Ar}] 4s^1 3d^5\).

Electron Configuration of Chromium Ion (Cr²⁺)

Cr²⁺ means Chromium loses 2 electrons, typically from the outermost energy levels. From \([ ext{Ar}] 4s^1 3d^5\), it loses 2 electrons from the \(4s\) and one from the \(3d\), resulting in \([ ext{Ar}] 3d^4\).

Compare Number of Electrons in Both Configurations

When you count the number of electrons in the electron configuration of Titanium (22 electrons) and Chromium ion \(Cr^{2+}\) (22 electrons), they match, even though electron filling patterns are slightly different due to, order based on stability and energy requirement.

Explanation of Discrepancy

The discrepancy arises because the stability gained by Chromium with a specific electron configuration that involves half-filled \(d\) orbitals is energetically preferred, resulting in a different pattern of filling compared to Titanium.

Conclusion

Titanium and \( ext{Cr}^{2+}\) have the same number of electrons, but \( ext{Cr}^{2+}\) prefers a different, energetically favorable electron configuration, leading to the observed difference.

Key concepts

Atomic Number

The concept of an atomic number is fundamental in chemistry. It refers to the number of protons present in the nucleus of an atom. Each element in the periodic table has a unique atomic number, which defines the element's identity.

• The atomic number of Titanium (Ti) is 22, meaning it has 22 protons and, in its neutral state, it also has 22 electrons.
• Chromium (Cr), on the other hand, has an atomic number of 24, signifying it has 24 protons and, in its uncharged form, 24 electrons.
• When an atom forms an ion, it can gain or lose electrons to achieve a more stable electronic configuration, but the number of protons (atomic number) remains unchanged.

In the case of \( ext{Cr}^{2+}\), chromium has lost two electrons, balancing its electron count with that of neutral titanium, resulting in both species having 22 electrons. Understanding atomic numbers helps comprehend why elements behave the way they do in chemical reactions and bond formations.

Electron Stability

Electron stability is a key factor that determines how electrons are arranged in an atom's orbitals. Atoms and ions tend to arrange their electrons in a way that achieves stable configurations, often through full or half-filled orbitals.

• Chromium is a good example where electron stability dictates its electron configuration. Instead of following the expected order, Chromium fills its orbitals as \([ ext{Ar}] 4s^{1} 3d^{5}\), opting for a half-filled \(3d\) subshell, which provides increased stability.
• When electrons are arranged in this manner, the system gains extra stabilization through lower energy states. As a result, electrons may occupy orbitals in a way that seems unexpected when only considering the Aufbau principle, which states that electrons fill orbitals from lowest to highest energy.
• This concept explains why chromium ions are stable with the configuration \([ ext{Ar}] 3d^{4}\) after losing two electrons compared to titanium, despite both having an equal number of electrons.

Therefore, electron stability can lead to deviations from typical orbital filling orders, all in the pursuit of more energetically favorable atomic arrangements.

Electron Orbitals

Electron orbitals are regions around an atom's nucleus where electrons are most likely to be found. These orbitals have distinct shapes and energy levels based on quantum mechanical principles. Understanding orbitals is essential to grasp why atoms exhibit specific electron configurations.

• There are different types of orbitals including \(s, p, d, \) and \(f\) orbitals. Each type can hold a set number of electrons (for instance, \(s\) holds 2, \(p\) holds 6, and \(d\) holds 10).
• The arrangement of electrons within these orbitals defines the electron configuration of an element or ion.
• In the case of titanium, the configuration \([ ext{Ar}] 4s^{2} 3d^{2}\) indicates that after the \(4s\) orbital is filled with 2 electrons, the next electrons occupy the \(3d\) orbital.
• For the \( ext{Cr}^{2+}\) ion, with a configuration of \([ ext{Ar}] 3d^{4}\), the \(4s\) electrons are removed first upon ionization, leaving electrons organized as such to maintain remaining electron stability.

Electron orbitals play a crucial role in chemistry as they define how atoms bond, interact, and form compounds based on these electron arrangements.