Problem 12 - Chemistry The Central Science

Question

(a) Write the electron configuration for the element titanium, Ti. How many valence electrons does this atom possess? (b) Hafnium, Hf, is also found in group 4 \(\mathrm{B}\) . Write the electron configuration for Hf. (c) Ti and Hf behave as though they possess the same number of valence electrons. Which of the subshells in the electron configuration of \(\mathrm{Hf}\) behave as valence orbitals? Which behave as core orbitals?

Step-by-Step Solution

Answer

The electron configuration of Titanium (Ti) is 1s²2s²2p⁶3s²3p⁶4s²3d², and it has 4 valence electrons (located in 4s²3d² orbitals). Hafnium (Hf) has the electron configuration 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶5s²4d¹⁰5p⁶6s²4f¹⁴5d², and also has 4 valence electrons (located in 5d²6s² orbitals). Both Ti and Hf have the same number of valence electrons, which are found in their respective outermost orbitals. The valence orbitals for Hf are 5d and 6s, while all other orbitals are considered core orbitals.

Step 1: Determine the electron configuration of Titanium (Ti)

To find the electron configuration of Titanium (Ti), we first look at its atomic number which is 22. This means that Ti has 22 electrons. We will fill the orbitals following the Aufbau principle, Hund's rule, and the Pauli exclusion principle. The electron configuration of Ti is given by the arrangement: 1s²2s²2p⁶3s²3p⁶4s²3d²

Step 2: Determine the number of valence electrons for Titanium (Ti)

Valence electrons are the electrons found in the outermost energy level of an atom. In the case of Ti, the outermost energy level is the 4th energy level. Therefore, Ti's valence electrons are present in the 4s and 3d orbitals. There are 2 electrons in the 4s orbital and 2 electrons in the 3d orbital, so Ti has a total of 4 valence electrons.

Step 3: Determine the electron configuration of Hafnium (Hf)

To find the electron configuration of Hafnium (Hf), we need to look at its atomic number, which is 72. This means that Hf has 72 electrons. We will fill the orbitals following the same rules as for Ti. The electron configuration of Hf is as follows: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶5s²4d¹⁰5p⁶6s²4f¹⁴5d²

Step 4: Compare the valence electrons of Titanium (Ti) and Hafnium (Hf)

Observing the electron configuration of Hf, we can see that the valence electron levels are the 5d and 6s orbitals. There are 2 electrons in the 5d orbital and 2 electrons in the 6s orbital, so Hf also has a total of 4 valence electrons, just like Ti.

Step 5: Identify the valence and core orbitals of Hafnium (Hf)

In Hf's electron configuration, the valence orbitals are those that are the outermost and contain valence electrons, which are the 5d and 6s orbitals. All other orbitals in Hf's electron configuration are considered core orbitals as they contain the core electrons. These are the orbitals: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶5s²4d¹⁰5p⁶4f¹⁴.

Key Concepts

Valence Electrons

Valence electrons are crucial to understanding the behavior of atoms in chemical reactions. They are the electrons present in the outermost shell of an atom.

• They directly influence an element's chemical properties.
• These electrons partake in forming chemical bonds.

For example, when considering titanium (Ti), it has an atomic number of 22. This means it has 22 electrons. According to its electron configuration, which follows the Aufbau principle and other quantum mechanics rules, the outermost electrons are found in the 3d and 4s orbitals.
This makes a total of 4 valence electrons for titanium. Similarly, other elements have their own numbers of valence electrons depending on their electron configurations.

Ti Electron Configuration

Titanium, with the atomic number 22, follows a specific order in filling its electron orbitals. To determine its electron configuration, we begin by placing electrons in orbitals according to the Aufbau principle, Hund's rule, and the Pauli exclusion principle.

• The electrons fill in the order of increasing energy levels.
• Lower energy orbitals fill before higher energy orbitals.

The electron configuration for titanium is:\[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^2\]This tells us that the electrons fill the 1s, 2s, 2p, 3s, 3p, 4s, and finally 3d orbitals.The last filled orbitals, which are 4s and 3d, make up the valence electrons. The electron configuration helps to understand titanium's reactivity and place in the periodic table.

Hf Electron Configuration

Hafnium, with an atomic number of 72, has a more complex electron configuration due to a greater number of electrons. Filling these electrons also adheres to the same quantum rules:

• The Pauli exclusion principle, Hund's rule, and the Aufbau principle are critical.

The electron configuration for hafnium is:\[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6 6s^2 4f^{14} 5d^2\]Here, the electrons are distributed across many orbitals, but the outermost electrons that act as valence electrons are in the 5d and 6s orbitals.In the case of hafnium, these outer electrons, like in titanium, determine the element's chemical behavior. Despite having a complex configuration, both Ti and Hf have the same number of valence electrons due to their group placement, explaining their similar properties.