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 Hf behave as valence orbitals? Which behave as core orbitals?

Step-by-Step Solution

Answer

The electron configuration of titanium (Ti) is \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^2\), and it has 2 valence electrons. For hafnium (Hf), the electron configuration is \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^10 4p^6 5s^2 4d^10 5p^6 6s^2 4f^14 5d^2 \). The valence orbitals for Hf are \(6s^2, 5d^2\) and the rest are core orbitals.

Step 1: (a) Electron configuration for titanium (Ti)

To find the electron configuration for titanium (Ti), which has an atomic number of 22, we will follow the Aufbau principle and fill the orbitals in the increasing order of energy levels. Here's the electron configuration for Ti: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^2\) Now, let's find out the number of valence electrons.

Step 2: Valence electrons for titanium (Ti)

In the electron configuration above, the highest principal quantum number (n) is 4. Thus, the electrons in the 4s orbital are the valence electrons. Titanium has 2 valence electrons.

Step 3: (b) Electron configuration for hafnium (Hf)

Hafnium (Hf) has an atomic number of 72. To determine its electron configuration, we'll follow the Aufbau principle again and fill the orbitals in increasing order of energy levels. The electron configuration for hafnium is: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^10 4p^6 5s^2 4d^10 5p^6 6s^2 4f^14 5d^2 \)

Step 4: (c) Valence and core orbitals for hafnium (Hf)

Valence orbitals are the orbitals containing the outermost electrons of an atom. Thus, for Hf, the valence orbitals are the ones with the highest principal quantum number, which is 6 (6s^2) and also the partially filled 5d subshell (5d^2). The rest of the orbitals are core orbitals, as they contain the inner core electrons: Valence orbitals: \(6s^2, 5d^2\) Core orbitals: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^10 4p^6 5s^2 4d^10 5p^6 4f^14 \)

Key Concepts

Valence Electrons

Valence electrons are the electrons located in the outermost shell of an atom. These electrons play a crucial role in chemical bonding and determine how an element interacts with others.
Understanding the distribution of these electrons helps predict the chemical properties and reactivity of an element.

• Valence electrons are found in the highest principal quantum number (n).
• They are involved in forming bonds with other atoms.
• The number of valence electrons governs the electrical conductivity and other properties of materials.

For example, in titanium (Ti), the electron configuration shows that the 4s orbital holds two electrons, making them the valence electrons. This is because they reside in the outermost energy level. Similarly, hafnium (Hf) also shows valence characteristics in its 6s and partially filled 5d orbitals, which define its chemical behavior.

Aufbau Principle

The Aufbau principle is a fundamental concept used to determine the electron configuration of an atom. It describes how electrons fill the atomic orbitals based on their increasing energy levels.
This principle allows us to predict the arrangement of electrons in an atom.

• "Aufbau" is a German word meaning "building up".
• Electrons are placed into orbitals starting from the lowest energy level, moving to higher ones.
• Following the sequence provided by the Aufbau diagram ensures proper electron arrangement.

While applying the Aufbau principle, remember to consider the order in which orbitals fill, such as 1s, 2s, 2p, 3s, 3p, and so on. Keep in mind that, due to the way energy levels overlap, some higher principal orbitals may fill earlier than others, like how 4s fills before 3d. This is why titanium's configuration ends in 4s before 3d.

Titanium

Titanium (Ti) is a transition metal with the atomic number 22, known for its strength and corrosion resistance.
It has a distinct electron configuration that can be determined using the Aufbau principle.

• Atomic number: 22
• Electron configuration: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^2\)
• Valence Electrons: 2 (found in the 4s orbital)

The electron configuration reveals that titanium possesses two valence electrons. These electrons influence how titanium forms compounds and its reactivity with other elements. Despite only having two valence electrons, titanium can engage in various chemical reactions, often forming four covalent bonds in its common oxidation states.

Hafnium

Hafnium (Hf) is another transition metal, located in the same group as titanium. It is known for its high melting point and applications in nuclear reactors.
The electron configuration of hafnium showcases its complexity due to its larger number of electrons.

• Atomic number: 72
• Electron configuration: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6 6s^2 4f^{14} 5d^2\)
• Valence Orbitals: 6s and 5d

For hafnium, the highest principal quantum number is 6, with the electrons in 6s and partially in 5d acting as valence electrons. This sharing of valence electrons with the inner-transition orbitals allows hafnium to exhibit multiple oxidation states, making it similar in reactivity to titanium.