Problem 12 - Chemistry: The Central Science in SI Units, Global Edition

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. 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 \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^2\), with 4 valence electrons. The electron configuration of hafnium (Hf) is \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6 6s^2 4f^{14} 5d^2\). Hf's valence orbitals are 6s and 5d, while its core orbitals are 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, and 4f.

Step 1: (a) Electron Configuration of Titanium (Ti) and Valence Electrons

To write the electron configuration of titanium (Ti, atomic number 22), we follow the aufbau principle and the rules of the periodic table. The electron configuration can be given as follows: Ti: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^2\) The valence electrons of an element are the electrons in the outermost shell. In the case of titanium, the valence shell is the 4th shell with the 4s and 3d orbitals. The number of valence electrons for titanium is 4 (2 in the 4s orbital and 2 in the 3d orbital).

Step 2: (b) Electron Configuration of Hafnium (Hf)

To write the electron configuration for hafnium (Hf, atomic number 72), we also follow the aufbau principle and periodic table rules. The electron configuration is: Hf: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6 6s^2 4f^{14} 5d^2\)

Step 3: (c) Valence and Core Orbitals of Hafnium (Hf)

Since elements on the same group of the Periodic Table often show similar behavior, Hf has the same number of valence electrons as Ti. The outermost shell for hafnium is the 6th shell, so Hf's valence orbitals are in the 6s and 5d orbitals since they contain the valence electrons. Hf's Valence orbitals: 6s and 5d All the other orbitals preceding the valence orbitals are known as core orbitals. They don't participate in the chemical bonding, and these electrons shield the positive charges of the nucleus. Hf's Core orbitals: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, and 4f.

Key Concepts

Valence Electrons

Valence electrons are the electrons located in the outermost shell of an atom. These electrons are crucial because they play a key role in determining how an atom interacts with others.

• They are involved in forming chemical bonds.
• They influence the atom's reactivity and ability to engage in different chemical reactions.

For example, in titanium (Ti), which has an atomic number of 22, the electron configuration is: \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^2\] The valence electrons for titanium are found in the 4s and 3d orbitals, amounting to a total of 4 valence electrons. Similarly, for hafnium (Hf), although its electron configuration is more complex, with the presence of the 4f orbitals, the valence electrons are still located in the 6s and 5d orbitals, highlighting the similarities they share with titanium.

Aufbau Principle

The aufbau principle is a fundamental rule used to determine the electron configuration of atoms. It helps in understanding the arrangement of electrons in various orbitals.

• Electrons are added to the lowest energy orbitals first before moving to higher energy levels.
• This is why, during the filling of titanium's orbitals, electrons fill the 1s, 2s, and 2p orbitals first, as they are the lowest energy levels.

This principle helps us construct the electron configuration for any element in a systematic manner. In the case of hafnium (Hf), the aufbau principle guides the filling of electrons through orbitals in this sequence: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, before filling the 4f and 5d orbitals, which are closer in energy. It helps in understanding why elements, even in the same group like Ti and Hf, have configurations reflecting similar chemical properties.

Core Orbitals

Core orbitals are those which are filled prior to the valence orbitals and are tightly bound to the atomic nucleus. These orbitals include inner shells such as 1s, 2s, and 2p for titanium, which are not involved in chemical bonding.

• Core electrons are those found in core orbitals, providing stability to the atom.
• They serve to shield the nucleus from the valence electrons, reducing the effective nuclear charge experienced by the valence electrons.

For instance, in hafnium, core orbitals include 1s through 4f, as defined by the step solution. These orbitals are filled during earlier stages following the aufbau principle. Core orbitals do not change easily, maintaining their structure and contributing to the overall stability and shape of the electron cloud surrounding the nucleus. Understanding core orbitals is crucial in predicting the behavior of atoms in chemical reactions, as it's typically the valence electrons that interact rather than those in core orbitals.