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 4B. 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 for titanium (Ti) is \[ \mathrm{1s^2~2s^2~2p^6~3s^2~3p^6~4s^2~3d^2} \], and it has 2 valence electrons in the 4s orbital. Hafnium's (Hf) electron configuration is \[ \mathrm{1s^2~2s^2~2p^6~3s^2~3p^6~4s^2~3d^{10}~4p^6~5s^2~4d^{10}~5p^6~6s^2~4f^{14}~5d^2} \]. The valence orbitals for Hf are 5d and 6s, and the core orbitals are 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, and 4f.

Step 1: Identify the atomic number of Ti

From the periodic table, we can find that the atomic number of titanium (Ti) is 22.

Step 2: Write the electron configuration for Ti

Following the Aufbau principle, we will fill in the electrons in the orbitals following the order 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, and so on. Since Ti has 22 electrons, its electron configuration will be: \[ \mathrm{1s^2~2s^2~2p^6~3s^2~3p^6~4s^2~3d^2} \]

Step 3: Determine the number of valence electrons

We can see that the last three orbitals (3p, 4s, 3d) contain 14 electrons. However, the 3d orbital is not a valence orbital. So, only the electrons in the 4s orbital (2) are considered valence electrons in Ti. (b) Hafnium's electron configuration

Step 4: Identify the atomic number of Hf

From the periodic table, we can determine that the atomic number of hafnium (Hf) is 72.

Step 5: Write the electron configuration for Hf

Following the Aufbau principle, we will fill in the electrons in the orbitals. Since Hf has 72 electrons, its electron configuration will be: \[ \mathrm{1s^2~2s^2~2p^6~3s^2~3p^6~4s^2~3d^{10}~4p^6~5s^2~4d^{10}~5p^6~6s^2~4f^{14}~5d^2} \] (c) Identifying subshells as valence or core orbitals

Step 6: Identify the valence orbitals

We can see that for Hf, the valence orbitals are 5d and 6s. It behaves like Ti since both have 2 electrons in the outermost s-orbital.

Step 7: Identify the core orbitals

The core orbitals for Hf are the rest of the filled orbitals: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, and 4f.

Key Concepts

Valence Electrons

Valence electrons are the outermost electrons of an atom that can participate in chemical bonding. They are crucial for determining how an element reacts with others. The electron configuration of an element provides insight into where these electrons reside.
For example, in titanium (Ti) with electron configuration \(1s^2~2s^2~2p^6~3s^2~3p^6~4s^2~3d^2\), the electrons in the 4s orbital are considered as valence electrons because they are the outermost electrons orbiting the nucleus right after the inner 3d orbital. Although the 3d orbitals are filled after the 4s, they are considered part of the core in this context due to their energy levels.
Hafnium (Hf), another element with valence electrons behaving similarly to Ti, has the electron configuration \(1s^2~2s^2~2p^6~3s^2~3p^6~4s^2~3d^{10}~4p^6~5s^2~4d^{10}~5p^6~6s^2~4f^{14}~5d^2\). For Hf, the 6s and 5d electrons serve as the valence electrons. They define Hf’s similar reactivity in comparison to Ti, as both have two valence electrons in their outer s shell.

Periodic Table

The periodic table is a comprehensive chart that organizes all known chemical elements based on their atomic number, electron configuration, and recurring chemical properties. This powerful tool allows us to intuitively determine properties such as atomic radius, ionization energy, and, importantly, electron configuration.
Elements are arranged into periods (horizontal rows) and groups (vertical columns). Elements in the same group, like titanium (Ti) and hafnium (Hf), share similar characteristics because they have the same number of valence electrons. This similarity results in common chemical behaviors, which is evident in the same number of valence electrons for both Hf and Ti.
The periodic table also provides the atomic number of elements, which is indispensable for writing electron configurations. For instance, Ti is represented with an atomic number of 22, and Hf with an atomic number of 72. These numbers help in identifying the total number of electrons that need to be arranged when determining the electron configuration.

Aufbau Principle

The Aufbau principle is a guideline used in chemistry to determine the electron configuration of an atom. It provides a sequential order of filling electrons into atomic orbitals based on their increasing energy levels. According to the Aufbau principle, electrons fill the lowest energy orbitals first before moving to higher energy levels.
Some crucial points to remember about the Aufbau principle include:

• Electrons occupy the orbitals in the order starting from 1s up to the outermost levels. This sequence can be remembered with the mnemonic "1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f 6d 7p".
• This principle explains why titanium's electron configuration is structured with \(1s^2, 2s^2,\) up to the \(3d\) orbitals.
• For hafnium, following the Aufbau principle involves filling up orbitals as \(1s^2 \text{ to } 5d^2\), ensuring lower-energy orbitals are completed first.

Understanding the order of filling helps in crafting accurate electron configurations for any element on the periodic table. However, it's also essential to remember exceptions to this rule, especially in transition metals and lanthanides, where electron-electron interactions or energy differences between orbitals can cause deviations.