Problem 78 - Chemistry The Central Science In Si Units

Question

Identify the group of elements that corresponds to each of the following generalized electron configurations and indicate the number of unpaired electrons for each: (a) [noble gas]ns \({ }^{2} n p^{5}\) (b) [noble gas] \(n s^{2}(n-1) d^{2}\) (c) \([\) noble \(\operatorname{gas}] n s^{2}(n-1) d^{10} n p^{1}\) (d) [noble gas \(] n s^{2}(n-2) f^{6}\)

Step-by-Step Solution

Answer

(a) Group 17, 1 unpaired electron; (b) Group 4, 2 unpaired electrons; (c) Group 13, 1 unpaired electron; (d) Lanthanides, 4 unpaired electrons.

Step 1: Analyze configuration (a)

The configuration \([\text{noble gas}]ns^2np^5\) corresponds to elements in Group 17 (Halogens) of the periodic table, as they have five electrons in their p orbital. Since p orbitals can hold a maximum of six electrons, there is one unpaired electron in the p orbital.

Step 2: Analyze configuration (b)

The configuration \([\text{noble gas}]ns^2(n-1)d^2\) corresponds to elements in Group 4 of the periodic table, as they have two electrons in their d orbital. These are the transition metals. The two d electrons are unpaired, because when filling d orbitals, each orbital gets one electron before any pairing occurs in accordance with Hund's rule.

Step 3: Analyze configuration (c)

The configuration \([\text{noble gas}]ns^2(n-1)d^{10}np^1\) represents elements in Group 13 (Boron Group) of the periodic table. The d subshell is completely filled with 10 electrons, while the p subshell has a single electron, resulting in one unpaired electron.

Step 4: Analyze configuration (d)

The configuration \([\text{noble gas}]ns^2(n-2)f^6\) corresponds to the Lanthanide series, specifically to elements around Group 3. The f subshell with six electrons typically has four unpaired electrons due to the complex filling pattern of f orbitals in which, initially, each orbital gains one electron before pairing occurs.

Key Concepts

periodic table

The periodic table is an essential tool for understanding the properties and behaviors of elements. It organizes elements based on their atomic number, electron configurations, and recurring chemical properties. By arranging the elements into groups and periods, the periodic table helps us predict the characteristics of elements based on their position.

• **Groups** are the vertical columns in the periodic table. Elements in the same group share similar chemical properties and usually have the same number of valence electrons. For example, the elements in Group 17, known as halogens, all have the general electron configuration \([noble\, gas] ns^2np^5\).
• **Periods** are the horizontal rows. As you move across a period, the atomic number of the elements increases, meaning more electrons are added to the outermost shell, influencing their chemical properties.

Understanding the layout of the periodic table is crucial for predicting the behavior of elements and how they interact with one another.

unpaired electrons

Unpaired electrons play a significant role in determining the magnetic and chemical properties of an atom. An unpaired electron is one that occupies an orbital by itself, without a partner electron of opposite spin. This situation arises because electrons will fill available orbitals singly before pairing up, as suggested by Hund's rule.

• Elements with one or more unpaired electrons are often more reactive, as these electrons can easily participate in chemical bonding.
• The presence of unpaired electrons also contributes to the magnetic properties of a substance. Materials with unpaired electrons are paramagnetic and are attracted to magnetic fields, while those with all paired electrons are typically diamagnetic and slightly repelled by magnetic fields.

By analyzing the electron configuration, one can determine the number of unpaired electrons in an atom, which is vital in understanding its reactivity and magnetic behavior.

orbital filling

Orbital filling follows a specific order based on increasing energy levels described by the Aufbau principle. This principle helps predict the electron configuration of atoms. The order of filling is primarily determined by the energy levels and a sub-level's capacity to hold electrons.

• **Order of Fillings** - Electrons fill from lower to higher energy levels, starting with the 1s orbital, followed by 2s, 2p, 3s, and so on. Thus, for an electron configuration like \([noble\, gas] ns^2(n-1)d^2\), the s orbitals fill before the d orbitals.
• **Capacity of Each Subshell** - Each subshell has a different electron-holding capacity: s (2 electrons), p (6 electrons), d (10 electrons), and f (14 electrons). Comprehending orbital filling is essential for determining an element's electron configuration.

Understanding the specifics of orbital filling helps clarify why certain elements react the way they do and aids in predicting possible chemical reactions.

Hund's rule

Hund's rule is an important guideline for predicting the arrangement of electrons in the orbitals of an atom. It states that every orbital in a given subshell is singly occupied before any orbital is doubly occupied, and all electrons singly occupying orbitals have the same spin. This rule helps in achieving the lowest energy state for an atom.

• **Achieving Stability** - By maximizing the number of electrons with parallel spins, atoms are typically more stable because electron-electron repulsion is minimized.
• **Example in Action** - Consider an electron configuration \([noble\, gas] ns^2(n-1)d^2\). Here, the two d electrons will occupy separate orbitals before any pairing happens since it leads to a lower-energy configuration.

Applying Hund's rule is crucial for correctly predicting an atom's electronic structure and understanding its chemical properties and reactivity.