Problem 104 - Chemistry: An Atoms-Focused Approach

Question

Which monatomic ion has a charge of \(1+\) and the electron configuration \([\mathrm{Kr}] 4 d^{10} 5 s^{2} ?\) How many unpaired clectrons are there in the ground state of this ion?

Step-by-Step Solution

Answer

Question: Identify the ion with the electron configuration [Kr] 4d^10 5s^2 and a charge of 1+, and determine the number of unpaired electrons in its ground state. Answer: The ion is Cd^+, and it has one unpaired electron in its ground state.

Step 1: Identify the parent element corresponding to the given electron configuration

To find the element that corresponds to the given electron configuration \([\mathrm{Kr}] 4 d^{10} 5 s^{2}\), we first need to know that Kr, or Krypton, has an atomic number of 36. The given electron configuration represents the electron configuration of the element with the next 12 electrons beyond Krypton. So, we add 12 to the atomic number of Kr (36), which is \(36+12=48\). The element with an atomic number of 48 is Cadmium (Cd).

Step 2: Determine the electron configuration of the ion

We are told that the ion has a charge of \(1+\). This means that the ion has lost one electron. Since Cd has the electron configuration \([\mathrm{Kr}] 4 d^{10} 5 s^{2}\), losing an electron would result in the configuration \([\mathrm{Kr}] 4 d^{10} 5 s^{1}\). This is the electron configuration of the ion.

Step 3: Calculate the number of unpaired electrons in the ground state

We are now asked to find the number of unpaired electrons in the ground state of the ion with the electron configuration \([\mathrm{Kr}] 4 d^{10} 5 s^{1}\). The first step is to look at each subshell's electron configuration. In this case, the 4d subshell is fully occupied with 10 electrons, which means that all 5 available d orbitals are filled, and thus, no unpaired electrons are present. The last subshell is the 5s, which has one electron. This electron is unpaired since the 5s subshell has room for two electrons. Thus, there is only one unpaired electron in the ground state of this ion.

Key Concepts

Electron Configuration

Electron configuration is a method used to represent how electrons are arranged around the nucleus of an atom. It describes which orbitals the electrons occupy. The configuration is written using numbers, letters, and superscripts that indicate the number of electrons in various orbitals.
For example, the electron configuration of an element starting from Krypton (Kr) and ending with "5 s^2" signifies the filled orbitals from previous elements and additional electrons in the current element. The configuration \([\mathrm{Kr}] 4 d^{10} 5 s^{2}\) indicates that the electrons fill up the orbitals in a sequence where Krypton provides the base configuration with additional 12 electrons filling up subsequent 4d and 5s orbitals.

• "Kr" stands for the noble gas krypton, and beginning the configuration with "Kr" is shorthand for the extensive electron configuration up to krypton.
• The sequence continues with \(4d^{10}\) showing a collective filling of the d orbitals with 10 electrons.
• The last part, \(5s^{2}\), indicates two electrons filling the s orbital in the fifth energy level.

Understanding electron configurations helps in predicting chemical properties, such as bonding behavior and ion formation.

Ground State

The ground state of an atom or ion is its lowest energy state, where the electrons are in the least energetic and most stable arrangement. This configuration tells us how atoms or ions usually exist when they are not excited. In the context of ions, the electronic configuration provides the minimum energy layout of electrons even if the ion has gained or lost some.
In the example given, we have a monatomic ion that forms when Cadmium (Cd) loses an electron. The lost electron leads to configurations rearranging to reduce energy and reach the ground state. The ground state configuration here is \([\mathrm{Kr}] 4 d^{10} 5 s^{1}\). This setup

• minimizes the energy and is preferred naturally.
• The \(4d\) subshell stays fully filled, stabilizing its electronic presence.
• The single electron in the \(5s\) orbital governs certain physical and chemical properties due to its unpaired nature.

It is essential to note that the ground state's fundamental role is to represent the most chemically stable form.

Unpaired Electrons

Unpaired electrons are electrons that reside in an atom's orbital without a matching electron to pair with. These electrons are crucial because they exhibit magnetic properties and significantly influence the atom's interaction with other entities.
When examining electron configurations, particularly in ions and atoms, these unpaired electrons are evident when there is an odd number of electrons in certain orbitals or subshells less than filled capacity. For instance, in the Cd ion configuration, \([\mathrm{Kr}] 4 d^{10} 5 s^{1}\), the \(4d^{10}\) is entirely filled; the electrons pair perfectly across the five orbitals.
However, the \(5s^{1}\) subshell only has one electron:

• This means there's one unpaired electron, influencing chemical reactivity.
• In chemistry, unpaired electrons typically contribute to the formation of bonds where they seek pairing via covalent interactions.
• Additionally, unpaired electrons make the ion paramagnetic, meaning it will react to magnetic fields.

Understanding the impact of unpaired electrons is fundamental for predicting how atoms behave in various environments and how they bond.