Question

Identify two ions that have the following ground-state electron configurations: \((\mathbf{a}) [\) Ar \(],(\mathbf{b})[\) Ar \(] 3 d^{5},(\mathbf{c})[\mathrm{Kr}] 5 s^{2} 4 d^{10}\).

Short answer

The ions with the given ground-state electron configurations are: a) \(K^+\) b) \(V^{+5}\) c) \(Cd^{+2}\)

Step-by-step solution

Identify the noble gas represented in each configuration

In each configuration, we are given the electron configuration in terms of a noble gas. We need to identify the atomic number of the given noble gas. a) [Ar]: Argon has an atomic number of 18. b) [Ar]: Argon has an atomic number of 18. c) [Kr]: Krypton has an atomic number of 36.

Calculate the total number of electrons in each ion

Now that we know the atomic number of the noble gas represented in each configuration, we need to add the additional electrons mentioned in the configurations to find the total number of electrons in each ion. a) [Ar]: Argon has 18 electrons, so this configuration has a total of 18 electrons. b) [Ar] 3d^5: Argon has 18 electrons, and the 3d^5 term means that there are 5 more electrons in the 3d orbital. So, this configuration has a total of 18 + 5 = 23 electrons. c) [Kr] 5s^2 4d^10: Krypton has 36 electrons, 5s^2 means there are 2 more electrons in the 5s orbital, and 4d^10 means there are 10 more electrons in the 4d orbital. So, this configuration has a total of 36 + 2 + 10 = 48 electrons.

Convert the electron number to their corresponding elements or ions

Now that we have the total number of electrons in each configuration, we can use the periodic table to identify the corresponding element or ion: a) 18 electrons: The element with 18 electrons (and 18 protons) is Argon (Ar). However, since the question asks for ions, we need to look for an element whose ion would have 18 electrons. Since Argon has 18 electrons itself, the element with 18 electrons in its ion would be one atomic number away from Argon. Potassium (K) with 19 electrons forms K+ ion by losing one electron, giving it 18 electrons. So, the ion represented by this configuration is K+. b) 23 electrons: The element with 23 electrons (and 23 protons) is Vanadium (V). This element forms different ions by losing electrons. Vanadium has 5 valence electrons, so it can lose 5 electrons to form a V+5 ion with 23 - 5 = 18 electrons. So, the ion represented by this configuration is V+5. c) 48 electrons: The element with 48 electrons (and 48 protons) is Cadmium (Cd). Cadmium forms ions by losing electrons. Cadmium has 12 valence electrons, so it can lose 2 electrons to form a Cd+2 ion with 48 - 2 = 46 electrons. So, the ion represented by this configuration is Cd+2. In conclusion, we have identified the following ions: a) K+ b) V+5 c) Cd+2

Key concepts

Noble Gas Electron Configuration

Understanding electron configurations can be made simpler by using the noble gas shortcut method. This involves referencing the configuration of the nearest noble gas that comes before an element in the periodic table.

For example, when we denote the electron configuration as \[ \text{[Ar]} \], it's a shorthand saying that the element or ion has the same electron configuration as argon (Ar) up to the 3p subshell, which is completely filled in the case of argon. Noble gases have very stable electron configurations, making them an ideal reference point.

The electron configuration of argon, which is a noble gas, is particularly stable due to a filled valence shell. When ions have a noble gas configuration, it usually indicates a stable and low-energy state, which is often the case for cations or anions that have complete valence shells.

Atomic Number

The atomic number of an element plays a crucial role in understanding its properties, including its electron configuration. This number, often denoted by the symbol \(Z\), represents the number of protons found in the nucleus of an atom. It is the defining trait of an element, as no two different elements can have the same number of protons.

Since neutral atoms have equal numbers of protons and electrons, the atomic number also tells us the number of electrons in an atom when it is in its ground-state. For instance, argon has an atomic number of 18, implying it has 18 protons and, in its neutral state, 18 electrons. When considering ions, however, the number of electrons may vary due to the gain or loss of electrons to achieve stability.

Electron Configuration Notation

Electron configuration notation is a way to describe the arrangement of electrons around the nucleus of an atom. It follows a format where the energy levels and sublevels are listed, along with the number of electrons in each subshell, represented by superscripts.

For example, the notation \[ \text{[Ar] 3d}^5 \] means the ion or atom has an electron configuration up to argon, with an additional five electrons in the 3d subshell. Recognizing this notation allows one to determine the specific subshells that are occupied by electrons, which is vital for predicting the chemical properties and reactivity of the element or ion in question.

A full electron configuration can be quite long, so using noble gas notation as a starting point simplifies this process, focusing only on the electrons that differ from the noble gas' closed-shell configuration.

Periodic Table

The periodic table is not only a pivotal tool for chemists but also serves as a guide for decoding electron configurations. It organizes elements based on increasing atomic number and groups them into blocks, such as s, p, d, and f, according to their valence electron configurations.

By using the periodic table, one can track how electrons fill into different atomic orbitals. When identifying ions as in our exercise, we rely on the periodic table to determine the element's position, which then helps ascertain what ions it might form to achieve stability. For example, elements that are one atomic number higher than a noble gas, such as potassium (K), have a tendency to lose an electron, forming ions with the same electron configuration as the noble gas.

Thus, utilizing the periodic table is indispensable for understanding not just the arrangement of elements and their properties, but also how ions are formed and what their electron configurations signify in terms of chemical behavior.