Problem 91 - Chemistry An Atoms First Approach

Question

Write the expected ground-state electron configuration for the following. a. the element with one unpaired \(5 p\) electron that forms a covalent compound with fluorine b. the (as yet undiscovered) alkaline earth metal after radium c. the noble gas with electrons occupying \(4 f\) orbitals d. the first-row transition metal with the most unpaired electrons

Step-by-Step Solution

Answer

a. Bismuth (Bi) has a ground-state electron configuration of \[1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^{10} \, 4p^6 \, 5s^2 \, 4d^{10} \, 5p^6 \, 6s^2 \, 4f^{14} \, 5d^{10} \, 6p^3\] b. The undiscovered alkaline earth metal after Radium (Ubn) has a ground-state electron configuration of \[1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^{10} \, 4p^6 \, 5s^2 \, 4d^{10} \, 5p^6 \, 6s^2 \, 4f^{14} \, 5d^{10} \, 6p^6 \, 7s^2 \, 5f^{14} \, 6d^{10} \, 7p^6 \, 8s^2\] c. Radon (Rn) has a ground-state electron configuration of \[1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^{10} \, 4p^6 \, 5s^2 \, 4d^{10} \, 5p^6 \, 6s^2 \, 4f^{14} \, 5d^{10} \, 6p^6\] d. Manganese (Mn) has a ground-state electron configuration of \[1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^5\]

Step 1: (a) Identify the element with one unpaired 5p electron and forms covalent compound with fluorine

The element with one unpaired 5p electron must belong to the fifth period in the periodic table and should be located in the p-block. Since it has an unpaired electron, it must be from Group 15, or Nitrogen family. Counting down the periodic table, the element in Group 15 and Period 5 is Bismuth (Bi).

Step 2: (a) Write the ground-state electron configuration for Bismuth

Bismuth has an atomic number of 83. Its electron configuration is: \[1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^{10} \, 4p^6 \, 5s^2 \, 4d^{10} \, 5p^6 \, 6s^2 \, 4f^{14} \, 5d^{10} \, 6p^3\]

Step 3: (b) Identify the (undiscovered) alkaline earth metal after Radium

Alkaline earth metals belong to Group 2 in the periodic table. Radium (Ra) is the last known alkaline earth metal and belongs to the Period 7. The undiscovered alkaline earth metal after radium would belong to Period 8 with the symbol Ubn.

Step 4: (b) Write the ground-state electron configuration for the undiscovered alkaline earth metal after Radium

Ubn would have an atomic number of 120. Its electron configuration is \[1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^{10} \, 4p^6 \, 5s^2 \, 4d^{10} \, 5p^6 \, 6s^2 \, 4f^{14} \, 5d^{10} \, 6p^6 \, 7s^2 \, 5f^{14} \, 6d^{10} \, 7p^6 \, 8s^2\]

Step 5: (c) Identify the noble gas with electrons occupying 4f orbitals

Noble gases are elements in Group 18 that have completed electron shells. In this case, the noble gas will have completed its 4f orbitals. The noble gas with electrons in 4f orbitals is Radon (Rn).

Step 6: (c) Write the ground-state electron configuration for Radon

Radon has an atomic number of 86. Its electron configuration is: \[1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^{10} \, 4p^6 \, 5s^2 \, 4d^{10} \, 5p^6 \, 6s^2 \, 4f^{14} \, 5d^{10} \, 6p^6\]

Step 7: (d) Identify the first-row transition metal with the most unpaired electrons

Transition metals are found in the d-block. In the first row of transition metals, unpaired electrons go up until the element has 5 unpaired electrons. The element with the most unpaired electrons in its ground state is Manganese (Mn).

Step 8: (d) Write the ground-state electron configuration for Manganese

Manganese has an atomic number of 25. Its electron configuration is: \[1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^5\]

Key Concepts

Understanding the Periodic Table

Many students find the periodic table to be a complex checkerboard of letters and numbers, but it's actually a systematic representation of the elements. The periodic table is organized by increasing atomic number (the number of protons in the nucleus of an atom) and by chemical properties. Elements are arranged in rows, called periods, and columns, known as groups or families.

Let's consider the element Bismuth from the exercise, which has one unpaired electron in the 5p orbital. It's located in group 15, period 5. This position informs us not only about its reactivity and the formation of covalent compounds with fluorine but also leads us to its ground-state electron configuration. By moving along the periods and down the groups, we can deduce properties and behaviors of elements just by their position on the table.

Delving into Transition Metals

Transition metals are fascinating due to their unique properties such as colored compounds and variable oxidation states. They occupy the d-block of the periodic table, which holds the elements from groups 3 to 12. These metals have incompletely filled d orbitals and can bond with a variety of ligands to form complex ions.

For instance, Manganese (Mn), the element discussed in the exercise, is a first-row transition metal with a notable number of unpaired electrons, resulting in its distinctive magnetic properties. Knowledge of electron configurations, specifically unpaired electrons, is crucial for understanding the behavior of these metals in reactions, which is essential for numerous industrial and chemical processes.

Exploring Alkaline Earth Metals

The alkaline earth metals, found in group 2 of the periodic table, are recognized for their shiny silver surfaces and high reactivity. They have two valence electrons that they readily lose to form divalent cations. This makes them highly reactive, particularly with halogens and water.

A hypothetical example mentioned would be the undiscovered element after Radium (Ra), which would be an alkaline earth metal in period 8 with a predictable electron configuration. Understanding these configurations allow chemists to make educated guesses about the properties of even undiscovered elements that fit within the established framework of the table.

Investigating Noble Gases

The noble gases are the elements in group 18 of the periodic table and are best known for their extreme unreactivity due to their filled valence shells. This results in very low chemical reactivity, making them ideal for use in non-reactive environments, like lighting or welding applications.

For example, radon (Rn) has a complete set of 4f orbitals and a completed outer electron shell, which is why it's classified as a noble gas. Through the understanding of their electron configurations, one can predict the stability and reactivity of these gases, which has implications in both practical and theoretical chemistry.