Problem 102 - Chemistry: The Central Science in SI Units, Global Edition

Question

Using the periodic table as a guide, write the condensed electron configuration and determine the number of unpaired electrons for the ground state of (a) \(\mathrm{Cl},(\mathbf{b}) \mathrm{Al},(\mathbf{c}) \mathrm{Zr},(\mathbf{d})\) As, (e) \(\mathrm{Sb},(\mathbf{f}) \mathrm{W}\)

Step-by-Step Solution

Answer

The condensed electron configurations and number of unpaired electrons for the given elements are: a) Cl: [Ne] 3s² 3p⁵, 3 unpaired electrons b) Al: [Ne] 3s² 3p¹, 1 unpaired electron c) Zr: [Kr] 5s² 4d², 2 unpaired electrons d) As: [Ar] 4s² 3d¹⁰ 4p³, 3 unpaired electrons e) Sb: [Kr] 5s² 4d¹⁰ 5p³, 3 unpaired electrons f) W: [Xe] 6s² 4f¹⁴ 5d⁴, 4 unpaired electrons

Step 1: a) Electron Configuration and Unpaired Electrons for Chlorine (Cl)

Chlorine (Cl) has an atomic number (Z) of 17, so it has 17 electrons in its ground state. Following the order in the periodic table: 1s² 2s² 2p⁶ 3s²3p⁵ Condensed Electron Configuration: [Ne] 3s² 3p⁵ Number of Unpaired Electrons: Since the last subshell (3p) has five electrons, there are three unpaired electrons.

Step 2: b) Electron Configuration and Unpaired Electrons for Aluminum (Al)

Aluminum (Al) has an atomic number (Z) of 13, so it has 13 electrons in its ground state. Following the order in the periodic table: 1s² 2s² 2p⁶ 3s² 3p¹ Condensed Electron Configuration: [Ne] 3s² 3p¹ Number of Unpaired Electrons: Since the last subshell (3p) has only one electron, there is one unpaired electron.

Step 3: c) Electron Configuration and Unpaired Electrons for Zirconium (Zr)

Zirconium (Zr) has an atomic number (Z) of 40, so it has 40 electrons in its ground state. Following the order in the periodic table: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d² Condensed Electron Configuration: [Kr] 5s² 4d² Number of Unpaired Electrons: Since the last subshell (4d) has two electrons, there are two unpaired electrons.

Step 4: d) Electron Configuration and Unpaired Electrons for Arsenic (As)

Arsenic (As) has an atomic number (Z) of 33, so it has 33 electrons in its ground state. Following the order in the periodic table: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p³ Condensed Electron Configuration: [Ar] 4s² 3d¹⁰ 4p³ Number of Unpaired Electrons: Since the last subshell (4p) has three electrons, there are three unpaired electrons.

Step 5: e) Electron Configuration and Unpaired Electrons for Antimony (Sb)

Antimony (Sb) has an atomic number (Z) of 51, so it has 51 electrons in its ground state. Following the order in the periodic table: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p³ Condensed Electron Configuration: [Kr] 5s² 4d¹⁰ 5p³ Number of Unpaired Electrons: Since the last subshell (5p) has three electrons, there are three unpaired electrons.

Step 6: f) Electron Configuration and Unpaired Electrons for Tungsten (W)

Tungsten (W) has an atomic number (Z) of 74, so it has 74 electrons in its ground state. Following the order in the periodic table: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p⁶ 6s² 4f¹⁴ 5d⁴ Condensed Electron Configuration: [Xe] 6s² 4f¹⁴ 5d⁴ Number of Unpaired Electrons: Since the last subshell (5d) has four electrons, there are four unpaired electrons.

Key Concepts

Periodic Table

The periodic table is a chart that organizes elements by increasing atomic number and similar chemical properties. It serves as a guide in determining the electron configuration of elements. By placing elements in order, we can see the filling order of electrons in their atomic orbitals.

Each row, or period, represents the filling of a set of orbitals. For example, elements in the second period fill the 2s and 2p orbitals. This orderly pattern allows us to predict and write electron configurations for elements.

Using the periodic table, we can determine the electronic arrangement of elements efficiently and predict their chemical behavior. Recognizing groups, like the noble gases or transition metals, helps in predicting specific properties and behaviors.

Ground State

The ground state of an atom is its lowest energy state where all the electrons are in their lowest possible energy levels. Think of it as the perfectly relaxed state of the atom, where no extra energy is used to excite electrons to a higher level.

The determination of an atom's ground state configuration is critical since it's the most stable and common form found in nature. In chemistry, knowing the ground state helps us understand how an element will interact in chemical reactions.

By using the atom's atomic number, which tells us how many electrons it has, we can distribute these electrons into orbitals following specific rules (like the Aufbau principle), ensuring they are in positions of least energy.

Unpaired Electrons

Unpaired electrons are single electrons present in an atomic orbital that are not paired with another electron with an opposite spin. Recognizing unpaired electrons is important because they contribute greatly to the magnetic properties and reactivity of an element.

Elements like chlorine, with the electron configuration [Ne] 3s² 3p⁵, have unpaired electrons in their outer orbitals.

• The presence of unpaired electrons often leads to paramagnetism, where elements are attracted to magnetic fields.
• As such, unpaired electrons are also clues to predict how elements will interact or bond with others.

Knowing the number of unpaired electrons allows chemists to predict the type and strength of chemical bonds that an element might form.

Condensed Electron Configuration

Condensed electron configuration is a shorthand method of writing the electron configuration of an element. It uses the nearest noble gas that precedes the element in the periodic table to represent filled electron shells.

Take aluminum (Al) for example, with the electron configuration 1s² 2s² 2p⁶ 3s² 3p¹. Its condensed form is [Ne] 3s² 3p¹ by using neon ([Ne]) to represent the completed electron shells up to 2p.

• This method simplifies the electron configuration, making it easier to identify valence electrons.
• Condensed configurations highlight the outermost electrons directly involved in chemical reactions.

Using the condensed configuration is not only efficient but also provides clarity when studying complex elements. It directly reflects the element's reactivity and interactions with other atoms.