Problem 2 - General Chemistry: Principles and Modern Applications

Question

Arrange the following species according to the number of unpaired electrons they contain, starting with the one that has the greatest number: \(\mathrm{Fe}, \mathrm{Sc}^{3+}, \mathrm{Ti}^{2+}\) \(\mathrm{Mn}^{4+}, \mathrm{Cr}, \mathrm{Cu}^{2+}\).

Step-by-Step Solution

Answer

The arrangement of the species according to their unpaired electrons is: \(\mathrm{Cr}, \mathrm{Fe}, \mathrm{Ti}^{2+}, \mathrm{Sc}^{3+}, \mathrm{Mn}^{4+}, \mathrm{Cu}^{2+}\)

Step 1: Determine the Electron Configuration of Each Species

Use the Periodic Table to find the electron configurations:\(\mathrm{Fe}\)=[Ar] 4s2 3d6, \(\mathrm{Sc}^{3+}\)=[Ar], \(\mathrm{Ti}^{2+}\)=[Ar] 3d2, \(\mathrm{Mn}^{4+}\)=[Ar], \(\mathrm{Cr}\)=[Ar] 4s1 3d5, \(\mathrm{Cu}^{2+}\)=[Ar].

Step 2: Count the Unpaired Electrons

By analyzing the electron configuration, figure out the number of unpaired electrons in each species: \(\mathrm{Fe}\) has 4 unpaired electrons, \(\mathrm{Sc}^{3+}\) has no unpaired electrons, \(\mathrm{Ti}^{2+}\) has 2 unpaired electrons, \(\mathrm{Mn}^{4+}\) has no unpaired electrons, \(\mathrm{Cr}\) has 6 unpaired electrons, \(\mathrm{Cu}^{2+}\) has no unpaired electrons.

Step 3: Arrange the Species

With the numbers of unpaired electrons, arrange the species in decreasing order: \(\mathrm{Cr}, \mathrm{Fe}, \mathrm{Ti}^{2+}, \mathrm{Sc}^{3+}, \mathrm{Mn}^{4+}, \mathrm{Cu}^{2+}\)

Key Concepts

Unpaired Electrons

Understanding unpaired electrons is crucial for determining the magnetic properties and reactivity of chemical species. Unpaired electrons are those that are not paired with another electron in an orbital. Typically, electrons are found in pairs within an atomic or molecular orbital, each with opposite spins. However, when there is an unpaired electron, it gives rise to magnetic properties, known as paramagnetism.

• If an atom or molecule has all electrons paired, it is diamagnetic and does not have any net magnetic moment.
• Species with one or more unpaired electrons are paramagnetic, which means they can be attracted to a magnetic field.

In transition metals, unpaired electrons are common due to the specific arrangement of d-orbitals, which we'll explore in detail when discussing transition metals. Knowing about unpaired electrons is key when predicting how different elements and compounds will behave in various conditions.

Periodic Table

The Periodic Table is a fundamental tool in chemistry, organizing all known elements in a meaningful way. Each element’s position is based on its atomic number and electron configuration. The table is arranged in rows called periods and columns called groups.

• Elements in the same group have similar properties because they have the same number of electrons in their outer shell.
• The electron configuration, which can be determined using the Periodic Table, provides insights into the number of unpaired electrons an element might have.

By utilizing the periodic table, you can quickly find the electron configuration necessary to determine properties like unpaired electrons. This is particularly useful for elements in the transition metals section, where electron configurations significantly impact chemical behavior.

Transition Metals

Transition metals are elements found in the central block of the Periodic Table, specifically groups 3 to 12. These metals are characterized by their ability to form various oxidation states and complex ions. The presence of d-orbitals that can be partially filled leads to unique properties, including the presence of unpaired electrons.

• Transition metals often have one or more unpaired electrons due to their d-orbital configurations.
• This results in diverse chemical behavior and magnetic properties not typically found in other elements.

Understanding electron configurations in transition metals is essential in predicting and explaining their chemical properties, such as magnetic characteristics and compounds' color. This explains why elements like Chromium (Cr) and Iron (Fe) show varied numbers of unpaired electrons.

Chemical Species

Chemical species refer to atoms, ions, molecules, or elements that participate in chemical reactions or serve as reactants, products, or intermediates. Each species has a unique electron configuration that influences its chemical behavior, including the number of unpaired electrons.

• Neutral atoms like Chromium (Cr) may have different physical and chemical properties compared to their ionized forms, like Cr³⁺, due to changes in the electron configuration.
• The loss or gain of electrons to form ions alters the electron distribution, impacting magnetic and chemical reactivity.

Recognizing these differences helps in arranging chemical species by properties like the number of unpaired electrons, crucial for predicting reactivity and bonding properties in various chemical contexts.