Question

How many unpaired electrons are present in the tetrahedral ion \(\mathrm{FeCl}_{4}^{-?}\)

Short answer

The tetrahedral ion \(\mathrm{FeCl}_{4}^{-}\) has 5 unpaired electrons.

Step-by-step solution

Determine the oxidation state of iron (Fe)

In the ion \(\mathrm{FeCl}_{4}^{-}\), there are four chlorine (Cl) atoms surrounding the central iron (Fe) atom. The oxidation state of chlorine (Cl) is generally -1. Let x be the oxidation state of the iron (Fe) atom. Using the algebraic sum of the oxidation states, we get: x + 4(-1) = -1, where -1 is the overall charge of the ion. Solving for x: x - 4 = -1 => x = -1 + 4 => x = +3 The oxidation state of iron (Fe) in \(\mathrm{FeCl}_{4}^{-}\) is +3.

Find the number of unpaired electrons using the electron configuration

Now that we know the oxidation state of iron (Fe) is +3, we can find out the electron configuration for Fe. The atomic number of iron (Fe) is 26. So, its ground state electron configuration is: \[1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{2} 3d^{6}\] For the iron ion with +3 oxidation state, it means it has lost 3 electrons. These electrons will be removed first from 4s orbitals and then from 3d orbitals. Therefore, the electron configuration for the \(\mathrm{Fe}^{3+}\) ion becomes: \[1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 3d^{5}\] Now, we can count the number of unpaired electrons in the 3d orbitals: The configuration for 3d orbitals is \((\uparrow\downarrow) (\uparrow\downarrow) (\uparrow\downarrow) (\uparrow) (\uparrow)\) We can see that there are 5 unpaired electrons in the \(\mathrm{Fe}^{3+}\) ion. Therefore, the tetrahedral ion \(\mathrm{FeCl}_{4}^{-}\) has 5 unpaired electrons.

Key concepts

Oxidation State

Understanding the oxidation state of an element in a compound is crucial to predicting its chemical behavior, such as bonding and reactivity. The oxidation state indicates the degree of oxidation of an atom, signified as an integer. In simple terms, it can give you clues about the number of electrons an atom has gained, lost, or shared when forming a compound.

Oxidation states are typically determined by following specific rules. For example, the oxidation state of hydrogen is usually +1 and oxygen is usually -2, while the oxidation state of halogens like chlorine is typically -1. However, these states can vary depending on the compound's particular chemical context.

In the case of the ion \(\mathrm{FeCl}_{4}^{-}\), the chlorine atoms each have an oxidation state of -1. Since we are dealing with an ion, the sum of the oxidation states must equal the ion's charge. For the \(\mathrm{FeCl}_{4}^{-}\) ion, this is -1. By setting up an equation and solving for the unknown oxidation state of iron (Fe), we determine it to be +3. This value affects the chemical properties and is foundational to finding the electron configuration of the iron ion, which leads us to understanding unpaired electrons.

Electron Configuration

Electron configuration describes the distribution of electrons around the nucleus of an atom or ion in atomic or molecular orbitals. It's like a map that shows where the electrons 'live'. Each orbital can hold a specific number of electrons, and they are filled in a certain order following the Aufbau principle, which states that electrons occupy the lowest energy orbitals first.

For the iron atom (\(\text{Fe}\)), which has 26 electrons, the electron configuration in the uncharged state spells out as \[1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{2} 3d^{6}\]. However, when it forms an ion with a +3 oxidation state, it loses electrons. According to the rules, electrons are first taken from the higher energy orbitals, which is the 4s orbital followed by the 3d orbitals, leading to a new configuration of \[1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 3d^{5}\] for \(\text{Fe}^{3+}\).

From this configuration, one can examine the 3d orbitals to determine the number of unpaired electrons, which are important for magnetic properties and chemical bonding. In this case, the five 3d orbitals each have one unpaired electron, evidenced by the notation \(\uparrow\downarrow\) \(\uparrow\downarrow\) \(\uparrow\downarrow\) \(\uparrow\) \(\uparrow\), totaling five unpaired electrons in the \(\text{Fe}^{3+}\) ion.

Tetrahedral Ion

When discussing molecular geometry, 'tetrahedral' refers to a structure where a central atom is surrounded symmetrically by four other atoms at the corners of a tetrahedron. This shape is a consequence of the atoms attempting to stay as far apart as possible in a 3-dimensional space to minimize the repulsion of electron pairs.

In a tetrahedral ion like \(\mathrm{FeCl}_{4}^{-}\), iron (Fe) sits at the center with four chlorides (Cl) at each corner. The 3-dimensional shape of this tetrahedral ion affects the distribution and overlap of electron orbitals and is important for predicting the molecule's physical and chemical properties, including its reactivity and interaction with other molecules. The arrangement of these atoms influences the magnetic properties as well, since the spatial distribution of the electrons can affect how the unpaired electrons are aligned.

When combined with the information about the oxidation state and electron configuration of iron as discussed earlier, we can deduce not just the number of unpaired electrons but also begin to understand the chemical and physical behavior of this tetrahedral ion. As a result of its geometry and unpaired electrons, \(\mathrm{FeCl}_{4}^{-}\) can display interesting magnetic qualities that can be explored further in the context of inorganic chemistry and materials science.