Problem 50 - Chemistry: An Atoms-Focused Approach

Question

Chromium picolinate is an over-thecounter diet aid sold in many pharmacies. The \(\mathrm{Cr}^{3+}\) ions in this coordination compound are in an octahedral field. Is the compound paramagnetic or diamagnetic?

Step-by-Step Solution

Answer

Answer: The chromium picolinate compound is paramagnetic.

Step 1: Determine the electron configuration of the \(\mathrm{Cr}\) atom

To find the electron configuration of the \(\mathrm{Cr}^{3+}\) ion, we first need to know the electron configuration of the neutral \(\mathrm{Cr}\) atom. Chromium has an atomic number of 24, meaning it has 24 electrons in its neutral state. Its electron configuration is \([\mathrm{Ar}]\ 3d^5 4s^1\).

Step 2: Determine the electron configuration of the \(\mathrm{Cr}^{3+}\) ion

Now we need to find the electron configuration of the \(\mathrm{Cr}^{3+}\) ion. Since the ion has a charge of +3, that means it has lost 3 electrons compared to the neutral atom. The 4s electrons are lost first when removing electrons, so the electron configuration for the \(\mathrm{Cr}^{3+}\) ion will be \([\mathrm{Ar}]\ 3d^3\).

Step 3: Check for unpaired electrons in the \(\mathrm{Cr}^{3+}\) ion

The \(\mathrm{Cr}^{3+}\) ion has 3 electrons in its 3d orbitals. In an octahedral field, the 3d orbitals split into two sets. In this case, the three electrons will occupy the three lower energy 3d orbitals with parallel spins before filling the higher energy orbitals. So, there are three unpaired electrons in the \(\mathrm{Cr}^{3+}\) ion.

Step 4: Determine if the chromium picolinate compound is paramagnetic or diamagnetic

Since the \(\mathrm{Cr}^{3+}\) ion has unpaired electrons, the chromium picolinate compound will be paramagnetic, as compounds with unpaired electrons exhibit paramagnetism.

Key Concepts

Electron Configuration

The electron configuration of an atom provides us with insight into the arrangement of electrons in the atom's energy levels. For chromium (Cr), which has an atomic number of 24, the electron configuration is unique. It is written as \([ ext{Ar}] \; 3d^5 \; 4s^1\), rather than the expected \([ ext{Ar}] \; 3d^4 \; 4s^2\). This occurs due to the additional stability gained by having a half-filled d subshell.

When forming a \( ext{Cr}^{3+}\) ion, the atom loses three electrons. Electrons are typically removed from the highest energy level first, which in this case are the 4s and 3d orbitals. Thus, the electron configuration for \( ext{Cr}^{3+}\) becomes \([ ext{Ar}] \; 3d^3\). Understanding this is essential for predicting the properties of chromium compounds, such as paramagnetism.

Octahedral Coordination

In chemistry, coordination compounds involve a central metal atom bonded to surrounding ligands. Chromium picolinate is a coordination compound in which the \( ext{Cr}^{3+}\) ion is surrounded by other molecules, creating an octahedral field. This term 'octahedral' indicates that the ligands form an arrangement around the chromium ion very much like the corners of an octahedron shape.

This octahedral arrangement affects how the electron orbitals in the chromium ion split in energy. Typically, the five \(d\) orbitals split into two groups when subjected to an octahedral field: the lower energy \(t_{2g}\) orbitals and the higher energy \(e_g\) orbitals. This splitting is significant because it influences the electronic and magnetic properties of chromium coordination compounds.

Unpaired Electrons

Unpaired electrons are a key factor in determining the magnetic properties of a compound. In an atom or ion, if there are electrons that are not paired (meaning they do not have opposite spins), these electrons contribute to magnetism. This is because unpaired electrons generate a magnetic field, responding to external magnetic fields.

For the \(\text{Cr}^{3+}\) ion in chromium picolinate, there are three electrons that are not paired in its \(3d\) orbital. In an octahedral field, these three electrons fill the lower energy orbitals first and remain unpaired due to Hund's rule (the maximum multiplicity rule), which states that electrons occupy separate orbitals before pairing up.

The presence of these unpaired electrons signals that chromium picolinate is paramagnetic. Paramagnetic substances are attracted by external magnetic fields due to their unpaired electrons, unlike diamagnetic compounds, which have all electrons paired and are slightly repelled by a magnetic field.