Question

The complex ion \(\left[\mathrm{PdCl}_{4}\right]^{2-}\) is known to be diamagnetic. Use this information to determine if it is a tetrahedral or square planar structure.

Short answer

The complex ion \(\left[\mathrm{PdCl}_{4}\right]^{2-}\) is likely to have a square planar structure due to the diamagnetic nature and the electron configuration of Pd(II) as \(4d^8\), which allows for all electrons to be paired in this geometry.

Step-by-step solution

- Understand the Concept of Magnetic Properties

First, it's important to note that diamagnetism in a compound occurs when all electrons are paired. Since the complex ion \(\left[\mathrm{PdCl}_{4}\right]^{2-}\) is diamagnetic, we can deduce that all its electrons are paired. Thus, there are no unpaired electrons in the d-orbital of the central metal ion, Palladium (Pd).

- Determine the Oxidation State

Calculate the oxidation state of Pd in \(\left[\mathrm{PdCl}_{4}\right]^{2-}\) to know how many d-electrons it has. Chloride (Cl) has a charge of -1, and there are four Cl ions, summing up to a charge of -4. Since the overall complex has a charge of -2, Pd must have an oxidation state of +2 to balance the charges (\(4(-1) + x = -2\), solving for x gives +2).

- Determine the Electron Configuration

With Pd in the 2+ oxidation state, it loses the 4s electrons first, then any additional electrons must come from the 4d subshell. Pd has an atomic number of 46, corresponding to a ground state electron configuration of \(4d^{10} 5s^{0}\) after losing 2 electrons. Therefore, Pd(II) has a \(4d^8\) electron configuration.

- Predict the Structure

A square planar structure is often favored by d8 metal ions in complex ions because this allows for the pairing of all electrons. Since there are only 8 d-electrons, they can fit into the lower energy orbitals and become paired. In contrast, a tetrahedral geometry would result in higher energy and possibly unpaired electrons, contradicting the diamagnetic nature of the ion.

Key concepts

Understanding Diamagnetism

Diamagnetism is a fundamental property related to the magnetic behavior of materials. It's indicative of substances where all the electrons are paired, resulting in no net magnetic moment. These substances are repelled by a magnetic field rather than attracted. The reason behind this behavior lies in the electronic structure of the atoms or ions. Every electron is associated with its own magnetic moment, and when electrons are paired, their magnetic moments cancel each other out.

In the case of the complex ion \(\left[\mathrm{PdCl}_{4}\right]^{2-}\), its diamagnetic nature tells us immediately that there are no unpaired electrons present in the metal center, palladium (Pd). Briefly touching upon how this relates to the structure, certain geometric arrangements favor electron pairing. For instance, a square planar coordination allows d-electron pairs to stay at a lower energy state compared to a tetrahedral arrangement, which might force electrons into higher energy levels, potentially resulting in unpaired electrons. So, the diamagnetism indicates a possible square planar geometry for the \(\left[\mathrm{PdCl}_{4}\right]^{2-}\) ion.

Determining Oxidation State

The oxidation state is like the financial balance sheet of an atom within a compound, revealing the number of electrons it has gained or lost relative to its elemental state. It's vital for predicting reactivity, bonding, and magnetic properties. In coordination complexes, such as \(\left[\mathrm{PdCl}_{4}\right]^{2-}\), the oxidation state can be calculated using simple arithmetic, balancing the charges of the ligands (in this case, chloride ions) with the overall charge of the complex.

The calculation involves assigning a -1 charge to each chloride ion. With four chloride ions, the total charge they contribute is -4. To balance the \(\left[\mathrm{PdCl}_{4}\right]^{2-}\) complex's overall charge of -2, palladium must have an oxidation state of +2. This piece of information is crucial as it directly influences the electron configuration of palladium, which in turn affects the magnetic properties and possible geometrical structure of the complex.

Electron Configuration in Complex Ions

Electron configuration describes the distribution of electrons of an atom or molecule in atomic or molecular orbitals. In transition metal complexes, the electron configuration of the metal ion dictates the chemical bonding and magnetic properties. For palladium (Pd), with an atomic number of 46, it typically has a full 4d subshell with ten electrons and an empty 5s subshell.

However, in the \(\left[\mathrm{PdCl}_{4}\right]^{2-}\) complex, Pd is in a +2 oxidation state, indicating the removal of two electrons. The electron configuration becomes \(4d^{8}\), with all eight d electrons optimally paired in a square planar geometry. This is an excellent example of how oxidation states and electron configurations combine to determine the structure of complex ions. Ultimately, for Pd(II), the lower energy state and absence of unpaired electrons, as evidenced by the diamagnetic property of the complex, confirms the electron configuration that supports a square planar structure over a tetrahedral one.