Question

Are compounds of these ground-state ions paramagnetic? (a) \(\mathrm{Ti}^{2+}\) (b) \(\mathrm{Zn}^{2+}\) (c) \(\mathrm{Ca}^{2+}\) (d) \(\mathrm{Sn}^{2+}\)

Short answer

(a) Paramagnetic, (b) Diamagnetic, (c) Diamagnetic, (d) Diamagnetic

Step-by-step solution

Determine the Electronic Configuration of Each Ion

Determine the ground-state electronic configuration of the neutral atoms and then account for the loss of electrons to form the ions. (a) \(\text{Ti: } 1s^2 2s^2 2p^6 3s^2 3p^6 3d^2 4s^2\) \( \text{Ti}^{2+}: 1s^2 2s^2 2p^6 3s^2 3p^6 3d^2 \) (b) \(\text{Zn: } 1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 \) \( \text{Zn}^{2+}: 1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} \) (c) \(\text{Ca: } 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 \) \( \text{Ca}^{2+}: 1s^2 2s^2 2p^6 3s^2 3p^6 \) (d) \(\text{Sn: } [Kr] 4d^{10} 5s^2 5p^2 \) \( \text{Sn}^{2+}: [Kr] 4d^{10} 5s^2 \)

Check for Unpaired Electrons

Evaluate the electronic configurations to see if there are any unpaired electrons, as unpaired electrons indicate paramagnetism. (a) \( \text{Ti}^{2+}: 3d^2 \rightarrow 2 \text{ unpaired electrons} \) (b) \( \text{Zn}^{2+}: 3d^{10} \rightarrow 0 \text{ unpaired electrons} \) (c) \( \text{Ca}^{2+}: 3p^6 \rightarrow 0 \text{ unpaired electrons} \) (d) \( \text{Sn}^{2+}: 5s^2 \rightarrow 0 \text{ unpaired electrons} \)

Determine Paramagnetic or Diamagnetic

Based on the presence of unpaired electrons, determine if the ion is paramagnetic (has unpaired electrons) or diamagnetic (no unpaired electrons). (a) \( \text{Ti}^{2+} \text{ is paramagnetic} \) (b) \( \text{Zn}^{2+} \text{ is diamagnetic} \) (c) \( \text{Ca}^{2+} \text{ is diamagnetic} \) (d) \( \text{Sn}^{2+} \text{ is diamagnetic} \)

Key concepts

Electronic Configuration

Understanding the electronic configuration of ions is crucial for determining their magnetic properties. The electronic configuration describes how electrons are distributed in an atom's orbitals. For an ion, we start with the neutral atom's configuration and then remove electrons to account for its charge.

For example, the neutral titanium atom (\text{Ti}) has the configuration: \(\text{1s}^2 2s^2 2p^6 3s^2 3p^6 3d^2 4s^2\). When forming \text{Ti}^{2+}, we lose two electrons, resulting in: \(\text{1s}^2 2s^2 2p^6 3s^2 3p^6 3d^2\).

Each ion’s electronic configuration helps us identify how many unpaired electrons it has, which is crucial for determining whether the ion is paramagnetic or diamagnetic.

Unpaired Electrons

The presence or absence of unpaired electrons in an ion directly affects its magnetic properties. Electrons fill orbitals following the Aufbau principle, Pauli exclusion principle, and Hund's rule.

An example is the \text{Ti}^{2+} ion, where the electronic configuration is \(\text{1s}^2 2s^2 2p^6 3s^2 3p^6 3d^2\). The 3d subshell has two electrons, both of which are unpaired.

In contrast, \text{Zn}^{2+} has the configuration \(\text{1s}^2 2s^2 2p^6 3s^2 3p^6 3d^{10}\), with a completely filled 3d subshell and no unpaired electrons.

Identifying unpaired electrons is essential for determining an ion's magnetic properties, and it is often done by drawing the electron distribution in the orbitals and observing whether each electron has a paired partner.

Diamagnetism

Diamagnetism is a property of materials where all electrons are paired, resulting in no net magnetic moment. When placed in a magnetic field, diamagnetic materials are weakly repelled. This is due to the generation of tiny currents in response to the external field, which create opposing magnetic fields.

An example of a diamagnetic ion is \text{Ca}^{2+}, which has an electronic configuration of \(\text{1s}^2 2s^2 2p^6 3s^2 3p^6\). Since all electrons are paired in \text{Ca}^{2+}, it has no net magnetic moment and is considered diamagnetic. Other diamagnetic ions from our exercise include \text{Zn}^{2+} and \text{Sn}^{2+}, both of which similarly have fully paired electrons in their respective configurations.

In contrast to paramagnetic substances, which have unpaired electrons and are attracted to magnetic fields, diamagnetic substances do not have unpaired electrons and are slightly repelled by magnetic fields.