Question

How could you determine experimentally whether the compound \(\mathrm{Ga}_{2} \mathrm{Cl}_{4}\) contains two gallium(Il) ions or one gallium(I) and one gallium(III) ion? (Hint: Consider the electron configurations of the three possible ions.)

Short answer

To determine experimentally whether the compound \(\mathrm{Ga}_{2}\mathrm{Cl}_{4}\) contains two gallium(II) ions or one gallium(I) and one gallium(III) ion, perform X-ray photoelectron spectroscopy (XPS) on the compound. XPS will reveal the number of 4s electrons present in the bonding environment of the gallium ions. If the XPS results show equal numbers of 4s electrons for both gallium ions, it indicates the presence of two gallium(II) ions. If the results show a difference in the number of 4s electrons between the two gallium ions, it indicates the presence of one gallium(I) ion and one gallium(III) ion in the compound.

Step-by-step solution

Identify the electron configuration of gallium

The first step is to determine the electron configuration of a neutral gallium (Ga) atom. Gallium is element number 31, so it has 31 electrons in its neutral state. The electron configuration for gallium is: \[ 1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{10}4s^{2}4p^{1} \]

Determine electron configurations of possible gallium ions

Next, we will determine the electron configurations of the possible gallium ions: 1. Gallium(I) ion: This ion would have a single positive charge, meaning it has lost one electron. The electron configuration would be: \[ 1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{10}4s^{2}4p^{0} \] 2. Gallium(II) ion: This ion would have two positive charges, meaning it has lost two electrons. The electron configuration would be: \[ 1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{10}4s^{1}4p^{0} \] 3. Gallium(III) ion: This ion would have three positive charges, meaning it has lost three electrons. The electron configuration would be: \[ 1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{10}4s^{0}4p^{0} \]

Analyze the electron configurations

Two possible structures of the \(\mathrm{Ga}_2\mathrm{Cl}_4\) compound result from either two gallium(II) ions or one gallium(I) ion and one gallium(III) ion. 1. Two gallium(II) ions: If two gallium(II) ions are present, each ion would have the following electron configuration: \[ 1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{10}4s^{1}4p^{0} \] 2. One gallium(I) ion and one gallium(III) ion: In this case, one ion would have the electron configuration of a gallium(I) ion, while the other ion would have the electron configuration of a gallium(III) ion: - Gallium(I) ion: \[ 1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{10}4s^{2}4p^{0} \] - Gallium(III) ion: \[ 1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{10}4s^{0}4p^{0} \]

Design an experiment to differentiate between the two possibilities

One way to experimentally differentiate between the two possibilities is by analyzing the differences in their electron configurations, particularly the number of 4s electrons. In the case of two gallium(II) ions, each ion has one 4s electron. In the case of one gallium(I) ion and one gallium(III) ion, one ion has two 4s electrons while the other has none. An experiment that takes advantage of this difference is to perform X-ray photoelectron spectroscopy (XPS) on the \(\mathrm{Ga}_{2}\mathrm{Cl}_{4}\) compound. XPS can provide information about the elemental composition, chemical state, and electronic state of the elements within a material. In this case, XPS would reveal the number of 4s electrons present in the bonding environment of the gallium ions. If the XPS results show that there is an equal number of 4s electrons for both gallium ions, it would support the presence of two gallium(II) ions. If the results show a difference in the number of 4s electrons between the two gallium ions, it would support the presence of one gallium(I) ion and one gallium(III) ion in the compound.

Key concepts

X-ray photoelectron spectroscopy (XPS)

X-ray Photoelectron Spectroscopy, commonly referred to as XPS, is a powerful analytical technique used to study the surface chemistry of a material. By directing an X-ray beam onto the substance, electrons are knocked out from the atoms' core levels. These ejected electrons are then analyzed, providing detailed insights into the electrons' binding energies.
This information reveals not just the chemical composition of the material but also the electronic states of the elements present.

• Elemental Analysis: XPS is capable of identifying all elements except for hydrogen and helium.
• Chemical States: The method can identify different ionization states. Variations in electron binding energies can indicate different oxidation states of the same element.
• Surface Sensitivity: XPS is surface-sensitive, meaning it provides insights into the top few nanometers of a material.
• Non-destructive: As a non-destructive technique, XPS can analyze materials without causing undue damage.

In the context of our exercise, XPS helps differentiate between gallium ions with different electronic properties as indicated by their 4s electron count.

Ionization states

Understanding ionization states is crucial in exploring how atoms lose or gain electrons to form ions. Ionization refers to the process through which an atom loses electrons, resulting in positively charged ions.
Electrons are removed from the outer shell, transforming a neutral atom into an ion with a specific charge. The charge corresponds to the number of electrons lost.

• Gallium Ionization: Gallium can exist in multiple ionization states, such as Ga(I), Ga(II), and Ga(III), depending on how many electrons are removed from the neutral atom.
• Conceptual Understanding: The different ionization states of gallium reflect the atom’s ability to participate in various chemical reactions and bonding scenarios.
• Binding Energies: The energy required for removing an electron from an atom increases as more electrons are removed, which is a reflection of growing positive charge and stronger electron attraction.

In the problem, identifying the ionization states of gallium ions helps distinguish between potential ionic configurations in the compound \(\mathrm{Ga}_2\mathrm{Cl}_4\).

Electron configurations

Electron configurations describe the arrangement of electrons in the atomic orbitals of an atom. In the context of gallium, understanding the electron configuration is essential to predict how it forms ions and bonds.
The electron configuration of gallium is: \[ 1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{10}4s^{2}4p^{1} \]
When gallium ionizes, electrons are removed starting from the outermost shell.

• Electron Loss: As gallium becomes ionized, electrons are lost successively from the 4p, then 4s, and possibly from 3d orbitals.
• Gallium(I): Configuration becomes \[ 1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{10}4s^{2}4p^{0} \]
• Gallium(II): Configuration changes to \[ 1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{10}4s^{1}4p^{0} \]
• Gallium(III): Loses a third electron, resulting in \[ 1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{10}4s^{0}4p^{0} \]

These configurations are the blueprint for understanding how gallium will behave in different chemical situations. In analyzing \(\mathrm{Ga}_2\mathrm{Cl}_4\), the electron configuration sheds light on the possible oxidation states gallium can achieve.

Chemical composition analysis

Chemical composition analysis is the process of identifying the different elements present in a compound and determining their proportions. This analysis is vital for understanding the properties and potential applications of a substance.
Both qualitative and quantitative approaches are used to analyze chemical compositions.

• Qualitative Analysis: This aspect focuses on identifying the elements present without regard to their abundance.
• Quantitative Analysis: This involves determining the exact percent composition of each element within the compound.
• XPS for Analysis: XPS can serve a key role in chemical composition analysis by detecting elemental presence and their respective oxidation states.

In the case of our compound, \(\mathrm{Ga}_2\mathrm{Cl}_4\), determining the chemical composition involves analyzing the type of gallium ions present and how these align with the ionic charges of chlorine. By doing so, one can infer whether the composition supports the hypothesis of having two gallium(II) ions or a mixture of gallium(I) and gallium(III) ions.