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.)

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: \[ 1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{10}4s^{2}4p^{1} \]

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: \[ 1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{10}4s^{0}4p^{0} \]

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: \[ 1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{10}4s^{0}4p^{0} \]

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.