Question

Mercury in the environment can exist in oxidation states \(0,+1\), and \(+2\). One major question in environmental chemistry research is how to best measure the oxidation state of mercury in natural systems; this is made more complicated by the fact that mercury can be reduced or oxidized on surfaces differently than it would be if it were free in solution. XPS, X-ray photoelectron spectroscopy, is a technique related to PES (see Exercise 7.111), but instead of using ultraviolet light to eject valence electrons, \(\mathrm{X}\) rays are used to eject core electrons. The energies of the core electrons are different for different oxidation states of the element. In one set of experiments, researchers examined mercury contamination of minerals in water. They measured the XPS signals that corresponded to electrons ejected from mercury's \(4 f\) orbitals at \(105 \mathrm{eV}\), from an X-ray source that provided \(1253.6 \mathrm{eV}\) of energy. The oxygen on the mineral surface gave emitted electron energies at \(531 \mathrm{eV}\), corresponding to the \(1 s\) orbital of oxygen. Overall the researchers concluded that oxidation states were \(+2\) for \(\mathrm{Hg}\) and \(-2\) for \(\mathrm{O}\). (a) Calculate the wavelength of the \(\mathrm{X}\) rays used in this experiment. (b) Compare the energies of the \(4 f\) electrons in mercury and the \(1 s\) electrons in oxygen from these data to the first ionization energies of mercury and oxygen from the data in this chapter. (c) Write out the ground-state electron configurations for \(\mathrm{Hg}^{2+}\) and \(\mathrm{O}^{2-}\); which electrons are the valence electrons in each case? (d) Use Slater's rules to estimate \(Z_{\text {eff }}\) for the \(4 f\) and valence electrons of \(\mathrm{Hg}^{2+}\) and \(\mathrm{O}^{2-}\); assume for this purpose that all the inner electrons with \((n-3)\) or less screen a full \(+1\).

Short answer

In this exercise, we calculated the wavelength of the X-rays used in the experiment as \(9.875 \times 10^{7} \text{m}\). We compared the energies of the 4f electrons in Mercury and the 1s electrons in Oxygen with the first ionization energies to find that they differ significantly. We also determined the ground-state electron configurations for Hg^2+ and O^2-, and using Slater's rules, estimated the effective nuclear charge (Zeff) for the valence electrons in both ions to be +4.

Step-by-step solution

(a) Use Planck's equation to find the wavelength

From the given energy (1253.6 eV), we should first convert it into joules: 1 eV = 1.602 × 10^(-19) J So, 1253.6 eV = 1253.6 × 1.602 × 10^(-19) J = 2.008 × 10^(-16) J Now, we use Planck's equation to find the wavelength (λ): \[E = h \frac{c}{\lambda }\] Where E is the energy (in joules), h is Planck's constant (6.62607 x 10^(-34) Js), and c is the speed of light (3 × 10^8 m/s). Rearranging for λ, we get: \[\lambda = \frac{hc}{E}\] Now we plug in the values: \[\lambda = \frac{6.62607 \times 10^{-34} \text{ Js} \times 3 \times 10^8 \text{ m/s}}{2.008 \times 10^{-16} \text{ J}}\] \[\lambda = 9.875 \times 10^7 \text{ m}\] 2. (b) Compare the energies of the 4f electrons and 1s electrons to the first ionization energies

(b) Calculate energies of the 4f electrons and 1s electrons

We have the energies of the 4f orbitals for mercury (Hg) and the 1s orbitals for oxygen (O): - Mercury's 4f orbital = 105 eV - Oxygen's 1s orbital = 531 eV Now, we need to compare these with the first ionization energies from the text: - Mercury's first ionization energy = 1007.1 kJ/mol - Oxygen's first ionization energy = 1313.9 kJ/mol To compare, we need to convert these ionization energies into eV per atom as well: 1 kJ/mol = 96.49 eV/mol, so: - Mercury's first ionization energy = 1007.1 kJ/mol * (1/96.49 eV/mol) = 10.44 eV/atom - Oxygen's first ionization energy = 1313.9 kJ/mol * (1/96.49 eV/mol) = 13.62 eV/atom 3. (c) Write the ground-state electron configurations for Hg^2+ and O^2-

(c) Determine the electron configurations for Hg^2+ and O^2-

We should write the standard electron configuration for each ion: - Mercury (Hg): \[1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}3d^{10}4p^{6}5s^{2}4d^{10}5p^{6}6s^{2}5d^{10}4f^{14}5d^{10}6s^{2}\] Since it's Hg^2+ (meaning it lost 2 electrons), its electron configuration is: \[1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}3d^{10}4p^{6}5s^{2}4d^{10}5p^{6}6s^{2}4f^{14}5d^{10}\] - Oxygen (O): \[1s^{2}2s^{2}2p^{4}\] Since it's O^2- (meaning it gained 2 electrons), its electron configuration is: \[1s^{2}2s^{2}2p^{6}\] 4. (d) Estimate Zeff for the 4f and valence electrons of Hg^2+ and O^2-

(d) Calculate the effective nuclear charge (Zeff) for Hg^2+ and O^2-

We have to apply Slater's rules to estimate the effective nuclear charge (Zeff) for the valence electrons. The 4f electrons are the valence electrons for Hg^2+ and the 2p electrons for O^2-. We will assume that all the inner electrons with (n-3) or less screen a full +1 shield. - For the 4f electrons in Hg^2+: Zeff = Z - S = (80 - Total screening constant) = 80 - (2 + 2 + 6 + 2 + 6 + 2 + 10 + 6 + 2 + 10 + 6 + 2 + 14 + 10) = 80 - 76 = +4 - For the 2p electrons in O^2-: Zeff = Z - S = (8 - Total screening constant) = 8 - (2 + 2) = 8 - 4 = +4 So, Zeff for the 4f electrons in Hg^2+ is +4, and for the 2p electrons in O^2- is also +4.

Key concepts

Oxidation State Measurement

Understanding the oxidation states of elements, particularly in environmental chemistry, is crucial for interpreting how elements interact with their surroundings. The oxidation state, often referred to as the oxidation number, is a measure of the degree of oxidation of an atom in a chemical compound. Technically, it represents how many electrons an atom either gains or loses when it forms chemical bonds.

One common way to measure the oxidation state is by assessing the electron configuration of atoms in a molecule and following certain rules. For instance, the oxidation state of an atom in its elemental form is zero. When combined in a compound, the electron configuration changes and one can assign oxidation states based on the atom's tendency to attract electrons. In common practice, oxygen is usually assigned an oxidation state of (-2) and hydrogen is (+1), unless bonded to metals where it can be (-1).

However, a more sophisticated method used for determining oxidation states in a more complex environment, such as a mineral surface in water, is X-ray photoelectron spectroscopy (XPS). This process involves the analysis of the energy of electrons ejected from atoms in response to X-ray irradiation, which can reveal detailed information about the chemical state and environment of the atoms being studied. The variation in energy levels of emitted electrons corresponds to different oxidation states. This is because binding energies of core-level electrons are influenced by the effective nuclear charge experienced by these electrons, which changes with different oxidation states.

X-ray Photoelectron Spectroscopy (XPS)

XPS stands for X-ray photoelectron spectroscopy, a versatile and non-destructive analytical technique used to study the surface composition of materials. It operates on the basic principle of the photoelectric effect, where X-rays are used to eject core electrons from atoms, and the kinetic energy of these ejected electrons is measured.

In practice, a material is irradiated with an X-ray beam of known energy. Electrons are emitted from the sample's surface due to the interaction and their kinetic energy is analyzed. The analysis requires precise energy measurements since the differences in binding energies are often subtle. The binding energy depends on the electron configuration of the atom and is specific to each element and its oxidation state. As seen in the exercise, energies of mercury's 4f orbitals and oxygen's 1s orbitals were measured, offering insights into their respective chemical states.

An advantage of XPS is its ability to provide both quantitative and qualitative data about the surface layers of a material, often up to 10nm deep. It can determine not only what elements are present but also their chemical states, which can be crucial for environmental research where the surfaces of materials, and interactions at those surfaces, are of significant interest.

Electron Configuration

The electron configuration of an atom describes the distribution of electrons in atomic orbitals. Each electron occupies the lowest energy orbital available, a pattern known as the Aufbau principle. The electron configuration can predict chemical and physical properties, such as magnetism, chemical reactivity, and different state interactions.

For a neutral or charged atom (an ion), the electron configuration changes to reflect the gain or loss of electrons. For example, mercury in its 2+ ion state has lost two electrons compared to its neutral state. This electrons are lost from the outermost shell, altering the electron configuration significantly. Similarly, when oxygen gains two electrons to form an O2- ion, it achieves a noble gas configuration, which impacts its reactivity and interactions with other elements. Determining the electron configurations for elements in different oxidation states, as was done in the exercise for Hg2+ and O2-, is foundational for predicting how ions will behave chemically.

As students encounter problems like this, it's essential to comprehend how and why electron configurations change with ionization. This understanding leads to deeper insights into the fundamentals of chemistry, including the engagements of ions with their environments or in a variety of chemical reactions.