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 7.107 ), but instead of using ultraviolet light to eject valence electrons, 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 forbitals 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 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

The wavelength of the X-rays used in this experiment is calculated as λ ≈ \(9.92 \times 10^{-11} m\). Comparing the energies of the 4f electrons in Mercury and the 1s electrons in Oxygen to their first ionization energies, it's seen that the core electron energies are much higher than the valence electron energies. Hg^(2+) has an electron configuration of [Xe] 4f^14 5d^8 with valence electrons in the 5d orbital, and O^(2-) has an electron configuration of [He] 2s^2 2p^6 with valence electrons in the 2s and 2p orbitals. Estimating Z_eff using Slater's rules, we find that Hg^(2+) has a Z_eff of 5 for its 4f electrons, and O^(2-) has a Z_eff of 7.3 for its valence electrons.

Step-by-step solution

(a) Calculate the wavelength of the X-rays used in this experiment

To find the wavelength of the X-rays used in the experiment, we can use the relation between energy and wavelength of an electromagnetic wave, given by Planck's equation: \(E = h \cdot c / \lambda\) where: E = energy (1253.6 eV = 1253.6 * 1.6 × 10^(-19) J) h = Planck's constant (\(6.626 \times 10^{-34} \text{J s}\)) c = speed of light (\(3.00 \times 10^8 \text{m s}^{-1}\)) \(\lambda\) = wavelength Solving for \(\lambda\), we have: \(\lambda = \frac{h \cdot c}{E}\)

(b) Compare the energies of the 4f electrons in mercury and the 1s electrons in oxygen

The energies of the 4f electrons in mercury and the 1s electrons in oxygen can be found from the given code in the problem: 105 eV for Mercury and 531 eV for Oxygen. The first ionization energies of Mercury and Oxygen can be found from provided data or literature values: - First ionization energy of Mercury: 10.44 eV - First ionization energy of Oxygen: 13.61 eV Now we can compare the energies: Mercury: 105 eV (4f electrons) compared to 10.44 eV (first ionization) Oxygen: 531 eV (1s electrons) compared to 13.61 eV (first ionization)

(c) Ground-state electron configurations and valence electrons of Hg^(2+) and O^(2-)

The ground-state electron configurations for Hg^(2+) and O^(2-) are: - Hg^(2+): [Xe] 4f^14 5d^8 - O^(2-): [He] 2s^2 2p^6 In each case, the valence electrons are: - Hg^(2+): 5d - O^(2-): 2s and 2p

(d) Z_eff estimation for the 4f and valence electrons of Hg^(2+) and O^(2-)

Using Slater's rules, we can estimate the effective nuclear charge (Z_eff) for the 4f and valence electrons of each ion: Hg^(2+): Z_eff (4f) = Z - S Z = atomic number of Hg = 80 S = total shielding factor due to other electrons: S(4f) = screening effect from 1s + 2s + 2p + ... + 3d = 1 * 75 = 75 Z_eff (4f) = 80 - 75 = 5 O^(2-): Z_eff (valence) = Z - S Z = atomic number of O = 8 S = total shielding factor due to other electrons: S(2s) = screening effect from 1s = 2 * 0.35 = 0.7 S(2p) = screening effect from 1s = 2 * 0.35 = 0.7 Z_eff (valence) = 8 - 0.7 = 7.3 Estimated Z_eff values: - Hg^(2+) 4f electrons: 5 - O^(2-) valence electrons: 7.3

Key concepts

Oxidation States

Oxidation states refer to the charge of an element in a compound, which results from its loss or gain of electrons. For mercury, common oxidation states include 0, +1, and +2. In environmental contexts, understanding these states helps determine how mercury interacts with other elements, such as oxygen, particularly on mineral surfaces. This interaction can differ greatly from mercury's behavior in solution. X-ray Photoelectron Spectroscopy (XPS) is a pivotal technique used to identify these oxidation states. XPS measures the energy levels of core electrons, revealing differences in the oxidation states of an element like mercury.

• 0 - No net charge, elemental mercury
• +1 - One electron lost, forming mercurous ions
• +2 - Two electrons lost, forming mercuric ions

This technique becomes essential in diagnosing mercury contamination and its potential impacts on the environment.

Effective Nuclear Charge

The effective nuclear charge ( Z_{eff} ) is the net positive charge experienced by electrons in an atom. It's important for understanding how tightly an electron is held by the nucleus. Calculating Z_{eff} requires considering both the proton's positive charge and the negating effects of inner electron repulsion or shielding. For mercury ( Hg^{2+} ), the calculation involves its 80 protons and inner electron shielding:

• Using Slater's rules, we estimate the shielding effect ( S ) based on other electrons (1s to 3d ), which strongly repel the 4f electrons.
• The resulting Z_{eff} for 4f electrons is 5, signifying moderate attraction.

For oxygen's anion ( O^{2-} ):

• The presence of 8 protons and shielding mainly from the 1s level, provides a less obstructive environment.
• The Z_{eff} for valence electrons, typically in 2s and 2p orbitals, is 7.3, indicating high effective nuclear charge compared to their shielding.

Understanding Z_{eff} aids in analyzing electron configurations and predicting ion properties.

Ground-State Electron Configuration

Electron configuration describes the distribution of electrons around an atom's nucleus. For ions like Hg^{2+} and O^{2-}, this reflects their stable states after electron gain or loss.**Mercury (Hg^{2+}):**The ground-state configuration is \([Xe] 4f^{14} 5d^{10} 6s^0\). This order highlights:

• Removal of two 6s electrons upon ionization.
• The stability and full filling of 4f and 5d orbitals, noting 5d acts as valence electrons.

**Oxygen (O^{2-}):**For this reduced ion, the configuration is \([He] 2s^2 2p^6\), achieving:

• Full 2p orbital, gaining two electrons for stability.
• The 2s and 2p levels are considered valence electrons, contributing to reactivity.

These configurations clarify the electronic structure and align with the element's chemical behavior, particularly in compound formation.

Ionization Energy

Ionization energy is the energy required to remove an electron from an isolated atom. It serves as an indicator of an atom's hold on its electrons, influenced by the effective nuclear charge. For mercury and oxygen, there are distinct differences:

• Mercury's first ionization energy is relatively low, at 10.44 eV. This reflects the higher shielding effects from inner layers, making outer electrons easier to remove, particularly from the 6s level.
• Oxygen has a higher ionization energy of 13.61 eV, indicative of its stronger hold on valence electrons due to the lesser shielding effect experienced by electrons in the 2p orbital.

Comparing these ionization energies with the core electron energies further through XPS data reveals deeper insights. While outer electrons are the focus in ionization energy, core electrons require significantly more energy to eject, as seen in mercury's 4f (105 eV) and oxygen's 1s (531 eV) electrons. Understanding these relationships helps predict the reactivity and interaction of elements.