Problem 112 - Chemistry The Central Science In Si Units

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, 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 \(\mathrm{X}\) -ray source that provided \(1253.6 \mathrm{eV}\) of energy \(\left(1 \mathrm{ev}=1.602 \times 10^{-19} \mathrm{~J}\right)\) 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 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?

Step-by-Step Solution

Answer

The wavelength of the X-rays is 0.988 nm. Hg\(^{2+}\): \([Xe] 4f^{14} 5d^{10}\); O\(^{2-}\): \([He] 2s^2 2p^6\).

Step 1: Calculate the Wavelength of X-rays

To find the wavelength \( \lambda \) of the X-rays used in the experiment, use the relation between energy \( E \), wavelength \( \lambda \), and the speed of light \( c \): \[ E = \frac{hc}{\lambda} \] where \( h \) is Planck's constant \( 6.626 \times 10^{-34} \text{ J s} \) and \( c \) is the speed of light \( 3.00 \times 10^8 \text{ m/s} \). The energy of the X-rays is given as 1253.6 eV, converting this to Joules: \[ 1253.6 \times 1.602 \times 10^{-19} \text{ J/eV} = 2.007 \times 10^{-16} \text{ J} \] Substitute the values into the equation to find \( \lambda \): \[ \lambda = \frac{6.626 \times 10^{-34} \times 3.00 \times 10^8}{2.007 \times 10^{-16}} \approx 9.88 \times 10^{-10} \text{ m} \] This corresponds to 0.988 nm.

Step 2: Compare Energy Levels

The ejected electrons from mercury's \( 4f \) orbitals have an energy of 105 eV and those from oxygen's \( 1s \) orbitals have 531 eV. To compare with the first ionization energies, note that ionization energy is the energy required to remove the most loosely bound electron (usually a valence electron). For mercury, the ionization energy is much lower (10.4375 eV), meaning that core electrons require much higher energy to be ejected compared to valence electrons. Similarly, the \( 1s \) electrons in oxygen require 531 eV, whereas the oxygen's ionization energy for valence electrons is approximately 13.618 eV.

Step 3: Write Electron Configurations

**Hg\(^{2+}\) Configuration:** Mercury (Hg) has an atomic number of 80, electron configuration: \([Xe] 4f^{14} 5d^{10} 6s^2\). Removing 2 electrons from the \( 6s \) orbital gives \([Xe] 4f^{14} 5d^{10}\). The valence electrons are the \( 5d \) electrons. **O\(^{2-}\) Configuration:** Oxygen has an atomic number of 8, electron configuration: \([He] 2s^2 2p^4\). Adding 2 electrons gives \([He] 2s^2 2p^6\). The valence shell includes the \( 2s \) and \( 2p \) electrons.

Step 4: Conclusion

The wavelength of the X-rays is 0.988 nm. The energies of core electrons are greater than those for ionization of valence electrons, indicating that energy is needed to remove inner electrons. The ground-state configurations reveal that \( 5d \) and \( 2p \) orbitals hold the respective valence electrons for Hg\(^{2+}\) and O\(^{2-}\).

Key Concepts

Oxidation States

An oxidation state in chemistry is the hypothetical charge that an atom would have if all bonds to atoms of different elements were fully ionic. The oxidation state represents the degree of oxidation of an atom within a molecule. In the case of mercury, it can exhibit various oxidation states, namely 0, +1, and +2. Being able to transition between these states complicates its behavior in different environments, such as natural systems. In the context of environmental chemistry, distinguishing the oxidation state of mercury is crucial for understanding its reactivity and potential toxicity. X-ray Photoelectron Spectroscopy (XPS) provides a powerful tool to determine these states by analyzing the energy required to eject core electrons, which differ with each oxidation state. This method provides scientists with essential insights into environmental processes and the chemistry involved.

Core Electrons

Core electrons are the electrons that reside close to an atom's nucleus. These electrons are not involved in bonding and are not as easily removed as valence electrons because they are held more tightly by the nucleus. Core electrons are crucial in determining the chemical properties of an element and can be studied using techniques like X-ray photoelectron spectroscopy (XPS).

• XPS involves using X-rays to eject core electrons from an atom.
• The energy needed to eject these core electrons is a reflection of how tightly bound they are.
• By analyzing the energies, scientists can infer information about the oxidation states and the chemical environment around the atoms.

Since core electrons are less affected by the environment compared to valence electrons, they offer more stable and reliable data in spectroscopic analysis.

Electron Configuration

Electron configuration is the distribution of electrons of an atom or molecule in atomic or molecular orbitals. Understanding electron configuration helps us predict chemical bonding, magnetic properties, and oxidation states of an atom. For instance, mercury (Hg) in its elemental form has an electron configuration of \([Xe] 4f^{14} 5d^{10} 6s^2\), but when it loses two electrons to form \(Hg^{2+}\), its configuration becomes\([Xe] 4f^{14} 5d^{10}\).

Here, the mercury ion is more stable as (\(Hg^{2+}\)) by the removal of the electrons in the 6s orbital.

• This shows why the core electrons, such as those in the 4f and 5d orbitals, are not typically involved in chemistry.
• Oxygen, on the other hand, normally has the electron configuration \([He] 2s^2 2p^4\). When it gains two electrons to become \(O^{2-}\), the configuration changes to\([He] 2s^2 2p^6\).
• The electron configurations thus help explain the forms and stability of ions.

Ionization Energy

Ionization energy is the amount of energy required to remove the most loosely bound electron of an isolated gaseous atom. This concept is important in understanding atom stability and reactivity. Ionization energy can differ greatly between core and valence electrons.

When core electrons are ejected, as in XPS experiments, much higher energies are necessary compared to merely removing a valence electron. The first ionization energy of mercury is remarkably low in comparison to the energy to remove its core 4f electrons. This phenomenon reflects the stability and shielding effect of full electron shells surrounding the nucleus.

• For instance, mercury's first ionization energy is 10.4375 eV, quite different from the 105 eV needed to remove a core electron.
• Oxygen exhibits similar behavior where losing a 1s core electron requires 531 eV, while the energy to lose a valence electron is just 13.618 eV.
• This difference demonstrates that more energy is required to remove core electrons due to the forces binding them within the atom.

High ionization energies for core electrons are essential for techniques like XPS, providing vital insights into atom composition and states.