Lattice energy, PES, e- and more

Lattice Energy

Lattice energy is the energy required to completely separate one mole of a solid ionic compound into its gaseous ions. It is an indicator of the strength of the ionic bonds within a crystal lattice.

Key factors influencing lattice energy:

• Ion Charge: As the magnitude of the ion charges increases, the electrostatic attraction between ions increases, leading to a higher (more negative) lattice energy. (e.g., $MgS$ has higher lattice energy than $NaCl$).

• Ion Size: As the ionic radii decrease, the distance between the nuclei of oppositely charged ions decreases, resulting in stronger electrostatic attraction and higher lattice energy. (e.g., $LiF$ has higher lattice energy than $KF$).

• It can be calculated using the Born-Haber cycle, which applies Hess's Law to relate standard enthalpy changes to lattice energy.

$E<em>{lattice} \propto \frac{q</em>1 q<em>2}{r}$ Where $q</em>1$ and $q_2$ are the charges of the ions and $r$ is the distance between their centers.

Photoelectron Spectroscopy (PES)

PES is an experimental technique used to determine the relative energies of electrons in atoms and molecules, providing direct evidence for electron shell structure within an atom.

• Principle: A high-energy photon (usually X-ray or UV) strikes an atom, ejecting an electron. The kinetic energy of the ejected electron is measured.

• Binding Energy: The energy required to remove an electron from an atom is called binding energy (also known as ionization energy). It is calculated as: $\text{Binding Energy} = E<em>{photon} - KE</em>{electron}$.

• PES Spectrum Interpretation:

  • Peaks: Each peak in a PES spectrum corresponds to a subshell (e.g., $1s, 2s, 2p$). Electrons in the same subshell have the same binding energy.

  • Binding Energy Values: Higher binding energies (farther to the left on most spectra) correspond to electrons closer to the nucleus (core electrons), as they are more strongly attracted to the nucleus. Lower binding energies (farther to the right) correspond to valence electrons.

  • Peak Intensity (Height): The relative height or area of a peak is proportional to the number of electrons in that subshell. A peak for a $2p$ subshell (6 electrons) will be three times as intense as a peak for a $2s$ subshell (2 electrons).

Electron Configurations

Electron configuration describes the arrangement of electrons within an atom's orbitals.

1. Rules for Filling Orbitals:

   • Aufbau Principle: Electrons fill orbitals starting with the lowest energy level first.

   • Pauli Exclusion Principle: Each orbital can hold a maximum of two electrons, and they must have opposite spins.

   • Hund's Rule: For degenerate orbitals (orbitals of the same energy), electrons fill each orbital singly with parallel spins before pairing up.

2. Standard Configurations:

   • Write orbitals in increasing energy: $1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p$

   • Each $s$ orbital holds 2 electrons, $p$ holds 6, $d$ holds 10, $f$ holds 14.

   • Example: Oxygen (Z=8): $1s^2 2s^2 2p^4$

   • Noble Gas Shorthand: Use the noble gas preceding the element in brackets. Example: $[Ne] 3s^2 3p^1$

3. Exceptions to Aufbau Principle:

   • Elements with half-filled or completely filled $d$ subshells are more stable.

   • Chromium (Cr, Z=24): Expected $[Ar] 4s^2 3d^4$ but observed $[Ar] 4s^1 3d^5$

   • Copper (Cu, Z=29): Expected $[Ar] 4s^2 3d^9$ but observed $[Ar] 4s^1 3d^{10}$

   • Similar exceptions occur for elements below Cr and Cu in the periodic table (e.g., Mo, Ag, Au).

4. Electron Configurations of Ions:

   • Cations (positive ions): Remove electrons from the highest principal energy level (largest $n$ value) first. If $s$ and $p$ subshells are available at the highest $n$, remove $p$ electrons before $s$ electrons. For transition metals, remove electrons from the $ns$ orbital before the $(n-1)d$ orbital.

     • Example: $Fe$ ($[Ar] 4s^2 3d^6$) becomes $Fe^{2+}$ ($[Ar] 3d^6$) and $Fe^{3+}$ ($[Ar] 3d^5$).

   • Anions (negative ions): Add electrons to the lowest energy empty or partially filled orbitals according to Aufbau, Pauli, and Hund's rules.

     • Example: $O$ ($[He] 2s^2 2p^4$) becomes $O^{2-}$ ($[He] 2s^2 2p^6$).

Periodic Trends

Periodic trends are predictable patterns in elemental properties across the periodic table, mainly influenced by effective nuclear charge ($Z_{eff}$) and shielding.

1. Effective Nuclear Charge ($Z_{eff}$):

   • The net positive charge experienced by an electron in an atom. $Z_{eff} = Z - S$, where $Z$ is the atomic number (total nuclear charge) and $S$ is the number of core electrons (shielding electrons).

   • Trend: Increases across a period (due to increasing $Z$ with constant $S$), and remains relatively constant or slightly increases down a group (due to increasing $Z$ and $S$ proportionally).

2. Atomic Radius:

   • The distance from the nucleus to the outermost electron shell.

   • Trend: Decreases across a period (increasing $Z_{eff}$ pulls valence electrons closer). Increases down a group (more electron shells are added).

3. Ionic Radius:

   • Cations: Smaller than their parent atoms because they lose valence electrons, reducing electron-electron repulsion and often removing the outermost shell. ($Na^+$ vs. $Na$).

   • Anions: Larger than their parent atoms because they gain electrons, increasing electron-electron repulsion and pushing the electrons further apart. ($Cl^-$ vs. $Cl$).

   • Isoelectronic Series: For ions with the same number of electrons, ionic radius decreases with increasing nuclear charge (O^{2-} > F^- > Na^+ > Mg^{2+}).

4. Ionization Energy (IE):

   • The energy required to remove one electron from a gaseous atom or ion. (First IE: $X(g) \rightarrow X^+(g) + e^-$; Second IE: $X^+(g) \rightarrow X^{2+}(g) + e^-$).

   • Trend: Increases across a period (increasing $Z_{eff}$ makes it harder to remove electrons). Decreases down a group (outermost electrons are further from the nucleus and more shielded, thus easier to remove).

   • Exceptions: Drops occur for Group 13 (removing a $p$ electron is easier than an $s$ electron in the same shell) and Group 16 (pairing an electron in a $p$ orbital increases repulsion, making it easier to remove).

5. Electron Affinity (EA):

   • The energy change when an electron is added to a gaseous atom. ($X(g) + e^- \rightarrow X^-(g)$). Generally, a more negative (exothermic) EA indicates a greater attraction for electrons.

   • Trend: Generally becomes more negative (increases attraction) across a period (increasing $Z_{eff}$ leads to stronger attraction for an added electron). Generally becomes less negative (decreases attraction) down a group (larger atoms have less attraction for an added electron).

   • Halogens have the most negative electron affinities.

6. Electronegativity:

   • A measure of an atom's ability to attract electrons in a chemical bond.

   • Trend: Increases across a period (increasing $Z_{eff}$). Decreases down a group (electrons are farther from the nucleus).

   • Fluorine is the most electronegative element.