Exam Study Notes

Electron Configurations and the Periodic Table

• The n=2 shell can hold 8 electrons.
• When starting the n=3 shell, the 3s and 3p subshells are close in energy, but the 3d subshell is much higher in energy.
• The 4s subshell lies lower in energy than the 3d subshell.
• After filling the 3s and 3p subshells with 8 electrons, we begin filling the 4s subshell.

Valence Electrons

• Electrons are arranged in shells (n), with the lowest n closest to the nucleus.
• At the end of each period, a new shell of electrons must be started.
• The outermost shell is the Valence Shell.
• Inner shells are the Core, and they are held tightly to the nucleus.
• All elements in a group have the same number and type of valence electrons that all feel the same effective nuclear charge: Z_{eff}.
  • Z_{eff} = #valence e-
• Only valence electrons are involved in interactions with other atoms.
• The number and type of valence electrons determine the chemical properties of an atom.

Periods and Groups in the Periodic Table

• The periodic table is organized into periods (rows) and groups (columns).
• Different blocks (s-block, p-block, d-block, f-block) correspond to the filling of different orbitals.
• Electron configurations are related to the position of an element in the periodic table.

Periodic Table and Quantum Mechanics

• The layout of the periodic table is determined by the rules of quantum mechanics.
• Two electrons can occupy each orbital.
• An s subshell has one orbital, so there are two columns in the s-block.
• A p subshell has three orbitals, so there are six columns in the p-block.
• A d subshell has five orbitals, so there are ten columns in the d-block.
• If the rules of quantum mechanics were different, the periodic table would be different. Hypothetically, if m_s could have three values, there would be three s columns instead of two.

Electron Configurations from Periodic Table Position

• The periodic table position determines the electron configuration.
• Example: Selenium (Se)
  • [Ar] 4s^2 3d^{10} 4p^4
  • Nearest noble gas Core configuration

Transition Elements

• At the start of the transition elements, the 4s orbital is lower in energy than the 3d orbital (4s < 3d).
• As we move across the period, we add 1 proton (p^+) and 1 electron (e^-).
• The 3d orbital drops in energy more rapidly than the 4s orbital.
• Chromium (Cr) and Copper (Cu) are exceptions.
  • Cr: [Ar] 4s^1 3d^5
• In Chromium, one electron will go into an empty 3d orbital rather than pair up in 4s because the 3d is close enough to 4s energy level.

Transition Elements Exceptions

• Chromium (Cr) and Copper (Cu) are exceptions that arise from the relative orbital energies, and there's no need to memorize them.
• The 4d/5s crossing occurs between Technetium (Tc) and Ruthenium (Ru), so there are different exceptions.
• For p-block elements, (n-1)d << ns, so only the s and p electrons are valence electrons. Hence, Selenium (Se) has the same valence electrons and similar chemical properties as Sulfur (S).
• Lanthanides and Actinides fill the f orbitals.
  • Here, (n-2)f, (n-1)d, and ns are all close in energy.

Ionic Compounds

• Ionic compounds are held together by the coulombic attraction between cations and anions, lattice energy (Chapter 10).
• To be stable, the energy to ionize the metal (form cations) must not be too large.
• Alkali metals have one valence electron in the outer shell, which is easy to remove. Removing the next electron would be from the core, so they always form 1+ ions.

Ion Configurations

• Cations: remove electron(s), 1 electron for each positive charge, highest energy electrons first.
• s-block elements lose all their valence electrons.
• p-block metals lose their p electrons and sometimes their s electrons.
• NEVER go beyond the valence shell – core electrons are very tightly held.

Electronic Configuration Examples

• Mg^{2+} ion (12-2) electrons: 1s^2, 2s^2, 2p^6 = [Ne]
• Sn^{2+} ion (4-2) valence electrons: [Kr]4d^{10}5s^2
• Sn^{4+} ion: [Kr]4d^{10}

Ion Configurations (Anions)

• Anions: add electron(s), 1 electron for each negative charge.
• p-block elements add electrons to fill their valence shell – a new shell would be too high in energy to enter.
• Example: S^{2-} ion (16 + 2) electrons: 1s^2, 2s^2, 2p^6, 3s^2, 3p^6 = [Ar]

Elements that form Ions with Noble Gas Configurations

• Elements close to the noble gases are very reactive, and they readily gain or lose electrons to reach the stable closed shell noble gas electron configuration.

Electron Configurations of Cations

• Always remove the highest energy electrons in the cation first.
• These are not necessarily the highest energy electrons for the neutral atom, as the extra positive charge can change the energy level ordering.
• The energy of the 3d orbitals lies below 4s for all the transition metal ions.
• (n-1)d < ns for all transition element ions.

Transition Metal Ions

• Hence, we remove the 4s before 3d electrons when making ions.
• Always remove the highest n electrons first.
  • Co: [Ar]4s^2 3d^7
  • Co^{2+}: [Ar]3d^7
  • Co^{3+}: [Ar]3d^6
• Many transition elements form stable 2+ ions by losing both of their s valence electrons.

Magnetism

• Magnetism is a result of the spin of unpaired electrons.
  • Diamagnetism: no unpaired electrons
  • Paramagnetism: one or more unpaired electrons
  • Ferromagnetism: case of paramagnetism where the spins of different nuclei are aligned

Example: Vanadium (V)

• V has 23 electrons.
• [Ar] 4s^2 3d^3
• Has 3 unpaired electrons.
• It is paramagnetic.

Atomic Radius

• Metals and noble gases: ½ the separation of atoms in a crystal.
• Nonmetals: covalent bonding radius – half the bond length in the diatomic molecule.

Trends in Atomic Radius

• Decreases left to right across a period.
• Increases top to bottom down a group.
• Largest radius in the bottom left of the periodic table.
• Smallest radius in the top right of the periodic table.
• Down a group, the principal quantum number n for the valence electrons increases, so the electron is further away from the nucleus.

Shielding

• Properties of the elements are determined by how strongly bound their valence electrons are.
• The greater the effective charge (Z_{eff} = Z - s) that an electron feels, the more strongly it is attracted to the nucleus, and thus the larger its ionization energy and smaller its radius.
• Simplest approximation: core electrons shield completely, and valence electrons do not shield at all. So, s = number of core electrons.
• For the main group (s & p blocks) elements Z_{eff} ≈ #valence electrons = group number.

Atomic Radius (Explanation)

• Decreases left to right across a period.
• Using our simple model, we see that the valence electrons in each successive element across a period feel a Z_{eff} 1 higher. From +1 for Li to +8 for Ne.
• Electrons are pulled in closer.
• Radius decreases.
• Valence electrons do in fact shield a little, but Z_{eff} really does increase steadily across a period.

Atomic Radius for Transition Metals

• First period has electron configuration [Ar]4s^2 3d^n where n=1 through 10.
• While the 4s orbital is slightly lower in energy it has a larger radius than 3d.
• With each successive element Z increases by 1, and a 3d electron is added.
• The 4s electrons are effectively shielded from the increasing charge across the period by the added 3d electrons so they feel a Z_{eff} » 2 in every element.
• The radius stays roughly constant.

Ionic Radii

• Positive ions are always smaller than the atom.
  • Same nuclear charge pulling on fewer electrons.
  • Pulls them in closer.
  • Often lose all valence electrons leaving only the core which is much smaller.
• Negative ions are always larger than the atom.
  • Same nuclear charge pulling on more electrons.
  • They end up further away.
• Cations show the same general trends as neutral atoms, smaller towards the top and right of the periodic table.
• Anions show the same general trends as neutral atoms, smaller towards the top and right of the periodic table.

Ionic Radius Isoelectronic Series

• Isoelectronic Series: series of negative and positive ions with the same electronic configuration. Example: S^{2-}, Cl^-, Ar, K^+, Ca^{2+}
• All have the same number of electrons, but as the nuclear charge increases it exerts a greater pull on the electrons.
• A greater charge pulls on the same number of electrons, so size decreases as the positive charge increases.