Periodic Properties of the Elements

THE DEVELOPMENT OF THE PERIODIC TABLE

  • Study the development of the Periodic Table through Section 8-2 on pages 303-304 (not covered in class).

ELECTRON CONFIGURATIONS, VALENCE ELECTRONS, & THE PERIODIC TABLE

  • Review Section 8-3 on pages 304-308 (not all material covered in class).
  • The periodic table can be categorized into four distinct blocks based on the subshells being filled:
    • s block: Highest principal quantum number ($n$) fills s orbitals.
    • p block: Highest principal quantum number ($n$) fills p orbitals.
    • d block: d orbitals of the electronic shell corresponding to $(n - 1)$ fill.
    • f block: f orbitals of the electronic shell corresponding to $(n - 2)$ fill.
  • These divisions facilitate the assignment of electron configurations.

THE EXPLANATORY POWER OF THE QUANTUM-MECHANICAL MODEL

  • Elements within the same group share similar electronic configurations (Section 8-4).
  • Similar chemical properties are observed in elements of a group.
  • The structure of the periodic table is experimental-based.
  • Quantum mechanics provide electron configurations that determine the chemical properties of elements, aligning theory with experimental results.
  • Refer to Section 8-4 on pages 308-309 (not covered in class).

PERIODIC TRENDS IN THE SIZE OF ATOMS & EFFECTIVE NUCLEAR CHARGE

Atomic Radius (Section 8-5)

  • Atomic radius: Distance between the nuclei of two atoms bonded together.
  • Covalent radius: Half the distance between the nuclei of two identical atoms bound by a single covalent bond.
  • Ionic radius: Distance between the nuclei of ions involved in an ionic bond. For instance, the radius of O$^{2-}$ is conventionally assigned as 140 pm.
  • Metallic radius: Half the distance between the nuclei of two atoms in contact in a crystalline metal.
  • Van der Waals radius: Similar to metallic radius but specifically applies to noble gases in solid form.
  • It is crucial to differentiate between covalent, ionic, metallic, and van der Waals radii.

Categories of Electrons (from Section 8-3)

  1. Inner (core) electrons: Electrons within the previous noble gas configuration and completed transition series; they entirely fill the lower energy levels of an atom.
  2. Outer electrons: Electrons in the highest energy level with the highest principal quantum number ($n$); these electrons typically reside furthest from the nucleus.
  3. Valence electrons: Electrons involved in compound formation;
    • Among main group elements, these are the outer electrons.
    • For transition elements, some inner d electrons also participate in bonding and count as valence electrons.

EFFECTIVE NUCLEAR CHARGE

  • The effective nuclear charge, denoted as $Z{eff}$, can be calculated using: Z{eff} = Z - S
    • Where:
      • $Z$: Actual nuclear charge.
      • $S$: Amount of charge shielded by all other electrons.
  • For most atoms (excluding Hydrogen), the $Z_{eff}$ for a valence electron is considerably less than $Z$ (Section 8-5).
    • This reduction is due to screening effects.
    • Valence electrons are significantly shielded by inner (core) electrons, but they only minimally shield each other.
    • $Z_{eff}$ decreases for electrons in the same shell as the azimuthal quantum number ($l$) increases, due to the penetration effects.
    • $Z_{eff}$ increases from left to right across a period and decreases from top to bottom.

SLATER’S RULES

  • Slater’s Rules help calculate the shielding contribution $S$ for a given electron:
    • Used to find contributions from different types of electrons:
    • Electron groups:
    • Core electrons (lower shells)
      • $0.35$ for electrons in same shell ($n$).
      • $0.85$ for core electrons in Shell $(n - 1)$.
      • $1.00$ for core electrons in shells < $(n - 1)$ (e.g., $n - 2, n - 3, \, ..$).
    • For ns or np electrons:
      • $S = N{ff} * 0.35 + N{ns, np} * 0.85 + N_{core} * 1.00$
    • For nd or nf electrons:
      • $S = N{ff} * 0.35 + N{nd, nf} * 1.00 + N_{core} * 1.00$.

EXAMPLES AND PRACTICE

  • Example: Calculate $Z_{eff}$ for F, Ar, Rb. See Practice Example 8-3 on page 314.

VARIATIONS IN ATOMIC RADIUS

  • The relationship between atomic radius $r \ ext{and} \ effective nuclear charge \ Z{eff}$ is expressed as: r{atomic} \propto n(Z_{eff})
    • Where $r_{atomic}$ is the average distance of an electron from the nucleus.
    • Down a group:
      • The value of $n$ dominates. The presence of more inner electrons enhances shielding on outer electrons.
      • $Z{eff}$ varies down the group, but $n^2$ increases more rapidly than $Z{eff}$.
      • More significant $n$ value corresponds to electrons being positioned further away from the nucleus, leading to an increase in atomic radius from top to bottom.
      • General trend: Atomic radius increases from top to bottom within a group.
    • Across a period:
      • $Z_{eff}$ dominates. As electrons are added to the same outer level across a period, $n$ remains constant.
      • Outer electrons minimally shield each other, but as $Z_{eff}$ increases, outer electrons are drawn closer to the nucleus.
      • General trend: Atomic radius decreases from left to right across a period.

TRANSITION METALS

  • In transition metals:
    • Filling of inner d orbitals occurs.
    • The outer s electrons experience approximately the same $Z_{eff}$ for row 4 transition elements.
    • As you move down a group, $n$ increases, but the shielding results in minimal size changes.
    • No size variations from period 4 to period 5 and no change from periods 5 to 6.
    • Shielding by d electrons causes significant size reduction from group 2 to group 13 in periods 4 to 6.
    • 3rd row transition elements size remains stable compared to 2nd row due to ineffective shielding by 4f electrons. This phenomenon is referred to as lanthanide contraction.

IONIC RADIUS

  • Isoelectronic ions: Ions possessing the same number of electrons in identical configurations (Section 8-6).
    • Example: Na$^{+}$ and Mg$^{2+}$ both exhibit the electronic configuration of 1s$^2$2s$^2$2p$^6$.
  • Ionic Radius:
    • Cations are smaller than their parent atoms; for isoelectronic cations, a more positive charge correlates to a smaller radius.
    • For multiple cationization cases, the ionic radius decreases with increased positive charge (e.g., Fe$^{2+}$ > Fe$^{3+}$).
    • Conversely, anions are larger than their parent atoms; more negative charge corresponds to a larger ionic radius among isoelectronic anions.
    • In isoelectronic series containing both cations and anions, the size of anions from the lower period is larger than cations from the higher period due to greater $Z_{eff}$.

EXAMPLES RANKING ELEMENTS BY ATOMIC SIZE

  1. Rank in order of decreasing atomic size:
    • a) Cl, F, I, Br → I > Br > Cl > F (Atomic size diminishes up a group).
    • b) Br, As, Se → As > Se > Br (Atomic size diminishes across a period).
    • c) S, O, P → P > S > O (Atomic size decreases across a period and also S > O up a group).
  2. Determine decreasing radius order for species:
    • S, Ca, F, Rb, Si.
  3. Determine increasing size order:
    • Ti$^{2+}$, V$^{3+}$, Ca$^{2+}$, Br$^{–}$, Sr$^{2+}$.
  4. Identify the third largest species:
    • Among N, Cs, As, Mg$^{2+}$, and Br$^{–}$.

IONIZATION ENERGY

Definitions and Overview (Section 8-7)

  • Ionization Energy, E_i: Amount of energy required to expel an electron from a gaseous atom.
    • The electron expelled is the one most loosely held.
    • Multi-electron atoms can lose more than one electron.
    • The first ionization energy removes the outermost electron:
    • ext{atom (g)} \rightarrow \text{ion}^{+} (g) + e^– \quad (\Delta E = E_{i1} > 0)
    • The second ionization energy removes another electron:
    • \text{ion}^{+} (g) \rightarrow \text{ion}^{2+} (g) + e^– \quad (\Delta E = E{i2} ext{ always } > E{i1})

TRENDS IN IONIZATION ENERGY

  1. Down a group:
    • E_i generally decreases as atomic size increases.
  2. Across a period:
    • Ei increases due to higher $Z{eff}$ as atomic size decreases.
    • The attraction between the nucleus and outer electrons intensifies, making it harder to remove an electron.
  3. Observational anomalies:
    • Ei for B < Ei for Be;
    • Ei for Al < Ei for Mg;
    • Ei for O < Ei for N;
    • Ei for S < Ei for P.
    • Notably, removing core electrons requires significantly higher energy leading to significant jumps in E_i.

ELECTRON AFFINITIES & METALLIC CHARACTER

Electron Affinity, E_{ea} (Section 8-8)

  • Definition: Change in enthalpy, ΔeaH, that occurs when a gaseous atom gains an electron:
    • ext{atom (g)} + e^– \rightarrow \text{ion}^{–} (g) \quad (\Delta eaH = E_{ea1})
    • Alternatively, energy change that occurs when an anion loses an electron:
    • ext{ion}^{–} (g) \rightarrow ext{atom (g)} + e^– \quad (\Delta H = - \Delta eaH = - E_{ea1})
  • In a majority of scenarios, energy is released when the first electron is added, indicating a net attraction between the atom and incoming electron. Occasionally, energy is absorbed to add an electron.

TRENDS IN ELECTRON AFFINITY

  1. Down a group:
    • ΔeaH for $E_{ea1}$ is most negative in 3rd-period atoms (ignoring elements in groups 2, 15, 18).
    • ΔeaH becomes less negative for atoms in the 4th period or later.
  2. Across a period:
    • ΔeaH values become more negative from left to right (excluding groups 2, 15, 18).
    • This trend underscores a growing propensity of elements to attract electrons.
    • In general, $E_{ea1}$ is more negative as you traverse up a group and across a period.
  3. **Second electron affinity **:
    • The second electron affinity (EA2) remains positive due to the energy absorption required to overcome electrostatic repulsions when adding another electron:
    • O (g) + e^{–} \rightarrow O^{–} (g) \ (\Delta eaH [O (g)] = E_{ea1} = -141.0 \, \text{kJ/mol})
    • O^{–} (g) + e^{–} \rightarrow O^{2-} (g) \ (\Delta eaH [O^{–} (g)] = E_{ea2} = +744 \, \text{kJ/mol})

METALLIC PROPERTIES

  • Characteristics:
    • Metals exhibit moderate to high melting points, good electrical conductivity, malleability, ductility, and a propensity to lose electrons compared to non-metals.
  • Trends:
    • Metallic behavior increases down a group.
    • Metallic character increases from right to left across the period, owing to their low ionization energy.

OBJECTIVES OF STUDY

  • After studying this material, students should be able to:
    • Developments of the Periodic Table: Describe the evolution and structure of the Periodic Table.
    • Electron Configurations: Relate periodic table structure to electronic configurations and articulate configurations in elements, including transition metals.
    • Periodic Trends in Atomic Size: Explain variations in atomic radii with atomic number and relate this variation to effective nuclear charge.
    • Slater's Rules: Utilize Slater’s rules for effective nuclear charge calculations.
    • Ionic Radii: Define isoeletronic series and their influence on changes in ionic radii.
    • Ionization Energy: Account for observed variations in first ionization energies and changes in successive values for given atoms.
    • Electron Affinities & Metallic Character: Explain electron affinity concepts, variations with atomic number, and trends in metallic properties according to atomic number.

END OF NOTES