Periodic Properties Study Notes

Periodic Properties Subtopics

• Historical Development of Periodic Table

• Modern Periodic Table

• Structure, Merits and Demerits of Modern Periodic Table

• Screening effect

• Atomic Radii

• Ionic Radii

• Ionisation enthalpy

• Electron gain enthalpy or electron affinity

• Electronegativity

• Diagonal relationship

• Valency and oxidation state

Ionic Radii and Isoelectronic Species

• Definition of Isoelectronic Species: Atoms or ions that possess the same number of electrons (e.g., $10\,e^-$ or $18\,e^-$ clusters).

• Ionic Radii Comparison (Isoelectronic):

  • For isoelectronic species, as the positive nuclear charge increases, the ionic radius decreases.

  • Example for $10\,e^-$ species: The order of increasing ionic radii is Al^{3+} < Mg^{2+} < Na^+ < K^+.

  • Example for $18\,e^-$ species: In the case of $Cl^-, Ca^{2+}, K^+,$ and $S^{2-}$, the correct increasing order of ionic radii is Ca^{2+} < K^+ < Cl^- < S^{2-}.

• Assertion-Reason Case:

  • Assertion (A): The ionic radii of $O^{2-}$ and $Mg^{2+}$ are the same.

  • Reason (R): Both $O^{2-}$ and $Mg^{2+}$ are isoelectronic species.

  • Conclusion: (A) is false but (R) is true. While they have the same number of electrons ($10$), their different nuclear charges result in different radii (the cation $Mg^{2+}$ is smaller than the anion $O^{2-}$).

lonization Enthalpy (IE), Potential (IP), and Definition

• Definition: lonization energy (or ionization potential/enthalpy) is the minimum amount of energy required to remove an electron ($e^-$) from an isolated gaseous atom in its ground state.

• General Equation:

  • $A(g) \rightarrow A^+(g) + e^-(g)$

• Units of Measurement:

  • $eV/atom$

  • $J/atom$

  • $kJ/atom$

  • $Kcal/atom$

• Thermodynamics of Ionization:

  • Enthalpy change ($\Delta H$): This represents heat change.

  • Endothermic Process: Removing an electron requires an input of energy, so $\Delta H = +ve$. The ionization energy for an atom is always positive.

  • Exothermic Process: Highlighting that for an anion, $\Delta H$ may be negative ($\Delta H = -ve$), meaning heat is released.

Successive lonization Energy

• The energy required to remove electrons sequentially from an atom is termed successive ionization energy:

  1. First Ionization Energy ($IE_1$): $A(g) \rightarrow A^+(g) + e^-$

  2. Second Ionization Energy ($IE_2$): $A^+(g) \rightarrow A^{2+}(g) + e^-$

  3. Third Ionization Energy ($IE_3$): $A^{2+}(g) \rightarrow A^{3+}(g) + e^-$

  4. Fourth Ionization Energy ($IE_4$): $A^{3+}(g) \rightarrow A^{4+}(g) + e^-$

• Universal Rule: Successive ionization energies always increase because it becomes progressively harder to remove a negative electron from an increasingly positive ion.

  • Relationship: IE_1 < IE_2 < IE_3 < IE_4

• Case Study (Magnesium): If $IE_1$ for $Mg$ is $+737\,kJ/mol$, the estimated value of $IE_2$ is significantly higher ($+1450\,kJ/mol$).

• Identifying Groups via IE Jumps: Large gaps between successive ionization energies indicate the removal of an electron from a stable, inner shell (noble gas configuration).

  • Example: For an element with successive $IE$ values of $800, 2427, 3658, 25024$, and $32824\,kJ/mol$, the massive jump between $IE_3$ and $IE_4$ suggests there are $3$ valence electrons. Thus, the element belongs to Group 13.

Factors Affecting lonization Enthalpy

1. Atomic Size / Number of Shells:

   • Ionization Enthalpy is inversely proportional to atomic size: $IE \propto \frac{1}{\text{Atomic size}}$. As size increases, the outer electron is further from the nucleus and easier to remove.

2. Nuclear Charge:

   • Ionization Enthalpy is directly proportional to nuclear charge: $IE \propto \text{Nuclear charge}$. A higher positive charge holds electrons more tightly.

3. Shielding / Screening Effect (S.E.):

   • Ionization Enthalpy is inversely proportional to shielding: $IE \propto \frac{1}{S.E.}$.

   • Shielding power of orbitals: s > p > d > f. Best shielding leads to lower $IE$.

4. Electronic Configuration:

   • Atoms with exactly half-filled ($p^3, d^5, f^7$) or completely filled ($s^2, p^6, d^{10}, f^{14}$) subshells possess extra stability. Higher energy is required to remove electrons from these stable states.

Periodic Trends in Ionization Enthalpy

• Across a Period: Ionization enthalpy generally increases from left to right because the effective nuclear charge ($Z_{eff}$) increases and atomic size decreases.

  • Noble Gases: Possess the highest ionization enthalpies in their respective periods due to completely filled shells.

  • Alkali Metals: Possess the lowest ionization enthalpies in their periods.

• Down a Group: Ionization enthalpy decreases from top to bottom as the atomic size and number of shells increase.

Irregularities in Periodic Trends

• Period 2 Irregularities:

  • Expected: Li < Be < B < C < N < O < F < Ne

  • Actual: Li < B < Be < C < O < N < F < Ne

  • Reasoning:

    • Be > B: $Be$ ($1s^2 2s^2$) has a stable filled $s$-orbital, while $B$ ($1s^2 2s^2 2p^1$) loses a $p$-electron more easily.

    • N > O: $N$ ($1s^2 2s^2 2p^3$) has a half-filled, stable $p$-orbital compared to $O$ ($1s^2 2s^2 2p^4$).

• Period 3 Irregularities:

  • Actual: Na < Al < Mg < Si < S < P < Cl < Ar

  • Reasoning: Similar to Period 2, Mg > Al and P > S due to stable electronic configurations (filled $3s^2$ for $Mg$ and half-filled $3p^3$ for $P$).

• Group 13 Variation: Due to poor shielding by $d$ and $f$ electrons, the trend is non-linear (twisted):

  • Trend: B > Tl > Ga > Al > In

  • Values ($IE_1$ in $kJ/mol$): $B (801), Al (577), Ga (579), In (558), Tl (589)$.

• Group 14 Variation:

  • Trend: C > Si > Ge > Pb > Sn

  • Values ($IE_1$ in $kJ/mol$): $C (1086), Si (786), Ge (761), Sn (708), Pb (715)$.

Electron Gain Enthalpy (EGE) and Electron Affinity (EA)

• Definition: Electron gain enthalpy ($\Delta H_{eg}$) is the energy associated with adding one mole of electrons to one mole of an isolated gaseous atom in its ground state to form an anion.

  • $X(g) + e^- \rightarrow X^-(g)$

• Thermodynamics:

  • Exothermic: For most atoms (like halogens), energy is released: $\Delta H = -ve$.

  • Endothermic: For stable atoms (Noble gases, Group 2, Group 15), energy must be supplied to force an electron into the atom: $\Delta H = +ve$.

• Relationship between EA and EG:

  • $EA = -\Delta H_{eg}$ (considered at all temperatures for practical purposes).

  • Electron Affinity (EA) represents the "tendency" to gain electrons. A more positive EA signifies a stronger tendency.

• Successive Electron Affinity:

  • The first electron gain is usually exothermic ($O + e^- \rightarrow O^-; \Delta H_{eg} = -141\,kJ/mol$).

  • The second electron gain is ALWAYS endothermic due to inter-electronic repulsion ($O^- + e^- \rightarrow O^{2-}; \Delta H_{eg} = +844\,kJ/mol$).

Factors and Trends in Electron Affinity

• Factors Influence:

  • Atomic Radius: Inverse relationship ($EA \propto \frac{1}{\text{Atomic radius}}$).

  • Effective Nuclear Charge ($Z^*$): Direct relationship ($EA \propto Z^*$).

  • Shielding Effect (S.E.): Inverse relationship ($EA \propto \frac{1}{S.E.}$).

  • Stability of Electronic Configuration: Specifically stable configurations (half/fully filled) have very low or zero EA.

• Periodic Trends:

  • Across a Period: EA generally increases (becomes more negative) from left to right as size decreases and nuclear charge increases.

  • Down a Group: EA generally decreases from top to bottom as atomic radius increases.

• Group 17 (Halogens): Highest EA.

• Group 18 (Noble Gases): EA is approximately zero or positive because they are already stable.

• Exceptions/Anomalies:

  • In Group 16 and 17, the 2nd period elements ($O, F$) have lower (less negative) EA than the 3rd period elements ($S, Cl$). This is due to the small size of $O$ and $F$, leading to high electron-electron repulsion in the compact $2p$ subshell.

  • Group 16 Order: S (-200) > Se (-195) > Te (-190) > Po (-174) > O (-141).

  • Group 17 Order: Cl (-349) > F (-328) > Br (-325) > I (-295) > At (-270).

  • Winner: Chlorine ($Cl$) has the highest electron affinity in the entire periodic table.

Questions & Discussion

• Question: What is the correct order of the first ionization enthalpy for Na, Mg, Al, and Si?

• Answer: Na < Al < Mg < Si. ($496, 577, 737, 786\,kJ/mol$ respectively).

• Question: What is the correct increasing order of first ionization energy for Period 2 elements?

• Answer: Li < B < Be < C < O < N < F < Ne.

• Question: Which element in the set (C, Al, Si, N) has the highest first ionization enthalpy?

• Answer: Nitrogen (N), due to its small size and stable half-filled $p^3$ configuration.

• Question: Identify the correct trend for 1st IE in Period 3 elements:

• Answer: Al < Si < S < P < Cl.