Comprehensive Study Guide on Periodic Properties

Periodic Properties

• The following are the major periodic properties discussed in this study guide:
  • Atomic Radius
  • Ionic Radius
  • Ionization Energy
  • Electron Gain Enthalpy (Electron Affinity)
  • Electronegativity
  • Valency
  • Polarizability
  • Oxidation States
  • Coordination Number

Atomic Radius

• Definition: The distance from the center of the nucleus to the outermost shell of an atom is defined as the Atomic Radius.
• Types of Atomic Radii:
  • Covalent Radius: This is defined as half of the distance between the centers of two nuclei bonded by a single covalent bond. It involves the sharing of the electron cloud during bonding.
  • Van der Waals Radius: When two molecules are held together by intermolecular forces (without a bond), the half-distance between the nuclei of both adjacent atoms is the Van der Waals radius. This distance is significantly larger because there is no bond overlap.
  • Metallic Radius: Metals exist in a lattice with a metallic bond where electrons are flowing across the surface. The metallic radius is defined as half of the distance between the center of two metal nuclei.
• Comparison of Sizes: $\text{Van der Waals Radius} > \text{Metallic Radius} > \text{Covalent Radius}$.

Variation of Atomic Radius

• Along the Period (Left to Right): Atomic radius decreases.
  • Explanation: As we move from Lithium ($Li$) to Neon ($Ne$), the number of shells remains the same across the period (e.g., in Period 2, it is always 2 shells). However, the number of protons (nuclear charge) increases. For example, Lithium ($Li$, 3 protons) is pulling electrons less than Carbon ($C$, 6 protons) or Fluorine ($F$, 9 protons). Higher nuclear charge pulls the electrons closer, resulting in a smaller size.
• Down the Group (Top to Bottom): Atomic radius increases.
  • Explanation: Moving down a group (e.g., $Li \rightarrow Na \rightarrow K$), the number of shells increases ($n = 2, 3, 4,\dots$). The distance between the nucleus and the outermost shell increases, making the radius larger.

Exceptions in Atomic Radius

• Period 1: The atomic radius of Helium ($He$) is greater than Hydrogen ($H$). This is because Helium is a noble gas and its radius is measured as a Van der Waals radius, whereas Hydrogen is measured by its covalent radius. Van der Waals radius is always greater than covalent radius.
• Period 2: The atomic radius decreases from $Li$ to $F$, but Neon ($Ne$) has the largest radius in the period because it is a noble gas measured by Van der Waals forces. The actual sequence is: $Ne > Li > Be > B > C > N > O > F$.
• d-block Elements (Transition Metals):
  • In the $3d$ series ($Sc$ to $Zn$), one would expect a continuous decrease in radius.
  • Actual Trend:
  • $Sc \rightarrow Ti \rightarrow V \rightarrow Cr \rightarrow Mn$: Atomic radius decreases (protons pull closer).
  • $Fe \rightarrow Co \rightarrow Ni$: Atomic radius remains relatively constant.
  • $Cu \rightarrow Zn$: Atomic radius increases. Zinc ($Zn, 3d^{10}$) is a noble-like configuration with maximum electron-electron ($e^- - e^-$) repulsion, causing the size to expand.

Ionic Radius

• Definition: It is the distance from the nucleus to the outermost shell of an ion.
• Cations ($M^+$): Formed when an atom loses one or more electrons ($M \rightarrow M^+ + e^-$). Cations are smaller than their parent atoms because the remaining electrons feel more nuclear attraction.
• Anions ($M^-$): Formed when an atom gains one or more electrons ($M + e^- \rightarrow M^-$). Anions are larger than their parent atoms because extra electrons increase inter-electronic repulsion, causing the shell to expand.
• General Trend: $\text{Anion Size} > \text{Neutral Atom Size} > \text{Cation Size}$.

Isoelectronic Species

• Definition: Different species having the same number of electrons (e.g., $N^{3-}, O^{2-}, F^-, Na^+, Mg^{2+}$ all have 10 electrons).
• Rule: In isoelectronic species, the greater the atomic number ($Z$), the smaller the size. $\text{Size} \propto \frac{1}{Z}$.
• Ordering Example: $N^{3-} > O^{2-} > F^- > Na^+ > Mg^{2+}$.
• Variation of Ionic Radius:
  • Along the period (L-R): Decreases.
  • Along the group (Top-Bottom): Increases.

Ionization Energy (IE)

• Definition: The amount of energy required to remove the valence shell electron from an isolated, neutral gaseous atom.
• Equation: $A(g) + \text{Energy} \rightarrow A^+(g) + e^-$.
• Unit: $kJ/mol$.
• Factors Affecting Ionization Energy:
  • Size of Atom: Smaller size means electrons are held more strongly by the nucleus, leading to higher IE. $\text{IE} \propto \frac{1}{\text{Size}}$.
  • Nuclear Charge: Higher nuclear charge means more attraction to electrons, requiring more energy to remove them. $\text{IE} \propto \text{Nuclear Charge}$.
  • Screening / Shielding Effect: In multi-electron systems, inner electrons shield outer electrons from the nucleus. This repulsion reduces the attraction felt by the valence electrons. Order of shielding ability: $s > p > d > f$. ($s$ is spherical and closest to the nucleus, providing best shielding; $f$ has a poor/diffused shape with poor shielding).
  • Electronic Configuration: It is difficult to remove electrons from stable half-filled or fully-filled shells (e.g., $p^3, p^6, d^5, d^{10}, f^7, f^{14}$).
• Trend:
  • Along a period (L-R): Increases.
  • Down a group (Top-Bottom): Decreases.

Electron Gain Enthalpy ($\Delta H_{eg}$) and Electron Affinity ($EA$)

• Definition: It is the amount of energy released when an electron is added to the valence shell of a neutral gaseous atom.
• Example: $A(g) + e^- \rightarrow A^-(g) + \text{energy}$.
• Relationship: If energy released is $8\,ev$, then Electron Affinity is $+8\,ev$ and Electron Gain Enthalpy is $-8\,ev$.
• Unit: $kJ/mol$.
• Factors Affecting Electron Affinity:
  • Size: Larger size (down the group) means the nucleus is further from the incoming electron, so EA decreases.
  • Nuclear Charge: More nuclear charge means more attraction for the incoming electron, hence higher EA. $\text{EA} \propto \text{Nuclear Charge}$.
  • Electronic Configuration: Half-filled and fully-filled shells have less tendency to accept extra electrons.
• Trend:
  • Along the period (L-R): Increases.
  • Along the group (Top-Bottom): Decreases.

Electronegativity (EN)

• Definition: It is the tendency of an atom to attract a shared pair of electrons towards itself in a chemical bond.
• Differences Between EA and EN:
  1. EN is the tendency to attract electrons; EA is the tendency to accept/gain electrons.
  2. EN occurs between two bonded atoms (sharing needed); EA occurs in an isolated atom.
  3. EN has relative values (no units); EA has absolute values (e.g., $kJ/mol$ or $ev/atom$).
• Factors Affecting Electronegativity:
  • Size: Smaller size yields a greater attraction for electrons. $\text{EN} \propto \frac{1}{\text{Size}}$.
  • Nuclear Charge: More nuclear charge yields higher attraction. $\text{EN} \propto \text{Nuclear Charge}$.
  • Hybridization: EN increases with the percentage of s-character. $\text{sp (50\%)} > \text{sp}^2 (33.33\%) > \text{sp}^3 (25\%)$.
• Trend:
  • Period (L-R): Increases.
  • Group (Top-Bottom): Decreases.

Valency

• Definition: The number of electrons present in the outermost shell are valence electrons, and the combining capacity of an element is known as its Valency.
• Trend:
  • In Period (L-R): It increases from 1 to 4, then decreases from 4 back to 0.
  • In Group (Top-Bottom): The number of valence electrons remains the same; therefore, valency stays constant.

Polarizability

• Definition: Represents covalent character in an ionic bond. It involves the distortion or deformation of the anion's electron cloud by the attraction of the cation.
• Factors Affecting Polarization:
  • $\text{Polarization} \propto \text{Size of Anion}$.
  • $\text{Polarization} \propto \frac{1}{\text{Size of Cation}}$.
  • $\text{Polarization} \propto \text{Charge on Cation/Anion}$.
• Trend:
  • Period (L-R): Decreases.
  • Group (Top-Bottom): Increases.

Oxidation States

• Definition: The charge assigned to an element or atom within a compound or in its free state.
• Rules for Assigning Oxidation Numbers:
  1. Elements in their free/uncombined state have an oxidation number of zero (e.g., $H_2, P_4, O_2, S_8, Fe, Br_2$).
  2. Alkali metals ($Li, Na, K, Rb, Cs$) always have $+1$.
  3. Alkaline Earth metals ($Be, Mg, Ca, Sr, Ba, Ra$) always have $+2$.
  4. Hydrogen ($H$): Usually $+1$ when bonded to non-metals (more electronegative), but $-1$ when bonded to metals (metal hydrides, e.g., $NaH$).
  5. Oxygen ($O$): Usually $-2$ in oxides. In peroxides ($O-O$ bond), it is $-1$. In superoxides (e.g., $KO_2$), it is $-1/2$.
  6. Fluorine ($F$): Always has an oxidation state of $-1$.
  7. Evaluation Principle: The algebraic sum of oxidation numbers in a neutral compound is zero.
• Calculation Examples:
  • $KMnO_4$: $(+1) + (Mn) + 4(-2) = 0 \rightarrow Mn = +7$.
  • $H_3PO_4$: $3(+1) + (P) + 4(-2) = 0 \rightarrow P = +5$.
  • $H_3PO_3$: $3(+1) + (P) + 3(-2) = 0 \rightarrow P = +3$.
  • $H_3PO_2$: $3(+1) + (P) + 2(-2) = 0 \rightarrow P = +1$.

Coordination Number

• Definition: In an ionic crystal, it is the number of oppositely charged ions present around the Central Metal Ion (CMI).