Comprehensive Summary of Important Formulae from NCERT Chemistry Chapter 3: Elements and Periodicity in Properties

1. Atomic Structure and Atomic Radii

• Atomic Radius: $r_{\text{atomic}}=\frac{d_{\text{inter-nuclear}}}{2}$
• • Explanation: The atomic radius is half the distance between the nuclei of two atoms in a covalent bond. This is used to describe the size of an atom.
  • Units: Picometers (pm)
  • Conditions: Applicable for covalent radii in molecules, metallic radii in metals.
• Trends:
• • Decreases across a period due to increased nuclear charge.
  • Increases down a group due to added electron shells.

Common Mistake: Confusing atomic radius with ionic radius; remember that cations are smaller and anions are larger than their parent atoms.

2. Ionization Enthalpy (${\Delta }_{i}H$)

• First Ionization Enthalpy: $X(g)\to X^{+}(g)+e^{-}$${\Delta }_{i}H=E_{\text{required to remove first electron}}$
• • Explanation: Energy required to remove the outermost electron from a neutral atom in its gaseous state.
  • Units: $kJmo{l}^{-1}$
  • Conditions: First ionization enthalpy applies to the removal of the first electron.

Trend:

• Increases across a period (due to increasing nuclear charge).
• Decreases down a group (due to increased atomic size and shielding effect).

Common Mistake: Misinterpreting the first ionization energy as the energy to remove electrons beyond the first.

3. Electron Gain Enthalpy (${\Delta }_{\text{eg}}H$)

• Electron Gain Enthalpy: $X(g)+e^{-}\to X^{-}(g){\Delta }_{\text{eg}}H=E_{\text{released or required when an electron is added}}$
• • Explanation: The change in enthalpy when an electron is added to a neutral atom to form an anion.
  • Units: $kJmo{l}^{-1}$
  • Conditions: Can be either exothermic (negative) or endothermic (positive).

Trend:

• Becomes more negative across a period (due to increasing nuclear charge).
• Becomes less negative down a group (due to increasing atomic size).

Common Mistake: Confusing electron gain enthalpy with electron affinity; note that they are related but distinct concepts.

4. Electronegativity

• Pauling's Electronegativity: $\text{Electronegativity}=\text{Relative ability of an atom in a molecule to attract shared electrons}$
• • Explanation: Electronegativity is a qualitative measure and does not have a unit.
  • Trend:
  • • Increases across a period.
    • Decreases down a group.

Common Mistake: Assuming electronegativity is a fixed property; it can vary depending on the chemical environment.

Example Applications:

1. Atomic Radius Application:
2. • Problem: Calculate the atomic radius of Chlorine in $C{l}_2$ if the inter-nuclear distance is 198 pm.
   • Solution: $r_{\text{atomic}}=\frac{198\text{ pm}}{2}=99\text{ pm}$
2. Ionization Enthalpy Application:
3. • Problem: Compare the first ionization enthalpy of $Mg$ and $Al$.
   • Solution: $Al$ has a lower first ionization enthalpy than $Mg$ due to the shielding effect of 3s electrons over 3p in $Al$.

Common Mistakes and Strategies:

• Incorrect Unit Conversions: Always ensure that units like pm, $kJ/mol$ are correctly applied.
• Misinterpretation of Trends: Be careful when predicting trends across periods and groups; remember exceptions like the first ionization enthalpy of $Be$ and $B$.

Final Review and Quick Recap:

• Atomic Radius: Decreases across a period, increases down a group.
• Ionization Enthalpy: Increases across a period, decreases down a group.
• Electron Gain Enthalpy: More negative across a period, less negative down a group.
• Electronegativity: Increases across a period, decreases down a group.

This summary should help you quickly revise the critical formulae and concepts for NEET Chemistry, ensuring you understand the principles and can apply them effectively in problems.