Question

A molecule with the formula \( AX_4Y \) has all its elements from p-block. Element A is rarest, monoatomic, non-radioactive from its group and has the lowest ionization enthalpy value among A, X, and Y. Elements X and Y have first and second highest electronegativity values respectively among all the known elements. 
The shape of the molecule is:

• A. Square pyramidal
• B. Octahedral
• C. Planar
• D. Tetrahedral

Hint:

In molecules with elements from the p-block, consider the electron configuration and the electronegativity values to determine the most likely molecular geometry.

Answer 1

The Correct Option is A

This problem necessitates the determination of a molecule's shape, represented by the formula AX\(_4\)Y. The identities of elements A, X, and Y are deduced through a series of descriptive clues.

Concept Used:

Two primary concepts are applied:

1. Element Identification via Periodic Trends: Fundamental principles of the periodic table, including electronegativity, ionization enthalpy trends, and elemental properties (natural state, abundance), are utilized to identify A, X, and Y.
2. Valence Shell Electron Pair Repulsion (VSEPR) Theory: Upon identifying the molecule, VSEPR theory is employed to predict its shape. This theory posits that molecular geometry arises from minimizing electrostatic repulsion between electron pairs (bonding and lone pairs) around the central atom. The procedure involves:
   • Identifying the central atom.
   • Calculating the steric number (SN): \( \text{SN} = (\text{Number of atoms bonded to central atom}) + (\text{Number of lone pairs on central atom}) \).
   • Determining electron geometry based on SN (e.g., SN=6 implies Octahedral geometry).
   • Establishing the final molecular shape based on atom arrangement (VSEPR type AX\(_m\)E\(_n\)).

Step-by-Step Solution:

Step 1: Identify Element X.

The clue for X is its "first and highest electronegativity value... among all the known elements." Fluorine (F) is the most electronegative element on the periodic table.

\[ \text{Element X = Fluorine (F)} \]

Step 2: Identify Element Y.

The clue for Y is its "second highest electronegativity value... among all the known elements." Oxygen (O) is the second most electronegative element.

\[ \text{Element Y = Oxygen (O)} \]

Step 3: Identify Element A.

Element A is characterized by the following clues:

• It belongs to the p-block.
• It is the "rarest, monatomic, non-radioactive from its group." The monatomic characteristic suggests noble gases (Group 18). Among the non-radioactive noble gases (He, Ne, Ar, Kr, Xe), Xenon is the rarest.
• It exhibits the "lowest ionization enthalpy value among A, X and Y." Verification: IE\(_1\)(F) \(\approx\) 1681 kJ/mol; IE\(_1\)(O) \(\approx\) 1314 kJ/mol; IE\(_1\)(Xe) \(\approx\) 1170 kJ/mol. Xenon indeed possesses the lowest ionization enthalpy among the three.

Consequently, element A is Xenon (Xe).

\[ \text{Element A = Xenon (Xe)} \]

The resultant molecular formula is XeOF\(_4\).

Step 4: Apply VSEPR Theory to XeOF\(_4\).

• Central Atom: Xenon (Xe) is the central atom due to its lowest electronegativity.
• Valence Electrons of Xe: As a noble gas, Xenon possesses 8 valence electrons.
• Bonding and Lone Pairs:
  • Xe forms four single bonds with four fluorine atoms.
  • Xe forms one double bond with the oxygen atom (due to oxygen's divalent nature).
  • Total electrons from Xe engaged in bonding: 4 (for F atoms) + 2 (for O atom) = 6 electrons.
  • Remaining non-bonding electrons on Xe: 8 - 6 = 2 electrons.
  • This translates to 1 lone pair of electrons on the central Xe atom.

Step 5: Calculate Steric Number (SN) and Determine Shape.

• Number of atoms bonded to the central atom: 4 (F) + 1 (O) = 5.
• Number of lone pairs on the central atom: 1.
• Steric Number (SN) = (Number of bonded atoms) + (Number of lone pairs) = 5 + 1 = 6.
• A steric number of 6 dictates an octahedral electron geometry.
• The molecule's VSEPR type is AX\(_5\)E\(_1\) (5 bonding pairs, 1 lone pair).
• VSEPR theory indicates that a molecule with an AX\(_5\)E\(_1\) arrangement adopts a square pyramidal shape. The lone pair occupies an axial position to minimize repulsion, with the five atoms occupying the remaining vertices of the octahedron.

The molecular shape of XeOF\(_4\) is Square pyramidal.