Question

The number of molecules/ions having trigonal bipyramidal shape is:
\(\text{PF}_5, \, \text{BrF}_5, \, \text{PCl}_5, \, [\text{PtCl}_4]^{2-}, \, \text{BF}_3, \, \text{Fe(CO)}_5\)

Answer 1

Correct Answer: 3

PF₅, PCl₅, and Fe(CO)₅ have trigonal bipyramidal geometry.

BrF₅: square pyramidal

[PtCl₄]²⁻: square planar

BF₃: trigonal planar

Answer 2

The problem asks to identify the number of molecules or ions from the given list that have a trigonal bipyramidal shape.

Concept Used:

To determine the shape of a molecule or ion, we use the Valence Shell Electron Pair Repulsion (VSEPR) theory. The shape is determined by the number of bonding pairs and lone pairs of electrons around the central atom.

1. First, we calculate the Steric Number (SN) for the central atom: \[ \text{SN} = (\text{Number of atoms bonded to the central atom}) + (\text{Number of lone pairs on the central atom}) \]
2. The SN determines the electron geometry (the arrangement of all electron pairs). For a trigonal bipyramidal electron geometry, the SN must be 5.
3. The molecular shape (the arrangement of only the atoms) is trigonal bipyramidal only if there are zero lone pairs on the central atom. This corresponds to a molecule of the type AX₅, where A is the central atom and X is a bonded atom.

For coordination compounds like [PtCl₄]²⁻ and Fe(CO)₅, the shape is determined by the coordination number and hybridization of the central metal atom.

Step-by-Step Solution:

We will analyze each species individually to determine its shape.

1. PF₅ (Phosphorus Pentafluoride):

• Central atom: P (Group 15) has 5 valence electrons.
• Bonded atoms: 5 F atoms.
• Bonding pairs = 5.
• Lone pairs = \( \frac{1}{2}(5 - 5) = 0 \).
• Steric Number (SN) = 5 (bonding pairs) + 0 (lone pairs) = 5.
• Since there are no lone pairs (AX₅ type), the electron geometry and molecular shape are both trigonal bipyramidal.

2. BrF₅ (Bromine Pentafluoride):

• Central atom: Br (Group 17) has 7 valence electrons.
• Bonded atoms: 5 F atoms.
• Bonding pairs = 5.
• Lone pairs = \( \frac{1}{2}(7 - 5) = 1 \).
• Steric Number (SN) = 5 (bonding pairs) + 1 (lone pair) = 6.
• The electron geometry is octahedral. With one lone pair (AX₅E₁ type), the molecular shape is square pyramidal.

3. PCl₅ (Phosphorus Pentachloride):

• Central atom: P (Group 15) has 5 valence electrons.
• Bonded atoms: 5 Cl atoms.
• Bonding pairs = 5.
• Lone pairs = \( \frac{1}{2}(5 - 5) = 0 \).
• Steric Number (SN) = 5 (bonding pairs) + 0 (lone pairs) = 5.
• With no lone pairs (AX₅ type), the molecular shape is trigonal bipyramidal.

4. [PtCl₄]²⁻ (Tetrachloroplatinate(II)):

• This is a coordination complex. Platinum (Pt) is in the +2 oxidation state (d⁸ configuration).
• The coordination number is 4. For d⁸ metals in the 5d series like Pt, the crystal field splitting energy is very large, strongly favoring a square planar geometry.
• The hybridization is dsp². The shape is square planar.

5. BF₃ (Boron Trifluoride):

• Central atom: B (Group 13) has 3 valence electrons.
• Bonded atoms: 3 F atoms.
• Bonding pairs = 3.
• Lone pairs = \( \frac{1}{2}(3 - 3) = 0 \).
• Steric Number (SN) = 3 (bonding pairs) + 0 (lone pairs) = 3.
• With SN = 3 and no lone pairs (AX₃ type), the shape is trigonal planar.

6. Fe(CO)₅ (Iron Pentacarbonyl):

• This is a metal carbonyl complex with a coordination number of 5.
• The five identical CO ligands arrange themselves around the central Fe atom to minimize repulsion.
• The most stable arrangement for five ligands is a trigonal bipyramidal shape.

Final Computation & Result:

Based on the analysis, the molecules/ions from the list that have a trigonal bipyramidal shape are:

• PF₅
• PCl₅
• Fe(CO)₅

The total number of species with a trigonal bipyramidal shape is 3.