Understanding the Problem

We are given 8 interhalogen compounds and need to determine which are polar, non-polar, planar, and non-planar. Then we calculate the expression: $\frac{P^2-Q^2}{R+S}$, where:

• P = Total number of polar compounds
• Q = Total number of planar compounds
• R = Total number of non-polar compounds
• S = Total number of non-planar compounds

Step 1: Determine Molecular Geometry and Polarity

We analyze each compound's structure based on VSEPR theory and its polarity based on molecular symmetry.

Compound Analysis:

1. ICl (Iodine Monochloride)
   • Geometry: Linear (AX₂E₃ type).
   • Polarity: Polar (Different atoms, bond dipoles do not cancel).
   • Planarity: Linear molecules are planar.
   • Classification: Polar, Planar.
2. IBr (Iodine Monobromide)
   • Geometry: Linear (AX₂E₃ type).
   • Polarity: Polar (Different atoms, bond dipoles do not cancel).
   • Planarity: Planar.
   • Classification: Polar, Planar.
3. ICl₃ (Iodine Trichloride)
   • Geometry: T-shaped (AX₃E₂ type).
   • Polarity: Polar (Asymmetric shape).
   • Planarity: Non-Planar (The atoms are not all in one plane).
   • Classification: Polar, Non-Planar.
4. IF₅ (Iodine Pentafluoride)
   • Geometry: Square Pyramidal (AX₅E₁ type).
   • Polarity: Polar (The lone pair creates an asymmetric charge distribution).
   • Planarity: Non-Planar.
   • Classification: Polar, Non-Planar.
5. BrF₃ (Bromine Trifluoride)
   • Geometry: T-shaped (AX₃E₂ type).
   • Polarity: Polar (Asymmetric shape).
   • Planarity: Non-Planar.
   • Classification: Polar, Non-Planar.
6. IF₃ (Iodine Trifluoride)
   • Geometry: T-shaped (AX₃E₂ type).
   • Polarity: Polar (Asymmetric shape).
   • Planarity: Non-Planar.
   • Classification: Polar, Non-Planar.
7. BrF₅ (Bromine Pentafluoride)
   • Geometry: Square Pyramidal (AX₅E₁ type).
   • Polarity: Polar (The lone pair creates an asymmetric charge distribution).
   • Planarity: Non-Planar.
   • Classification: Polar, Non-Planar.
8. IF₇ (Iodine Heptafluoride)
   • Geometry: Pentagonal Bipyramidal (AX₇E₀ type).
   • Polarity: Non-Polar (Highly symmetric shape, all bond dipoles cancel out).
   • Planarity: Non-Planar.
   • Classification: Non-Polar, Non-Planar.

Step 2: Categorize the Compounds

Let's create lists based on our analysis.

Polar Compounds (P): ICl, IBr, ICl₃, IF₅, BrF₃, IF₃, BrF₅.
Count, P = 7

Planar Compounds (Q): ICl, IBr.
Count, Q = 2

Non-Polar Compounds (R): IF₇.
Count, R = 1

Non-Planar Compounds (S): ICl₃, IF₅, BrF₃, IF₃, BrF₅, IF₇.
Count, S = 6

Step 3: Substitute Values into the Formula

We plug the values into the given expression: $\frac{P^2-Q^2}{R+S}=\frac{7^2-2^2}{1+6}=\frac{49-4}{7}=\frac{45}{7}$

Final Answer

The value of $\frac{P^2-Q^2}{R+S}$ is $\frac{45}{7}$.

Related Topics & Formulae

Key Concepts:

• VSEPR Theory: Valence Shell Electron Pair Repulsion theory predicts molecular geometry based on the number of bonding pairs and lone pairs around the central atom. The notation AX_mE_n is used, where A is the central atom, X is a bonded atom, and E is a lone pair.
• Molecular Polarity: A molecule is polar if it has a net dipole moment. This occurs when there is an asymmetric distribution of electron density, often due to:
  • Polar bonds (difference in electronegativity).
  • Asymmetric molecular shape (lone pairs or different atoms).
  Symmetric shapes like linear (AX₂), trigonal planar (AX₃), tetrahedral (AX₄), square planar (AX₄E₂), and octahedral (AX₆) are non-polar only if all surrounding atoms are identical.
• Planarity: A molecule is planar if all its atoms lie in the same plane. Common planar geometries include linear, trigonal planar, and square planar.

Common VSEPR Geometries:

• AX₂: Linear (Planar, can be polar or non-polar)
• AX₃: Trigonal Planar (Planar, can be polar or non-polar)
• AX₂E: Bent (Non-Planar, Polar)
• AX₄: Tetrahedral (Non-Planar, can be polar or non-polar)
• AX₃E: Trigonal Pyramidal (Non-Planar, Polar)
• AX₂E₂: Bent (Non-Planar, Polar)
• AX₅: Trigonal Bipyramidal (Non-Planar, can be polar or non-polar)
• AX₄E: See-Saw (Non-Planar, Polar)
• AX₃E₂: T-shaped (Non-Planar, Polar)
• AX₆: Octahedral (Non-Planar, can be polar or non-polar)
• AX₅E: Square Pyramidal (Non-Planar, Polar)
• AX₄E₂: Square Planar (Planar, can be polar or non-polar)