For the following molecules :
`PCl_(5), BrF_(3), IC l_(2)^(-), XeF_(5)^(-),NO_(3)^(-),XeO_(2)F_(2),PCl_(4)^(+),CH_(3)^(+)`
Calculate the value of `(a+b)/(c )`
a = Number of species having `sp^(3)` d-hybridisation
b= Number of species which are planar
c= Number of species which are non-planar

Explanation

To solve the problem, we need to analyze each molecule given and determine the hybridization, planarity, and non-planarity of each species.

### Step-by-Step Solution:

1. **Identify Hybridization and Steric Number:**
- The steric number (SN) is calculated as the number of sigma bonds plus the number of lone pairs on the central atom.
- The hybridization can be determined from the steric number:
- SN = 2 → sp
- SN = 3 → sp²
- SN = 4 → sp³
- SN = 5 → sp³d
- SN = 6 → sp³d²

2. **Analyze Each Molecule:**
- **PCl₅:**
- SN = 5 (5 bond pairs, 0 lone pairs) → Hybridization: sp³d
- Planarity: Non-planar (trigonal bipyramidal structure)

- **BrF₃:**
- SN = 5 (3 bond pairs, 2 lone pairs) → Hybridization: sp³d
- Planarity: Non-planar (T-shaped structure)

- **ICl₂⁻:**
- SN = 5 (2 bond pairs, 3 lone pairs) → Hybridization: sp³d
- Planarity: Non-planar (linear structure)

- **XeF₅⁻:**
- SN = 7 (5 bond pairs, 2 lone pairs) → Hybridization: sp³d²
- Planarity: Non-planar (square pyramidal structure)

- **NO₃⁻:**
- SN = 3 (3 bond pairs, 0 lone pairs) → Hybridization: sp²
- Planarity: Planar (trigonal planar structure)

- **XeO₂F₂:**
- SN = 6 (4 bond pairs, 2 lone pairs) → Hybridization: sp³d²
- Planarity: Non-planar (square planar structure)

- **PCl₄⁺:**
- SN = 5 (4 bond pairs, 1 lone pair) → Hybridization: sp³d
- Planarity: Non-planar (seesaw structure)

- **CH₃⁺:**
- SN = 4 (4 bond pairs, 0 lone pairs) → Hybridization: sp³
- Planarity: Planar (tetrahedral structure)

3. **Count Values for a, b, and c:**
- **a** (Number of species with sp³ hybridization):
- PCl₅, BrF₃, ICl₂⁻, PCl₄⁺, CH₃⁺ → Total = 5
- **b** (Number of species that are planar):
- NO₃⁻, CH₃⁺ → Total = 2
- **c** (Number of species that are non-planar):
- PCl₅, BrF₃, ICl₂⁻, XeF₅⁻, XeO₂F₂, PCl₄⁺ → Total = 6

4. **Calculate (a + b) / c:**
- (a + b) = 5 + 2 = 7
- c = 6
- Therefore, (a + b) / c = 7 / 6

### Final Answer:
\[ \frac{(a + b)}{c} = \frac{7}{6} \]