Following compounds A and B have similar structure with delocalization of `pi`-electrons system. `(A)(PNCl_(2))_("x/2")` (B)`(CH)_(x)`
If value of x is 6, then calculate value of "P+Q", where 'P' is total no. of `sigma`-bonds in compounds A and B and 'Q' is total no. of `pi` bonds in compounds A and B.

Explanation

To solve the problem, we need to analyze the two compounds A (PNCl₂) and B (C₆H₆) and calculate the total number of sigma (σ) and pi (π) bonds in both compounds.

### Step 1: Identify the compounds
- Compound A is PNCl₂ (where x = 6 implies we have P(NCl₂)₃).
- Compound B is C₆H₆ (benzene).

### Step 2: Draw the structures
1. **Structure of Benzene (C₆H₆)**:
- Benzene has a hexagonal ring structure with alternating double bonds (delocalized π-electrons).
- Each carbon atom is bonded to one hydrogen atom.

The structure can be represented as:
```
H H
\ /
C=C
/ \
H H
\ /
C=C
/ \
H H
```

2. **Structure of PNCl₂**:
- The structure of PNCl₂ can be visualized as a cyclic compound similar to benzene, where phosphorus is at the center and nitrogen atoms are at the vertices of the triangle.
- Each nitrogen is bonded to two chlorine atoms and has a lone pair.

The structure can be represented as:
```
Cl Cl
\ /
N
/ \
P N
\ /
N
/ \
Cl Cl
```

### Step 3: Count the sigma (σ) and pi (π) bonds

1. **For Benzene (C₆H₆)**:
- **Sigma bonds**:
- Each C-C bond: 6 (C-C bonds)
- Each C-H bond: 6 (C-H bonds)
- Total σ bonds in benzene = 6 (C-C) + 6 (C-H) = 12 σ bonds.
- **Pi bonds**:
- There are 3 π bonds due to the alternating double bonds.

2. **For PNCl₂**:
- **Sigma bonds**:
- Each N-P bond: 3 (N-P bonds)
- Each N-Cl bond: 6 (2 Cl for each of the 3 N)
- Total σ bonds in PNCl₂ = 3 (N-P) + 6 (N-Cl) = 9 σ bonds.
- **Pi bonds**:
- There are 3 π bonds due to the delocalization similar to benzene.

### Step 4: Calculate total P and Q
- **Total σ bonds (P)**:
- P = σ bonds in benzene + σ bonds in PNCl₂ = 12 + 9 = 21 σ bonds.

- **Total π bonds (Q)**:
- Q = π bonds in benzene + π bonds in PNCl₂ = 3 + 3 = 6 π bonds.

### Step 5: Calculate P + Q
- P + Q = 21 + 6 = 27.

### Final Answer
The value of P + Q is **27**.

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