Which of the following are correct ?

Options

A. All the three N-O bond lengths in `HNO_(3)` are equal
B. All P-Cl bond lengths in `PCl_(5)` molecule in gaseous state are equal
C. `P_(4)` molecules in white phosphorous have angular strain therefore white phosphorus is very reactive
D. `PCl_(5)` is ionic in solid state in which cation is tetrahedral and anion is octahedral

Answer

To solve the question regarding the correctness of the statements about HNO3, PCl5, and P4, let's analyze each statement step by step.

### Step 1: Analyze the bond lengths in HNO3
- **Statement**: All the N-O bond lengths in HNO3 are equal.
- **Analysis**: HNO3 (nitric acid) has a resonance structure where nitrogen is bonded to three oxygen atoms: one with a double bond (N=O) and two with single bonds (N-O). Due to resonance, the bond lengths are not equal. The N=O bond is shorter than the N-O bonds. Therefore, this statement is **incorrect**.

### Step 2: Analyze the bond lengths in PCl5
- **Statement**: All P-Cl bond lengths in PCl5 molecules in the gaseous state are equal.
- **Analysis**: PCl5 has a trigonal bipyramidal structure. The P-Cl bonds in the equatorial positions are shorter than those in the axial positions due to the differences in bond angles and steric effects. The axial P-Cl bonds are longer than the equatorial ones. Therefore, this statement is also **incorrect**.

### Step 3: Analyze the reactivity of white phosphorus (P4)
- **Statement**: P4 molecules are in white phosphorus and white phosphorus has angular strain, making it very reactive.
- **Analysis**: White phosphorus (P4) has a tetrahedral structure, which does introduce some angular strain due to the bond angles being less than the ideal tetrahedral angle of 109.5 degrees. This strain contributes to its high reactivity. Therefore, this statement is **correct**.

### Step 4: Analyze the ionic nature of PCl5 in solid state
- **Statement**: PCl5 is ionic in solid state, where the cation is tetrahedral and the anion is octahedral.
- **Analysis**: In the solid state, PCl5 does exist as an ionic compound, with the cation (PCl4+) having a tetrahedral geometry and the anion (Cl-) being octahedral. Therefore, this statement is **correct**.

### Conclusion
The correct statements are:
- Statement 3: P4 molecules are in white phosphorus and white phosphorus has angular strain, making it very reactive.
- Statement 4: PCl5 is ionic in solid state, where the cation is tetrahedral and the anion is octahedral.

### Final Answer
The correct options are 3 and 4.

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