Which of the following statements is correct ?

Options

A. The `SO_3` molecule has `2 p pi - d pi` bonds in it
B. Isocyanate ion `(NCO^-)` ion is a bent shaped ion
C. The ethene molecule has a total of eight hybrid orbitals.
D. All phosphorous - chlorine bonds in the `PCI_5` molecule are equal in length.

Answer

To determine which of the statements is correct, we will analyze each statement provided in the question one by one.

### Step 1: Analyze the first statement about SO3
**Statement:** SO3 molecule has a 2P by D by bond in it.

- **Valence Electrons of Sulfur:** Sulfur (S) has 6 valence electrons (configuration: 3s² 3p⁴).
- **Hybridization:** In SO3, sulfur undergoes hybridization to form three sigma bonds with oxygen. The sulfur atom promotes one of its 3s electrons to the 3d orbital to achieve maximum covalency, resulting in a hybridization state of sp².
- **Bond Formation:** Each sulfur-oxygen bond consists of one sigma bond (formed from the overlap of sp² hybrid orbitals) and one pi bond (formed from the overlap of unhybridized p orbitals).
- **Conclusion:** The statement is incorrect because the bonds are primarily formed from sp² hybridization and not specifically a 2P by D by bond.

### Step 2: Analyze the second statement about isocyanate ion
**Statement:** Isocyanate ion is a bent-shaped ion.

- **Structure of Isocyanate Ion (NCO⁻):** The isocyanate ion has a linear structure. The central atom is carbon, which forms a triple bond with nitrogen and a single bond with oxygen.
- **Hybridization:** The steric number of carbon in isocyanate is 2 (one triple bond and one single bond), which leads to an sp hybridization and a linear shape.
- **Conclusion:** The statement is incorrect as the isocyanate ion is linear, not bent.

### Step 3: Analyze the third statement about ethene
**Statement:** Ethene molecule has a total of 8 hybrid orbitals.

- **Structure of Ethene (C2H4):** Each carbon atom in ethene is sp² hybridized, which means each carbon uses 3 hybrid orbitals to form sigma bonds (2 with hydrogen and 1 with the other carbon).
- **Total Hybrid Orbitals:** Since there are 2 carbon atoms, the total number of hybrid orbitals is 2 (carbons) × 3 (hybrid orbitals per carbon) = 6 hybrid orbitals.
- **Conclusion:** The statement is incorrect; ethene has a total of 6 hybrid orbitals, not 8.

### Step 4: Analyze the fourth statement about PCl5
**Statement:** All phosphorus-chlorine bonds in the PCl5 molecules are equal in length.

- **Structure of PCl5:** Phosphorus pentachloride has a trigonal bipyramidal structure due to its steric number of 5 (5 bond pairs and 0 lone pairs).
- **Bond Lengths:** In PCl5, there are two types of positions for the chlorine atoms: equatorial and axial. The axial bonds are longer and weaker due to increased electron repulsion and less s character compared to the equatorial bonds.
- **Conclusion:** The statement is incorrect because the bond lengths in PCl5 are not equal.

### Final Conclusion
After analyzing all the statements, we find that all of them are incorrect. Therefore, none of the statements provided in the question is correct.

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