Which one is false in the following statements ?

Options

A. Each carbon in ethylene is in `sp^(2)` hybridization
B. Each carbon in acetylene is in `sp^(3)` hybridization
C. Each carbon in benzene is in `sp^(2)` hybridization
D. Each carbon in ethane is in `sp^(3)` hybridization

Answer

To determine which statement is false among the given options, we will analyze each statement one by one.

### Step-by-Step Solution:

1. **Analyze the first statement: "Each carbon in ethylene is in sp² hybridization."**
- Ethylene (C₂H₄) has the structure H₂C=CH₂.
- Each carbon atom forms three sigma bonds (two with hydrogen and one with another carbon) and has no lone pairs.
- The steric number (number of sigma bonds + lone pairs) is 3.
- For a steric number of 3, the hybridization is sp².
- **Conclusion:** This statement is **true**.

2. **Analyze the second statement: "Each carbon in acetylene is in sp³ hybridization."**
- Acetylene (C₂H₂) has the structure HC≡CH.
- Each carbon atom forms one sigma bond with hydrogen and two pi bonds with the other carbon.
- Each carbon has only one sigma bond, leading to a steric number of 2.
- For a steric number of 2, the hybridization is sp (not sp³).
- **Conclusion:** This statement is **false**.

3. **Analyze the third statement: "Each carbon in benzene is in sp² hybridization."**
- Benzene (C₆H₆) has a cyclic structure with alternating double bonds.
- Each carbon atom forms three sigma bonds (two with other carbons and one with hydrogen) and has no lone pairs.
- The steric number is 3.
- For a steric number of 3, the hybridization is sp².
- **Conclusion:** This statement is **true**.

4. **Analyze the fourth statement: "Each carbon in ethane is in sp³ hybridization."**
- Ethane (C₂H₆) has the structure H₃C-CH₃.
- Each carbon atom forms four sigma bonds (three with hydrogen and one with another carbon).
- The steric number is 4.
- For a steric number of 4, the hybridization is sp³.
- **Conclusion:** This statement is **true**.

### Final Conclusion:
The only false statement among the options is the second one: "Each carbon in acetylene is in sp³ hybridization." The correct hybridization for each carbon in acetylene is sp.

### Answer:
The false statement is the second one.

---