Among the following compounds, which has the maximum number of sp-hybridized C atoms ?

Options

A. `(CN)_2`
B. `CH_2=C=CH-CN`
C. `HC-=C-CH_2CH=CH_2`
D. `HC-=C-CN`

Answer

To determine which compound has the maximum number of sp-hybridized carbon atoms, we need to analyze the hybridization of carbon atoms in each given compound. The hybridization can be determined based on the number of sigma bonds formed by the carbon atoms.

### Step-by-Step Solution:

1. **Understanding Hybridization**:
- Carbon can undergo different types of hybridization:
- **sp**: 2 sigma bonds (triple bond or two double bonds)
- **sp2**: 3 sigma bonds (one double bond)
- **sp3**: 4 sigma bonds (single bonds only)

2. **Analyzing Each Compound**:
- We will look at the given compounds and identify the hybridization of carbon atoms in each.

3. **Compound 1**:
- Let's say the compound is C-N (for example, CN2).
- The carbon in C-N has 2 sigma bonds (one with nitrogen and one with another carbon), so it is **sp hybridized**.
- If there are two carbon atoms in this compound, both are sp hybridized, giving us a total of **2 sp hybridized carbons**.

4. **Compound 2**:
- Consider the compound with the structure H2C=C=CH2 (for example, allene).
- The first carbon has 3 sigma bonds (two with hydrogens and one with the second carbon), making it **sp2 hybridized**.
- The second carbon has 2 sigma bonds (one with the first carbon and one with the third carbon), making it **sp hybridized**.
- The third carbon is similar to the first carbon, making it **sp2 hybridized**.
- In this case, there is **1 sp hybridized carbon**.

5. **Compound 3**:
- Consider a compound like C≡C-C≡C (for example, butadiyne).
- Each terminal carbon has 2 sigma bonds (one with hydrogen and one with the adjacent carbon), making them **sp hybridized**.
- The internal carbon atoms are also bonded with triple bonds, making them **sp hybridized**.
- Therefore, there are **4 sp hybridized carbons**.

6. **Compound 4**:
- Consider the compound H-C≡C-CN (for example, propyne).
- The terminal carbon (attached to hydrogen) has 2 sigma bonds, making it **sp hybridized**.
- The middle carbon (attached to the CN group) also has 2 sigma bonds, making it **sp hybridized**.
- Thus, there are **2 sp hybridized carbons**.

7. **Conclusion**:
- After analyzing all compounds, the compound with the maximum number of sp-hybridized carbon atoms is the one with the structure C≡C-C≡C, which has **4 sp hybridized carbons**.

### Final Answer:
The compound with the maximum number of sp-hybridized carbon atoms is the one with the structure C≡C-C≡C, which has **4 sp hybridized carbons**.