Which of the following molecules has the shortest carbon-carbon bond ?

Options

A. `C_2H_4`
B. `C_2H_6`
C. `C_2H_2`
D. `C_2CI_6`

Answer

To determine which of the given molecules has the shortest carbon-carbon bond, we need to analyze the bond order of each molecule. The bond length is inversely proportional to the bond order; that is, the greater the bond order, the shorter the bond length.

Let's analyze each option step by step:

1. **C2H4 (Ethene)**:
- Ethene has a double bond between the two carbon atoms (C=C).
- The bond order here is 2 (since there are two bonds between the carbon atoms).
- Therefore, the bond length is relatively short, but not the shortest.

2. **C2H6 (Ethane)**:
- Ethane has a single bond between the two carbon atoms (C-C).
- The bond order here is 1 (since there is only one bond between the carbon atoms).
- This bond length is longer than that of ethene.

3. **C2H2 (Ethyne)**:
- Ethyne has a triple bond between the two carbon atoms (C≡C).
- The bond order here is 3 (since there are three bonds between the carbon atoms).
- This bond length is shorter than that of both ethene and ethane.

4. **C2Cl6 (Dichloroethane)**:
- Dichloroethane has a single bond between the two carbon atoms (C-C).
- The bond order here is also 1 (similar to ethane).
- This bond length is the same as that of ethane and is longer than that of ethene and ethyne.

Now, comparing the bond orders:
- Ethene (C2H4) has a bond order of 2.
- Ethane (C2H6) has a bond order of 1.
- Ethyne (C2H2) has a bond order of 3.
- Dichloroethane (C2Cl6) has a bond order of 1.

Since ethyne has the highest bond order (3), it has the shortest carbon-carbon bond length among the given options.

**Final Answer**: C2H2 (Ethyne) has the shortest carbon-carbon bond.