Which of the following statements in incorrect for sigma and `pi` -bonds formed between two carbon atoms ?

Options

A. Sigma-bond is stronger than a `pi`-bond
B. Bond energies of sigma and `pi` -bonds are of the order of 264 kJ / mol and 347 kJ / mol
C. Free rotation of surrounding atoms about a sigma -bond is allowed but not in case of a `pi`-bond
D. Sigma-bond determines the direction between carbon atoms but a `pi`-bond has no primary effect in this regard

Answer

To determine which statement is incorrect regarding sigma (σ) and pi (π) bonds formed between two carbon atoms, we will analyze each statement carefully.

### Step-by-Step Solution:

1. **Understanding Sigma and Pi Bonds**:
- Sigma (σ) bonds are formed by the head-on overlap of atomic orbitals. They are generally stronger than pi (π) bonds, which are formed by the side-on overlap of p orbitals.

2. **Analyzing the Statements**:
- **Statement A**: "Sigma bond is stronger than a pi bond."
- This statement is **correct** because sigma bonds involve head-on overlap, which is stronger than the side-on overlap found in pi bonds.

- **Statement B**: "Bond energies of Sigma and Pi bonds are of the order 264 kilojoule per mole and 347 kilojoule per mole respectively."
- This statement is **incorrect**. Since sigma bonds are stronger than pi bonds, the bond energy of sigma bonds should be higher than that of pi bonds. Therefore, the bond energy for sigma should be greater than 347 kJ/mol, and for pi, it should be less than 264 kJ/mol.

- **Statement C**: "Free rotation of surrounding atoms about a sigma bond is allowed but not in the case of pi bond."
- This statement is **correct**. Free rotation is allowed around sigma bonds because they do not have the restrictions that pi bonds do, which are fixed in space due to their side-on overlap.

- **Statement D**: "Sigma bond determines the direction between carbon atoms but a Pi bond has no primary effect in this regard."
- This statement is **correct**. The sigma bond does determine the orientation of the bonded atoms, while the pi bond does not affect the directionality.

3. **Conclusion**:
- The incorrect statement is **Statement B**.

### Final Answer:
**The incorrect statement is B**: "Bond energies of Sigma and Pi bonds are of the order 264 kilojoule per mole and 347 kilojoule per mole respectively."