MHT CET · Chemistry · Chemical Bonding and Molecular Structure

What is bond length of \(\mathrm{C}-\mathrm{C}\) bond in alkane having all carbon atoms \(\mathrm{sp}^{3}\) hybrid?

A \(154 \mathrm{pm}\)
B \(133 \mathrm{pm}\)
C \(112 \mathrm{pm}\)
D \(120 \mathrm{pm}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(154 \mathrm{pm}\)

Step-by-step Solution

Detailed explanation

The carbon-carbon bond, with a bond length of \(1.54 ~Ã…\), is formed by overlap of one \(sp3\) orbital from each of the carbons, while the six carbon-hydrogen bonds are formed from overlaps between the remaining \(sp3\) orbitals on the two carbons and the \(1s\) orbitals of hydrogen atoms. All of these are sigma bonds.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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