Question

Cholesterol ${\mathit{C}}_{\mathbf{27}}{\mathit{H}}_{\mathbf{46}}\mathit{O}$has the following structure

In such shorthand structures, each point where lines meet represents a carbon atom and most H atom are not shown. Draw the complete structure showing all carbon and hydrogen atom (There will be four bonds to each carbon atom). Indicate which carbon atoms use sp₂or sp₃ hybrid orbital. Are all carbon atoms in the same plane as implied by the structure?

Short answer

Carbon which has four σ bonds with other atoms like hydrogen, oxygen, carbon, nitrogen is sp₃hybridized.

Carbon which has threeσ bonds and one π with other atoms like hydrogen, oxygen, carbon, nitrogen is sp₂.hybridized.

Each π bond has one σ and one π orbital.

Step-by-step solution

Step 1:

The structure of cholesterol is as follow

Step 2:

Counting the number of single bonds

There are four σ bond in

$$\begin{gathered} C_1,C_2,C_4,C_5,C_6,C_7,C_9,C_{10},C_{11},C_{12},C_{13},C_{14},C_{15},C_{16},C_{17},C_{18},C_{19},C_{20},C_{21} \\ {C}_{22},C_{23},C_{24},C_{25},C_{26},C_{27} \end{gathered}$$

Hence carbons which are sp₃ hybridized are

$$\begin{gathered} C_1,C_2,C_4,C_5,C_6,C_7,C_9,C_{10},C_{11},C_{12},C_{13},C_{14},C_{15},C_{16},C_{17},C_{18},C_{19},C_{20},C_{21} \\ {C}_{22},C_{23},C_{24},C_{25},C_{26},C_{27} \end{gathered}$$

And the carbon which is sp₂ hybridized are

$C_3,C_8$

Step 3:

The carbons which are sp₂ hybridized or attached to double bonded carbon lie in the plane $C_2,C_4,C_3,C_8,C_9$ rest lie in other plane.