Question

What is the number of $\text{sp}^{3}$ hybrid carbon atoms in $\text{HO(CH}_{2})_{3}\text{CH(CH}_{3})\text{CH(CH}_{3})_{2}$?

• A. Five
• B. Two
• C. Eight
• D. Four

Hint:

To determine the hybridization of a carbon atom, count the number of sigma bonds and lone pairs around it. If a carbon atom has four single bonds (and no lone pairs), it is $\text{sp}^{3}$ hybridized. If it has one double bond and two single bonds, it is $\text{sp}^{2}$ hybridized. If it has one triple bond and one single bond, or two double bonds, it is $\text{sp}$ hybridized.

Answer 1

The Correct Option is A

Step 1: Draw the expanded structural formula of the given compound $\text{HO(CH}_{2})_{3}\text{CH(CH}_{3})\text{CH(CH}_{3})_{2}$. The compound can be written as: \[ \text{HO-CH}_{2}\text{-CH}_{2}\text{-CH}_{2}\text{-CH(CH}_{3})\text{-CH(CH}_{3})_{2} \]
Step 2: Identify each carbon atom in the molecule. The carbon atoms are present in:

• One $\text{CH}_{2}$ group directly attached to the hydroxyl group ($\text{HO-CH}_{2}-$)
• Two $\text{CH}_{2}$ groups in the middle of the chain ($\text{-CH}_{2}\text{-CH}_{2}-$)
• One $\text{CH}$ group with a methyl branch ($\text{-CH(CH}_{3})-$)
• One $\text{CH}$ group with two methyl branches ($\text{-CH(CH}_{3})_{2}$)
• Three $\text{CH}_{3}$ (methyl) groups as branches (one from the $\text{CH(CH}_{3})$ part and two from the $\text{CH(CH}_{3})_{2}$ part)

Step 3: Determine the hybridization of each carbon atom. A carbon atom is $\text{sp}^{3}$ hybridized if it forms four single bonds (i.e., it is saturated). In the given compound, all carbon atoms are saturated, meaning they only form single bonds with other atoms (carbon or hydrogen). Let's count them:

• The carbon in $\text{HO-CH}_{2}$- (1 carbon, $\text{sp}^{3}$)
• The two carbons in the middle $\text{-CH}_{2}\text{-CH}_{2}$- (2 carbons, each $\text{sp}^{3}$)
• The carbon in $\text{-CH(CH}_{3})-$, which is part of the main chain (1 carbon, $\text{sp}^{3}$)
• The carbon in the $\text{CH}_{3}$ branch attached to the $\text{CH(CH}_{3})$ group (1 carbon, $\text{sp}^{3}$)
• The carbon in $\text{-CH(CH}_{3})_{2}$, which is part of the main chain (1 carbon, $\text{sp}^{3}$)
• The two carbons in the two $\text{CH}_{3}$ branches attached to the $\text{CH(CH}_{3})_{2}$ group (2 carbons, each $\text{sp}^{3}$)

Step 4: Sum the total number of $\text{sp}^{3}$ hybridized carbon atoms. Total $\text{sp}^{3}$ carbons = $1 + 2 + 1 + 1 + 1 + 2 = 8$. Therefore, there are 8 $\text{sp}^{3}$ hybrid carbon atoms in the molecule.