Which of the following is a secondary allylic alcohol?
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To classify an allylic alcohol, first identify the allylic carbon (the carbon bearing the -OH group and adjacent to a $C=C$ double bond). Then, count the number of alkyl or carbon groups directly attached to this allylic carbon (excluding the -OH group and considering the $C=C$ portion as one substituent if it's the chain). One alkyl group is primary, two are secondary, and three are tertiary.
Step 1: Definition of allylic alcohol
An allylic alcohol is an alcohol in which the hydroxyl group (${-}\mathrm{OH}$) is attached to a carbon atom adjacent to a carbon--carbon double bond ($\mathrm{C=C}$).
This adjacent carbon is called the \textit{allylic carbon}.
Step 2: Classification of allylic alcohols
Allylic alcohols are classified based on the number of carbon groups attached to the carbon bearing the $-\mathrm{OH}$ group:
Primary: Attached to one carbon and two hydrogens
Secondary: Attached to two carbons and one hydrogen
Tertiary: Attached to three carbons and no hydrogen
Step 3: Analysis of given options
A. $\mathrm{H_2C = CH - CH_2 - OH$}
The $-\mathrm{OH}$ is on $\mathrm{CH_2}$, which is bonded to one carbon and two hydrogens.
$\Rightarrow$ Primary allylic alcohol
B. $\mathrm{CH_3 - CH = CH - CH_2 - OH$}
The $-\mathrm{OH}$ is on $\mathrm{CH_2}$, bonded to one carbon and two hydrogens.
$\Rightarrow$ Primary allylic alcohol
C. $\mathrm{H_2C = CH - CH(CH_3) - OH$}
The $-\mathrm{OH}$ is on $\mathrm{CH}$, which is bonded to two carbon groups and one hydrogen.
$\Rightarrow$ Secondary allylic alcohol
D. $\mathrm{CH_2 = CH - C(CH_3)_2 - OH$}
The $-\mathrm{OH}$ is on a carbon bonded to three carbon groups and no hydrogen.
$\Rightarrow$ Tertiary allylic alcohol
Step 4: Conclusion
The compound that is a secondary allylic alcohol is:
\[
\boxed{\text{Option C
\]