Step 1: Understanding the Concept:
Glycerol is a polyhydric alcohol with three hydroxyl groups. Identifying the types of alcoholic groups requires examining the degree of the carbon atoms they are attached to.
Step 2: Key Formula or Approach:
Analyze the molecular structure of the compound (Propane-1,2,3-triol) to identify the number of carbon atoms attached to one (primary) or two (secondary) other carbon atoms, and count the respective attached hydroxyl groups.
Step 3: Detailed Explanation:
The chemical formula of glycerol is $CH_{2}OH-CHOH-CH_{2}OH$.
1. The two terminal $-OH$ groups are attached to $CH_{2}$ groups. Since these carbons are bonded to only one other carbon atom, they are primary ($1^{\circ}$) carbons. Hence, there are two primary alcoholic groups.
2. The middle $-OH$ group is attached to a $CH$ group. This carbon is bonded to two other carbon atoms, making it a secondary ($2^{\circ}$) carbon. Hence, there is one secondary alcoholic group.
Step 4: Final Answer:
Glycerol contains two primary and one secondary alcoholic groups.