Step 1: Understanding the Concept:
Alcohols react with sodium metal to give sodium alkoxide and hydrogen gas. The balanced equation tells the mole ratio.
Step 2: Balanced equation:
\[ 2\text{C}_2\text{H}_5\text{OH} + 2\text{Na} \to 2\text{C}_2\text{H}_5\text{ONa} + \text{H}_2 \]
Step 3: Calculate:
\(2\) mol of ethanol give \(1\) mol of \(\text{H}_2\). So \(6\) mol of ethanol give \(\frac{6}{2} = 3\) mol of \(\text{H}_2\).
Step 4: Other options:
\(6\) mol would be the answer if each ethanol released one \(\text{H}_2\). Each molecule only has one acidic hydrogen (the O-H), and two such hydrogens are needed per \(\text{H}_2\).
Final Answer:
Three moles of hydrogen are liberated, option (B).
\[ \boxed{3\ \text{mol}} \]