Step 1: Understanding the Concept:
Avogadro's law states that equal volumes of all ideal gases at the same temperature and pressure contain the same number of molecules. Standard Temperature and Pressure (STP) is defined such that $1$ mole of any ideal gas occupies a standard volume. Step 2: Key Formula or Approach:
Molar volume of a gas at STP \(\approx 22.4\text{ L/mol}\) (or \(22.4\text{ dm}^3\text{/mol}\)).
\[ \text{Volume} = \text{number of moles} \times \text{molar volume} \]
Step 3: Detailed Explanation:
Given:
Number of moles (\(n\)) = \(0.5\text{ mol}\)
Molar volume at STP = \(22.4\text{ dm}^3\text{/mol}\)
Substitute the values into the formula:
\[ \text{Volume} = 0.5\text{ mol} \times 22.4\text{ dm}^3\text{/mol} \]
\[ \text{Volume} = 11.2\text{ dm}^3 \]
Step 4: Final Answer:
The volume occupied is \(11.2\text{ dm}^3\), which matches option (B).