Step 1: Understanding the Concept:
Decarboxylation is the removal of CO\(_2\) from a carboxylic acid or its salt. Sodium salts of carboxylic acids on decarboxylation with soda lime (NaOH + CaO) yield alkanes.
Step 2: Detailed Explanation:
Sodium propionate is \(CH_3CH_2COONa\). Upon heating with soda lime, it undergoes decarboxylation:
\[ CH_3CH_2COONa + NaOH \xrightarrow{CaO, \Delta} CH_3CH_3 + Na_2CO_3 \]
The product is ethane.
Step 3: Final Answer:
Decarboxylation of sodium propionate gives ethane, option (D).