Step 1: Identify the reaction type.
Dry distillation of calcium salts of carboxylic acids results in the formation of symmetrical ketones. This reaction is also known as ketonic decarboxylation.
Step 2: Apply to calcium propionate.
Calcium propionate is the calcium salt of propanoic acid. On dry distillation, two propionyl groups combine to form a ketone.
Step 3: Write the reaction.
\[
\mathrm{(CH_3CH_2COO)_2Ca \xrightarrow{\Delta} CH_3CH_2COCH_2CH_3 + CaCO_3}
\]
Step 4: Identify the product.
The ketone formed is \(\mathrm{CH_3CH_2COCH_2CH_3}\), which is pentan-3-one.
Step 5: Conclusion.
Thus, dry distillation of calcium propionate yields pentan-3-one.