The carboxylic acid shown is converted to its sodium salt and heated with soda lime. Which structure is the hydrocarbon formed?

The compound shown is 3-methylbutanoic acid. Decarboxylation with soda lime removes the carboxyl carbon as carbonate and puts H in its place, so the alkane has one carbon fewer: the four-carbon branched 2-methylpropane. Butane has the wrong skeleton and 2-methylbutane has the carbon count of the acid.