The structure of the terpene limonene is shown in the margin. Identify the two 2-methyl-1,3-butadiene (isoprene) units in limonene. (a) Treatment of isoprene with catalytic amounts of acid leads to a variety of oligomeric products, one of which is limonene. Devise a detailed mechanism for the acid-catalyzed conversion of two molecules of isoprene into limonene. Take care to use sensible intermediates in each step. (b) Two molecules of isoprene may also be converted into limonene by a completely different mechanism, which takes place in the strict absence of catalysts of any kind. Describe this mechanism. What is the name of the reaction? 

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CH3 C. CH2 H;C Limonene