Myrcene, a fragrant compound found in bayberry wax, has the formula \mathrm{C}_{10} \mathrm{H}_{16}C 10 H 16 and is known not to contain any triple bonds. (a) What is the index of hydrogen deficiency of myrcene? When treared with excess hydrogen and a platinum caralyst, myrcene is converted to a compound (A) with the formula \mathrm{C}_{10} \mathrm{H}_{22}.C 10 H 22 (b) How many rings does myrcene contain? (c) How many double bonds? Compound A can be identificd as 2,6 -dimethyloctane. Oronolysis of myrcene followed by treatment with dimethyl sulfide yields 2 mol of formaldehyde (HCHO), 1 mol of acetone \left(\mathrm{CH}_{3} \mathrm{COCH}_{3}\right),(CH 3 COCH 3), and a third compound B with the formula \mathrm{C}_{5} \mathrm{H}_{6} \mathrm{O}_{3}.C 5 H 6 O 3. (d) What is che structure of compound B? (e) What is the structure of myrcene?