Calculate the percentage by mass of the indicated element in the following compounds: (a) hydrogen in methane, \(\mathrm{CH}_{4}\), the major hydrocarbon in natural gas; \((\mathbf{b})\) oxygen in vitamin $\mathrm{E}, \mathrm{C}_{29} \mathrm{H}_{50} \mathrm{O}_{2} ;$ (c) sulphur in magnesium sulphate, \(\mathrm{MgSO}_{4}\), a substance used as a drying agent; \((\mathbf{d})\) nitrogen in epinephrine, \(\mathrm{C}_{9} \mathrm{H}_{13} \mathrm{NO}_{3},\) also known as adrenalin, a hormone that is important for the fightor-flight response; (e) oxygen in the insect pheromone sulcatol, $\mathrm{C}_{8} \mathrm{H}_{16} \mathrm{O} ;\( (f) carbon in sucrose, \)\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11},$ the compound that is responsible for the sweet taste of table sugar.

First, we need to calculate the molar mass of each compound and the mass of the indicated element in each compound. (a) Methane (CH4): Molar mass of C = 12.01 g/mol Molar mass of H = 1.01 g/mol Molar mass of CH4 = (12.01 + 4 * 1.01) g/mol = 16.05 g/mol (b) Vitamin E (C29H50O2): Molar mass of C = 12.01 g/mol Molar mass of H = 1.01 g/mol Molar mass of O = 16.00 g/mol Molar mass of C29H50O2 = (29 * 12.01 + 50 * 1.01 + 2 * 16.00) g/mol = 430.72 g/mol (c) Magnesium sulphate (MgSO4): Molar mass of Mg = 24.31 g/mol Molar mass of S = 32.07 g/mol Molar mass of O = 16.00 g/mol Molar mass of MgSO4 = (24.31 + 32.07 + 4 * 16.00) g/mol = 120.38 g/mol (d) Epinephrine (C9H13NO3): Molar mass of C = 12.01 g/mol Molar mass of H = 1.01 g/mol Molar mass of N = 14.01 g/mol Molar mass of O = 16.00 g/mol Molar mass of C9H13NO3 = (9 * 12.01 + 13 * 1.01 + 14.01 + 3 * 16.00) g/mol = 183.22 g/mol (e) Sulcatol (C8H16O): Molar mass of C = 12.01 g/mol Molar mass of H = 1.01 g/mol Molar mass of O = 16.00 g/mol Molar mass of C8H16O = (8 * 12.01 + 16 * 1.01 + 16.00) g/mol = 128.22 g/mol (f) Sucrose (C12H22O11): Molar mass of C = 12.01 g/mol Molar mass of H = 1.01 g/mol Molar mass of O = 16.00 g/mol Molar mass of C12H22O11 = (12 * 12.01 + 22 * 1.01 + 11 * 16.00) g/mol = 342.34 g/mol

Now, we will calculate the mass percentage of each indicated element in the given compounds. (a) Hydrogen in methane: Percentage of H in CH4 = (4 * 1.01 / 16.05) * 100 = 25.17% (b) Oxygen in vitamin E: Percentage of O in C29H50O2 = (2 * 16.00 / 430.72) * 100 = 7.43% (c) Sulphur in magnesium sulphate: Percentage of S in MgSO4 = (32.07 / 120.38) * 100 = 26.65% (d) Nitrogen in epinephrine: Percentage of N in C9H13NO3 = (14.01 / 183.22) * 100 = 7.65% (e) Oxygen in sulcatol: Percentage of O in C8H16O = (16.00 / 128.22) * 100 = 12.48% (f) Carbon in sucrose: Percentage of C in C12H22O11 = (12 * 12.01 / 342.34) * 100 = 42.12% These calculated percentages are the mass percentages of the indicated element in each compound.