The amino acid methionine, which is essential in human diets, has the molecular formula \(\mathrm{C}_{5} \mathrm{H}_{11} \mathrm{NO}_{2} \mathrm{S}\) Determine (a) its molecular mass; (b) the number of moles of \(\mathrm{H}\) atoms per mole of methionine; (c) the number of grams of \(C\) per mole of methionine; (d) the number of \(C\) atoms in 9.07 mol methionine.

To calculate the molecular mass (in atomic mass units), one must add up the atomic masses of all the atoms present in the molecule. This can be achieved by looking up the atomic masses of \(\mathrm{C}\), \(\mathrm{H}\), \(\mathrm{N}\), \(\mathrm{O}\) and \(\mathrm{S}\), in the periodic table, then multiplying by the number of each atom in the molecular formula and summing up these values. For methionine with a formula of \(\mathrm{C}_{5} \mathrm{H}_{11} \mathrm{NO}_{2} \mathrm{S}\): Atomic masses are \(\mathrm{C}\) = 12.01 amu, \(\mathrm{H}\) = 1.008 amu, \(\mathrm{N}\) = 14.007 amu, \(\mathrm{O}\) = 15.999 amu, \(\mathrm{S}\) = 32.06 amu. Therefore, the molecular mass is \(5 × 12.01 + 11 × 1.008 + 1 × 14.007 + 2 × 15.999 + 1 × 32.06\) = 149.21 amu.

There are as many moles of an atom in a compound as the subscript after that atom in the molecular formula. In this case, the molecular formula tells us that there are 11 moles of H in every mole of methionine.

To calculate the number of grams of carbon (C) per mole of methionine, multiply the number of moles of C in methionine (which is 5 as per the molecular formula) by the atomic mass of carbon (12.01 g/mol). Therefore, the number of grams of carbon per mol of methionine is \(5 × 12.01 = 60.05\) g/mol.

Since there are 5 moles of carbon for every mole of methionine, there would be \(5 × 9.07 = 45.35\) moles of carbon in 9.07 mol methionine. Using Avogadro's number (\(6.022 × 10^{23}\) atoms/mole), we get the total number of carbon atoms to be \(45.35 × (6.022 × 10^{23})\), which rounds off to \(2.73 × 10^{25}\) carbon atoms.