(a) One molecule of the antibiotic penicillin G has a mass of \(5.342 \times 10^{-21} \mathrm{g} .\) What is the molar mass of penicillin G? (b) Hemoglobin, the oxygen-carrying protein in red blood cells, has four iron atoms per molecule and contains 0.340\(\%\) iron by mass. Calculate the molar mass of hemoglobin.

To calculate the molar mass of penicillin G, we need to find the mass of one mole of the compound. We are given the mass of one molecule of penicillin G, and we can use Avogadro's number to find the mass of one mole of penicillin G \(6.022 \times 10^{23}\). Molar mass of Penicillin G = Mass of one molecule × Avogadro's number = \(5.342 \times 10^{-21}\mathrm{g}\) × \(6.022 \times 10^{23}\) = \(3.216 \times 10^{3}\mathrm{g/mol}\) The molar mass of penicillin G is approximately 3.216 × 10³ g/mol.

We are given that hemoglobin contains 0.340% iron by mass and has four iron atoms per molecule. We can use this information to calculate the molar mass of hemoglobin. First, let's find the mass of iron per molecule of hemoglobin by dividing the total mass of all iron atoms in one molecule by the percentage of iron content: Mass of iron in one molecule of hemoglobin = \(4 \times\) molar mass of iron × (percentage mass of iron / 100%) Now, we know that the molar mass of iron (Fe) is approximately 55.85 g/mol. Mass of iron in one molecule of hemoglobin = \(4 \times 55.85 \times (0.340/100)\) = \(3.0356\) Since the mass of iron in one molecule of hemoglobin is 3.0356 g, the mass of one molecule of hemoglobin can be expressed as: Mass of one molecule of hemoglobin = Mass of iron in one molecule of hemoglobin / (percentage mass of iron / 100%) Mass of one molecule of hemoglobin = \(3.0356 / (0.340/100)\) = \(893.41\) Now that we have the mass of one molecule of hemoglobin, we can find the molar mass by multiplying it by Avogadro's number: Molar mass of hemoglobin = Mass of one molecule × Avogadro's number = \(893.41\) × \(6.022 \times 10^{23}\) = \(5.378 \times 10^{5}\mathrm{g/mol}\) The molar mass of hemoglobin is approximately 5.378 × 10⁵ g/mol.