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To do this, we'll use Avogadro's number, which is \(6.022 \times 10^{23}\) molecules/mol. Divide the mass of one molecule by Avogadro's number to get the mass in moles: \[\frac{5.342 \times 10^{-21}\mathrm{~g}}{6.022 \times 10^{23}\text{ molecules/mol}}\]

To find the molar mass, multiply the mass in moles (obtained in step 1) by Avogadro's number (in grams/mole): \[\text{Molar mass of penicillin G} = \frac{5.342 \times 10^{-21}\mathrm{~g}}{6.022 \times 10^{23}\text{ molecules/mol}} \times 6.022 \times 10^{23}\mathrm{~g/mol}\] The numbers \(6.022 \times 10^{23}\) molecules/mol and \(6.022 \times 10^{23}\) g/mol cancel each other out, and you are left with: \[\text{Molar mass of penicillin G} = 5.342 \times 10^{-21}\mathrm{~g} \times \frac{1\mathrm{~mol}}{6.022 \times 10^{23}\text{ molecules}} \times 6.022 \times 10^{23}\mathrm{~g/mol} = 5.342\mathrm{~g/mol}\] # For part (b) # Given that hemoglobin has four iron atoms per molecule, and it contains \(0.340\%\) iron by mass, let's proceed with the following steps to calculate the molar mass of hemoglobin:

To do this, we'll use the percentage of iron by mass: \[0.340\% = \frac{\text{Mass of iron}}{\text{Molar mass of hemoglobin}}\]

The molar mass of iron is \(55.8\mathrm{~g/mol}\). Given that there are four iron atoms in each hemoglobin molecule, the total mass of iron per hemoglobin molecule is: \(4 \times 55.8 = 223.2\mathrm{~g/mol}\)

Now, we can plug in the mass of iron into the equation from step 1 to find the molar mass of hemoglobin: \[0.340\% = \frac{223.2\mathrm{~g/mol}}{\text{Molar mass of hemoglobin}}\] Rearrange the equation and solve for the molar mass of hemoglobin: \[\text{Molar mass of hemoglobin} = \frac{223.2\mathrm{~g/mol}}{0.00340}\]

Divide the mass of iron by the percentage of iron by mass to get the molar mass of hemoglobin: \[\text{Molar mass of hemoglobin} = \frac{223.2\mathrm{~g/mol}}{0.00340} = 65647\mathrm{~g/mol}\] So, the molar mass of hemoglobin is approximately \(65647\mathrm{~g/mol}\).