Question

(a) Diamond is a natural form of pure carbon. How many moles of carbon are in a \(1.25\) -carat diamond (1 carat \(=0.200 \mathrm{~g}\) )? How many atoms are in this diamond? (b) The molecular formula of acetylsalicylic acid (aspirin), one of the most common pain relievers, is \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\). How many moles of \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\) are in a \(0.500-\mathrm{g}\) tablet of aspirin? How many molecules of \(\mathrm{C}_{9} \mathrm{H}_{6} \mathrm{O}_{4}\) are in this tablet?

Short answer

(a) The 1.25-carat diamond contains 0.0208 moles of carbon and \(1.253\times10^{22}\) atoms of carbon. (b) The 0.500-g tablet of aspirin contains 0.00277 moles of acetylsalicylic acid, and \(1.667\times10^{21}\) molecules of acetylsalicylic acid.

Step-by-step solution

Calculate the mass of the diamond in grams

Given that 1 carat = 0.200 g, we can calculate the mass of the 1.25-carat diamond by multiplying it by the number of carats: 1.25 carats × 0.200 g/carat = 0.250 g

Calculate the number of moles of carbon in the diamond

To convert the mass of the diamond in grams (0.250 g) to moles, we will need the molar mass of carbon, which is 12.01 g/mol: Moles of carbon = \(\frac{0.250 g}{12.01 g/mol} = 0.0208 mol\)

Calculate the number of carbon atoms in the diamond

To convert the number of moles (0.0208 mol) to atoms, we will need Avogadro's number, which is \(6.022\times10^{23}\) atoms/mol: Number of carbon atoms = \(0.0208 mol \times 6.022\times10^{23} atoms/mol = 1.253\times10^{22} atoms\) (b) Aspirin

Calculate the molar mass of acetylsalicylic acid

\(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\) has a molar mass of: \(9\times12.01 g/mol + 8\times1.01 g/mol + 4\times16.00 g/mol = 180.15 g/mol\)

Calculate the number of moles of acetylsalicylic acid in the aspirin tablet

Given a 0.500-g tablet of aspirin, we can calculate the number of moles by using the molar mass calculated in Step 1: Moles of acetylsalicylic acid = \(\frac{0.500 g}{180.15 g/mol} = 0.00277 mol\)

Calculate the number of molecules of acetylsalicylic acid in the aspirin tablet

To convert the number of moles (0.00277 mol) to molecules, we will need Avogadro's number, which is \(6.022\times10^{23}\) molecules/mol: Number of acetylsalicylic acid molecules = \(0.00277 mol \times 6.022\times10^{23} molecules/mol = 1.667\times10^{21} molecules\) Final answers: (a) The 1.25-carat diamond contains 0.0208 moles of carbon and \(1.253\times10^{22}\) atoms of carbon. (b) The 0.500-g tablet of aspirin contains 0.00277 moles of acetylsalicylic acid, and \(1.667\times10^{21}\) molecules of acetylsalicylic acid.