To determine the molar mass of C₁₆H₁₉N₃O₅S, we need to calculate the sum of the atomic masses of all the atoms in the molecule. Here's the breakdown:
C₁₆: 16 carbon atoms × atomic mass of carbon (12.01 g/mol) = 192.16 g/mol
H₁₉: 19 hydrogen atoms × atomic mass of hydrogen (1.01 g/mol) = 19.19 g/mol
N₃: 3 nitrogen atoms × atomic mass of nitrogen (14.01 g/mol) = 42.03 g/mol
O₅: 5 oxygen atoms × atomic mass of oxygen (16.00 g/mol) = 80.00 g/mol
S: 1 sulfur atom × atomic mass of sulfur (32.07 g/mol) = 32.07 g/mol
Adding all these values together, we get:
192.16 g/mol + 19.19 g/mol + 42.03 g/mol + 80.00 g/mol + 32.07 g/mol = 365.45 g/mol
So, the molar mass of C₁₆H₁₉N₃O₅S is approximately 365.45 g/mol.
To calculate the number of moles of C₁₆H₁₉N₃O₅S in a single tablet (500 mg), we need to convert the mass of the tablet to grams and then divide it by the molar mass.
500 mg = 0.5 g
Number of moles = Mass (in grams) / Molar mass
Number of moles = 0.5 g / 365.45 g/mol ≈ 0.00137 mol
Therefore, there are approximately 0.00137 moles of C₁₆H₁₉N₃O₅S in a single tablet.
If an adult has already taken three doses of C₁₆H₁₉N₃O₅S, we need to calculate the total number of moles consumed. Since each dose is two tablets, the number of moles consumed would be:
Number of moles = 3 doses × 2 tablets/dose × 0.00137 mol/tablet = 0.00822 mol
Therefore, the adult would have taken approximately 0.00822 moles of C₁₆H₁₉N