Lovastatin (C24H36O5) has a molar mass of 404.53 g/m. The normal dose of the drug lovastain is 20mg. How many molecules of lovastatin (C24H36O5) are in a normal dose?
How many moles are there in 20 mg?
0.020 grams/molar mass = moles lovastatin.
Now convert moles to molecules remembering that there are 6.022E23 molecules in 1 mole.
To determine the number of molecules of lovastatin (C24H36O5) in a normal dose, we need to use the concept of Avogadro's number and mole-to-molecule conversion.
1. Start by calculating the molar mass of lovastatin (C24H36O5):
- The molecular formula (C24H36O5) indicates that there are 24 carbon atoms (C), 36 hydrogen atoms (H), and 5 oxygen atoms (O) in one molecule of lovastatin.
- The atomic masses of carbon (C), hydrogen (H), and oxygen (O) are approximately 12.01 g/mol, 1.01 g/mol, and 16.00 g/mol, respectively.
- Multiply the number of atoms by their respective atomic masses and sum them up:
Molar mass of C = 24 × 12.01 g/mol = 288.24 g/mol
Molar mass of H = 36 × 1.01 g/mol = 36.36 g/mol
Molar mass of O = 5 × 16.00 g/mol = 80.00 g/mol
Total molar mass = 288.24 g/mol + 36.36 g/mol + 80.00 g/mol = 404.60 g/mol
2. The molar mass of lovastatin is determined to be 404.60 g/mol. However, there seems to be a discrepancy between the given value (404.53 g/mol) and the calculated value (404.60 g/mol). Therefore, we will use the calculated value (404.60 g/mol) to ensure accuracy in the calculation.
3. Convert the given dose of lovastatin to moles:
- The given dose is 20 mg (milligrams) = 20 × 10^(-3) g (grams).
- To convert grams to moles, divide the mass by the molar mass:
Moles of lovastatin = (20 × 10^(-3) g) / (404.60 g/mol)
≈ 4.94 × 10^(-5) mol
4. Apply Avogadro's number to convert moles to molecules:
- Avogadro's number (NA) is approximately 6.022 × 10^(23) molecules/mol.
- Multiply the number of moles by Avogadro's number to find the number of molecules:
Number of molecules = (4.94 × 10^(-5) mol) × (6.022 × 10^(23) molecules/mol)
≈ 2.97 × 10^(19) molecules
Therefore, in a normal dose of lovastatin (20 mg), there are approximately 2.97 × 10^(19) molecules of lovastatin (C24H36O5).