Answer :
The mass of carbon in 38.6 g of glucose (C₆H₁₂O₆) is calculated by finding the fraction of carbon's mass in the molecular mass of glucose and then multiplying the mass of glucose by this fraction, which results in 15.4 grams of carbon. Therefore, the correct option is B.
To calculate how many grams of carbon (C) are in 38.6 g of glucose (C₆H₁₂O₆), we first need to determine the molar mass of glucose and the proportion of carbon in it. Glucose has a molecular formula of C₆H₁₂O₆, which gives us:
- Carbon (C): 6 atoms
- Hydrogen (H): 12 atoms
- Oxygen (O): 6 atoms
The atomic mass of carbon is 12 g/mol. Thus, the total mass of carbon in one mole of glucose is
6 atoms * 12 g/mol = 72 g/mol. The molar mass of glucose is calculated as follows:
- C: 6 * 12.0 = 72.0 g/mol
- H: 12 * 1.0 = 12.0 g/mol
- O: 6 * 16.0 = 96.0 g/mol
The sum of these values gives us the molar mass of glucose, which is 72.0 + 12.0 + 96.0 = 180.0 g/mol. Next, we find the fraction of carbon's mass in glucose:
Fraction of carbon = Mass of carbon in glucose / Molar mass of glucose
= 72.0 g/mol / 180.0 g/mol
= 0.4 (or 40%)
Now, we multiply the mass of glucose by the fraction of carbon to get:
Mass of carbon in 38.6 g of glucose = 38.6 g * 0.4 = 15.44 g
Therefore, the correct answer to how many grams of carbon are in 38.6 g of glucose is:
15.4 g (Option b)
