Final answer:
The percent composition of carbon in caffeine (C8H10N4O2) is calculated by dividing the total mass of carbon in one mole of the substance by its molar mass and multiplying by 100, which equals 49.48%.
Step-by-step explanation:
The student has asked for the percent composition of carbon in caffeine, with the molecular formula C₈H₁₀N₄O₂. To calculate the percent composition, we first need to determine the molar mass of caffeine using the atomic masses of carbon (C), hydrogen (H), nitrogen (N), and oxygen (O). Then, we calculate the percentage by dividing the total mass of carbon in one mole of caffeine by the molar mass of caffeine and multiply by 100.
To calculate the percent composition of carbon in caffeine:
- The molar mass of carbon is approximately 12.01 g/mol.
- Caffeine contains 8 atoms of carbon, so the total mass of carbon in each molecule of caffeine is 8 × 12.01 = 96.08 g/mol.
- The molar mass of caffeine (C₈H₁₀N₄O₂) is calculated by adding the molar masses of all atoms in the molecule: (8 × 12.01) + (10 × 1.01) + (4 × 14.01) + (2 × 16.00) = 194.19 g/mol.
- Finally, the percent composition of carbon in caffeine is (96.08 g/mol ÷ 194.19 g/mol) × 100 = 49.48%.