Final answer:
To consume 0.0424 moles of sucrose, a student must eat approximately 790.945 grams of cereal, calculated using the molar mass of sucrose and the sucrose content per serving of cereal.
Step-by-step explanation:
To calculate how many grams of cereal must be eaten to consume 0.0424 moles of sucrose, we first need the molar mass of sucrose, which is C₁₂H₂₂O₁₁. The molar mass of sucrose is 342 g/mol because the formula includes 12 carbon atoms, 22 hydrogen atoms, and 11 oxygen atoms. Given that the cereal contains 11.0 g of sucrose per 60.0 g of cereal, we can set up a proportion to find the required amount of cereal.
Using the molar mass of sucrose (342 g/mol), we can find that to consume 0.0424 moles of sucrose, one would need:
0.0424 moles × 342 g/mol = 14.5008 g of sucrose
Next, since we know there are 11.0 g of sucrose in 60.0 g of cereal, we can calculate the grams of cereal needed:
11.0 g sucrose → 60.0 g cereal
14.5008 g sucrose → X g cereal
By cross-multiplication, we get:
X = (14.5008 g sucrose × 60.0 g cereal) / 11.0 g sucrose
X = 790.945 g cereal
Therefore, the student would need to consume approximately 790.945 grams of cereal to ingest 0.0424 moles of sucrose.