Final answer:
To calculate the mass of calcium carbonate needed to produce 224g of calcium oxide, a stoichiometric calculation is used. From the given examples, the ratio of CaCO3 to CaO is determined, and the calculation reveals that 400g of CaCO3 is required, which does not match any of the provided options.
Step-by-step explanation:
The student asks how to calculate the mass of calcium carbonate (CaCO3) needed to produce 224g of calcium oxide (CaO). The balanced chemical equation is CaCO3 → CaO + CO2. From previous examples, we know that 10.0 g of CaCO3 produces 5.6 g of CaO. Using stoichiometry, we can set up a proportion:
(10.0 g CaCO3) / (5.6 g CaO) = (x g CaCO3) / (224 g CaO).
To solve for x, which represents the mass of CaCO3, we multiply both sides by 224 g CaO and then divide by 5.6 g CaO:
x = (224 g CaO) * (10.0 g CaCO3) / (5.6 g CaO).
Doing the math yields:
x = 400 g CaCO3.
However, this is not one of the options given. There must have been an error in the calculation—it should be:
x = (224 g CaO) / (5.6 g CaO/g CaCO3).
x = 40.0 g of CaCO3 for each 5.6 g of CaO.
To find out how many grams of CaCO3 are needed for 224g of CaO, we calculate:
x = (224 g / 5.6 g) * 10 g.
x = 40.0 g * 40 = 400 g CaCO3.
The correct answer, therefore, is that 400g of calcium carbonate is needed to produce 224g of calcium oxide, which is not listed in the provided options, indicating either a potential mistake in the provided options or in the student's question. Nonetheless, the student should re-evaluate the question or the options provided.