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When 75.2 g of calcium and 32.8 g of nitrogen gas undergo a reaction that has a 94.2% yield, what mass of calcium nitride forms?

Be sure your answer has the correct number of significant figures.

a) 100.5 g
b) 67.8 g
c) 143.0 g
d) 115.2 g

Answer :

Final answer:

By calculating the moles of each reactant, determining the limiting reactant through stoichiometry, and adjusting for percent yield, we can find the mass of calcium nitride produced. With calcium being the limiting reactant, we calculate a theoretical yield of 92.76 g and apply the percent yield to find the actual yield, which should be 87.35 g with four significant figures.

Explanation:

To determine the mass of calcium nitride formed, first the stoichiometry of the reaction between calcium and nitrogen must be understood. The balanced equation is: 3Ca + N2
ightarrow Ca3N2. Next, we must find the limiting reactant by calculating the moles of each reactant. The molar masses are 40.08 g/mol for calcium and 28.02 g/mol for nitrogen gas (N2).

For calcium: 75.2 g Ca * (1 mol Ca / 40.08 g Ca) = 1.877 moles of Ca.
For nitrogen: 32.8 g N2 * (1 mol N2 / 28.02 g N2) = 1.171 moles of N2.

Now, we use the stoichiometry from the balanced chemical equation to find the limiting reactant: For every 1 mole of N2, 3 moles of Ca are required. So for 1.171 moles of N2, we would need 3.513 moles of Ca, which is more than we have, meaning calcium is the limiting reactant. Using the stoichiometry of the reaction, the moles of calcium will dictate the moles of calcium nitride product formed.

1.877 moles of Ca will produce 1.877/3 = 0.6257 moles of Ca3N2. The molar mass of Ca3N2 is (3*40.08) + (2*14.01) = 148.27 g/mol. Therefore, the theoretical yield of Ca3N2 is 0.6257 moles * 148.27 g/mol = 92.76 g.

To account for the actual yield, we multiply by the percent yield: 92.76 g * 94.2% = 87.35g. Given the significant figures from the mass of reactants, our answer will have four significant figures, which makes the final answer 87.35 g, as we can assume a theoretical option that is not listed here. This doesn't match the options given, indicating an error in the question or answer choices.

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