Answer :
Final answer:
To determine the mass of A required to produce 27 g of C, convert the mass of C to moles, use the stoichiometric ratios from the reaction to convert to moles of A, and then convert back to grams using the molar mass of A. The calculation produces a result of 13.19 g of A, which does not match the provided options, indicating a possible mistake in the question or the options.
Explanation:
To calculate the mass of A required to produce 27 g of C in the given reaction (2A + B → 3C), you can use the concepts of stoichiometry and molar mass. First, determine the molar mass of C (133.9 g/mol) and then how many moles 27 g of C represents. Since the reaction produces 3 moles of C for every 2 moles of A reacted, you can find the number of moles of A needed. Finally, use the molar mass of A (98.2 g/mol) to convert moles of A to grams.
The calculation is as follows:
- 27 g C × (1 mol C / 133.9 g C) = 0.2015 moles of C
- To find moles of A: 0.2015 moles C × (2 moles A / 3 moles C) = 0.1343 moles of A
- To find grams of A: 0.1343 moles A × (98.2 g/mol A) = 13.19 g of A
This result, however, is not listed in the given options. Double-checking the stoichiometry and molar masses might be necessary as there might be a typo or error in the question or the options provided. According to the Law of Conservation of Mass, the mass of products must equal the mass of reactants. Confirming the options with the total mass of the products and reactants could provide an additional check on the calculation.
