Final answer:
Calculating the moles of CO₂ produced and using the stoichiometry of the reaction, 30.5 g of CO₂ corresponds to a reaction with 1.386 moles of HCl. Multiplying by the molar mass of HCl gives 50.53 g, which suggests the closest answer option given is 61.0 g.
Step-by-step explanation:
The reaction of limestone with hydrochloric acid is given by CaCO₃(s) + 2HCl(aq) → CaCl₂(aq) + CO₂(g) + H₂O(l). To find out how many grams of HCl reacted to produce 30.5 g of CO₂, we look at the stoichiometry of the reaction. There is a 1:2 molar ratio between CO₂ and HCl. The molar mass of CO₂ is approximately 44.01 g/mol, and the molar mass of HCl is approximately 36.46 g/mol.
Calculating the moles of CO₂ produced:
moles of CO₂ = 30.5 g / 44.01 g/mol = 0.693 moles. Because the stoichiometry of the reaction dictates that 2 moles of HCl react with 1 mole of CO₂, this means that 0.693 moles × 2 = 1.386 moles of HCl reacted. Finding the mass of HCl:
mass of HCl = 1.386 moles × 36.46 g/mol = 50.53 g. The closest answer that fits the given options is c) 61.0 g, indicating either a rounding error in the options provided or an error in the calculation.