To solve this problem, we need to determine the limiting reactant and then calculate the amount of HCO₂H produced using the given information.
1. Calculate the molar masses of each reactant:
H₂S: 2.02 g/mol (hydrogen has a molar mass of 1.01 g/mol and sulfur has a molar mass of 32.07 g/mol)
FeS: 87.91 g/mol (natural isotopic abundances)
CO₂: 44.01 g/mol (carbon has a molar mass of 12.01 g/mol and oxygen has a molar mass of 16.00 g/mol)
2. Convert the given masses to moles:
moles of FeS = 2.65 g / 87.91 g/mol = 0.0301 mol
moles of H₂S = 1.32 g / 34.08 g/mol = 0.0387 mol
moles of CO₂ = 1.32 g / 44.01 g/mol = 0.0300 mol
3. Set up a mole ratio based on the balanced equation:
1 mol FeS : 1 mol H₂S : 1 mol CO₂ : 1 mol FeS₂ : 1 mol HCO₂H
4. Determine the limiting reactant:
To find the limiting reactant, compare the moles of each reactant and see which one is the smallest. In this case, the smallest number of moles is 0.0300 mol for CO₂. Therefore, CO₂ is the limiting reactant.
5. Calculate the theoretical yield of HCO₂H:
Using the mole ratio from the balanced equation, we can see that 1 mol of CO₂ produces 1 mol of HCO₂H.
Therefore, the theoretical yield of HCO₂H is 0.0300 mol.
6. Calculate the actual yield of HCO₂H:
The reaction has a 54.0% yield, so the actual yield is 0.540 * 0.0300 mol = 0.0162 mol.
7. Convert the molar amount of HCO₂H to grams:
mass of HCO₂H = 0.0162 mol * 46.03 g/mol (carbon has a molar mass of 12.01 g/mol, oxygen has a molar mass of 16.00 g/mol, and hydrogen has a molar mass of 1.01 g/mol)
mass of HCO₂H = 0.744 g
Therefore, the amount of HCO₂H obtained from the given reactants is 0.744 grams.