To determine the limiting reagent, we need to compare the amount of moles of each reactant used in the chemical reaction. The reactant that produces the least amount of product is the limiting reagent.
First, let's calculate the number of moles of each reactant:
- Moles of Ca3(PO4)2 = (155 g) / (310.18 g/mol) = 0.5 mol
- Moles of H2SO4 = (155 g) / (98.08 g/mol) = 1.58 mol
- Moles of H3PO4 = (88 g) / (97.99 g/mol) = 0.898 mol
According to the balanced chemical equation, 1 mole of Ca3(PO4)2 reacts with 3 moles of H2SO4 to produce 2 moles of H3PO4. Therefore, if we use 0.5 moles of Ca3(PO4)2, we need 1.5 moles of H2SO4 to react completely.
Since we only have 1.58 moles of H2SO4, this means that H2SO4 is not the limiting reagent. However, if we use 0.5 moles of Ca3(PO4)2, we will only produce 1 mole of H3PO4. Since we need 0.898 moles of H3PO4 to use up all of the available phosphoric acid, Ca3(PO4)2 is the limiting reagent.
Therefore, the limiting reagent in this reaction is Ca3(PO4)2.
Note: It is important to check the calculation for each reactant to ensure that we have the correct limiting reagent. In this case, we found that H2SO4 was not the limiting reagent because we had more moles of H2SO4 than what was needed to react with all of the Ca3(PO4)2. If we had found that H2SO4 was the limiting reagent, we would have needed to recalculate the amount of product produced using the moles of H2SO4 instead of Ca3(PO4)2.