Determine the mass of phosphoric acid that can be produced by the reaction of 1 ton of phosphate rock, Ca(PO4)2, and sulfuric acid.
To determine the mass of phosphoric acid produced, we need to first calculate the molar mass of phosphoric acid (H3PO4) and phosphorus pentoxide (P2O5), then use stoichiometry to find the mass of phosphoric acid produced from 1 ton of phosphate rock.
1. Calculate the molar mass of phosphoric acid (H3PO4):
- The molar mass of hydrogen (H) is 1 g/mol.
- The molar mass of phosphorus (P) is 31 g/mol.
- The molar mass of oxygen (O) is 16 g/mol.
The molar mass of H3PO4 = (3 * 1) + 31 + (4 * 16) = 97 g/mol.
2. Calculate the molar mass of phosphorus pentoxide (P2O5):
- The molar mass of phosphorus (P) is 31 g/mol.
- The molar mass of oxygen (O) is 16 g/mol.
The molar mass of P2O5 = (2 * 31) + (5 * 16) = 142 g/mol.
3. Determine the stoichiometry of the reaction between phosphate rock and sulfuric acid:
- The balanced equation for the reaction is:
Ca(PO4)2 + 3H2SO4 -> 2H3PO4 + CaSO4
- The ratio between Ca(PO4)2 and H3PO4 is 1:2. Thus, for every 1 mole of phosphate rock, we get 2 moles of phosphoric acid.
4. Convert 1 ton of phosphate rock to moles:
- 1 ton = 1000 kg = 1000000 g (since 1 ton = 1000 kg = 1000000 g)
- The molar mass of Ca(PO4)2 = (1 * 40.08) + (2 * 31.04) + (8 * 16.00) = 310.18 g/mol
- Moles of Ca(PO4)2 = mass / molar mass = 1000000 g / 310.18 g/mol = 3223.24 mol
5. Calculate the moles of phosphoric acid produced:
- Moles of H3PO4 = 2 * Moles of Ca(PO4)2 = 2 * 3223.24 mol = 6446.48 mol
6. Calculate the mass of phosphoric acid produced:
- Mass of H3PO4 = moles of H3PO4 * molar mass of H3PO4 = 6446.48 mol * 97 g/mol = 625,974.56 g
Therefore, the mass of phosphoric acid that can be produced by the reaction of 1 ton of phosphate rock and sulfuric acid is approximately 625,974.56 grams or 625.97 kilograms.