Answer :
Final Answer:
To produce 51.7 kg of the calcium sulfate-dihydrogen phosphate mixture, approximately 71.6 kg of sulfuric acid and 79.9 kg of calcium phosphate are required.
Explanation:
The largest application of sulphuric acid is in manufacturing phosphate fertilizers. It reacts with calcium phosphate at a 2:1 mole ratio, yielding calcium sulfate and calcium dihydrogen phosphate. This mixture is crushed and spread on fields where rainwater dissolves the salts. Given the desired product mass of 51.7 kg, we can calculate the required amounts of sulfuric acid and calcium phosphate.
The molar masses of sulfuric acid (H2SO4) and calcium phosphate (Ca3(PO4)2) are 98.08 g/mol and 310.18 g/mol respectively. Using these, we can calculate the moles of each compound required: 71.6 kg of sulfuric acid corresponds to approximately 731 moles, and 79.9 kg of calcium phosphate corresponds to approximately 129 moles.
These moles are in a 2:1 ratio in the reaction, so the limiting reactant is calcium phosphate. Thus, the resulting product will contain 129 moles of phosphate ions. This calculated amount of phosphate ions will contribute significantly to the fertilizing properties of the mixture when dissolved in rainwater, providing essential nutrients for plant growth.
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Final answer:
To produce 51.7 kg of the calcium sulfate dihydrogen phosphate mixture, approximately 58.86 kg of sulphuric acid and 94.08 kg of calcium phosphate are required. This mixture will provide around 300.34 moles of phosphate ion.
Explanation:
The question involves a stoichiometric calculation in chemistry, specifically looking at the production of calcium sulphate and calcium dihydrogen phosphate. The reaction between sulphuric acid and calcium phosphate occurs in a 2:1 mole ratio, meaning for every 1 mole of calcium phosphate, 2 moles of sulphuric acid are required.
According to the given question, we need to convert the mass of the produced compound to moles to perform the calculation. Let's assume the formula of calcium sulphate dihydrogen phosphate is CaH2(PO4)2. The molar mass of this compound is around 172.09 g/mol.
So, 51.7 kg (or 51,700 g) would be around 300.34 moles (51,700 g / 172.09 g/mol) of the mixture. As the reaction is balanced in a 2:1 mole ratio, this means that we would need approximately 600.68 moles (or 58.86 kg) of sulfuric acid (assuming a molar mass of 98.08 g/mol) and 300.34 moles (or 94.08 kg) of calcium phosphate (assuming an average molar mass of 310.18 g/mol).
As for the moles of phosphate ion this mixture will provide, every mole of calcium dihydrogen phosphate releases 1 mole of phosphate ion so 300.34 moles of calcium dihydrogen phosphate will give 300.34 moles of phosphate ion.
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