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Chapter 3: Problem 112

Phosphorus can be prepared from calcium phosphate by the following reaction: \(2 \mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}(s)+6 \mathrm{SiO}_{2}(s)+10 \mathrm{C}(s) \longrightarrow\) \(6 \mathrm{CaSiO}_{3}(s)+\mathrm{P}_{4}(s)+10 \mathrm{CO}(g)\) Phosphorite is a mineral that contains \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\) plus other non-phosphorus- containing compounds. What is the maximum amount of \(\mathrm{P}_{4}\) that can be produced from \(1.0 \mathrm{~kg}\) of phosphorite if the phorphorite sample is \(75 \% \mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\) by mass? Assume an excess of the other reactants.

Short Answer

Expert verified
The maximum amount of P4 that can be produced from 1.0 kg of phosphorite containing 75% Ca3(PO4)2 by mass is approximately 150 g.

Step by step solution

01

1. Calculate the mass of Calcium Phosphate in the Phosphorite sample

To determine the mass of Ca3(PO4)2 in the phosphorite sample, we will multiply the total mass of the phosphorite sample (1.0 kg) by the percentage of Ca3(PO4)2 available in it (75%). Mass of Ca3(PO4)2 = (total mass of phosphorite sample) x (percentage of Ca3(PO4)2) Mass of Ca3(PO4)2 = (1.0 kg) x (0.75) Mass of Ca3(PO4)2 = 0.75 kg
02

2. Convert the mass of Calcium Phosphate to moles

Next, we need to find the number of moles of Ca3(PO4)2 present in the phosphorite sample. For this, we will use the molar mass of Ca3(PO4)2, which is 310.18 g/mol. First, we need to convert the mass of Ca3(PO4)2 from kg to grams: Mass of Ca3(PO4)2 = 0.75 kg x (1000 g/kg) = 750 g Now, we can calculate the number of moles: Number of moles of Ca3(PO4)2 = (mass of Ca3(PO4)2) / (molar mass of Ca3(PO4)2) Number of moles of Ca3(PO4)2 = (750 g)/(310.18 g/mol) ≈ 2.42 mol
03

3. Find the moles of P4 produced using stoichiometry

From the balanced equation, we can see that 2 moles of Ca3(PO4)2 produce 1 mole of P4. Therefore, we will use the stoichiometry of the reaction to find the number of moles of P4 produced. Number of moles of P4 produced = (Number of moles of Ca3(PO4)2) x (1 mole of P4 / 2 moles of Ca3(PO4)2) Number of moles of P4 produced = (2.42 mol) x (1/2) = 1.21 mol
04

4. Calculate the mass of P4 produced

Now that we know the number of moles of P4 produced, we can calculate the mass of P4. The molar mass of P4 is 123.88 g/mol. Mass of P4 produced = (number of moles of P4) x (molar mass of P4) Mass of P4 produced = (1.21 mol) x (123.88 g/mol) ≈ 150 g The maximum amount of P4 that can be produced from 1.0 kg of phosphorite is approximately 150 g.

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