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Chapter 18: Problem 41

A first-stage recovery of magnesium from seawater is precipitation of \(\mathrm{Mg}(\mathrm{OH})_{2}\) with CaO: $$\mathrm{Mg}^{2+}(a q)+\mathrm{CaO}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Mg}(\mathrm{OH})_{2}(s)+\mathrm{Ca}^{2+}(a q)$$ What mass of \(\mathrm{CaO},\) in grams, is needed to precipitate 1000 lb of \(\mathrm{Mg}(\mathrm{OH})_{2} ?\)

Short Answer

Expert verified
To precipitate 1000 lb of Mg(OH)₂ from seawater, \(201,457.12 \ \text{grams}\) of CaO are needed.

Step by step solution

01

Convert mass of Mg(OH)₂ to grams

Given 1000 lb of Mg(OH)₂, we will convert it to grams using the conversion factor: 1 lb = 453.592 g. So, the mass of Mg(OH)₂ in grams is: 1000 lb × 453.592 g/lb = 453,592 g
02

Determine moles of Mg(OH)₂

Next, we will use the molar mass of Mg(OH)₂ to determine the number of moles. The molar mass of Mg(OH)₂ is 58.319 g/mol (Mg) + 2 × (15.999 g/mol (O) + 1.007 g/mol (H)) = 58.319 g/mol + 2 × 34.017 g/mol = 58.319 g/mol + 68.034 g/mol = 126.353 g/mol. Now, we can determine the moles: Moles of Mg(OH)₂ = (mass of Mg(OH)₂) / (molar mass of Mg(OH)₂) = 453,592 g / 126.353 g/mol ≈ 3591.68 mol
03

Determine moles of CaO needed

From the balanced chemical equation, we can see that 1 mole of CaO is needed to precipitate 1 mole of Mg(OH)₂: Mg²⁺(aq) + CaO(s) + H₂O(l) → Mg(OH)₂(s) + Ca²⁺(aq) Hence, the moles of CaO needed are equal to the moles of Mg(OH)₂, which is 3591.68 mol.
04

Convert moles of CaO to grams

Finally, we will convert the moles of CaO to grams, using its molar mass, which is 40.078 g/mol (Ca) + 15.999 g/mol (O) = 56.077 g/mol. Mass of CaO needed = (moles of CaO) × (molar mass of CaO) = 3591.68 mol × 56.077 g/mol ≈ 201,457.12 g Therefore, 201,457.12 grams of CaO are needed to precipitate 1000 lb of Mg(OH)₂.

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Most popular questions from this chapter

In the following three instances, which choice is greener in a chemical process? Explain. (a) A reaction that can be run at 350 \(\mathrm{K}\) for 12 h without a catalyst or one that can be run at 300 \(\mathrm{K}\) for 1 \(\mathrm{h}\) with a reusable catalyst. (b) A reagent for the reaction that can be obtained from corn husks or one that is obtained from petroleum. (c) A process that produces no by-products or one in which the by-products are recycled for another process.

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