At the first-stage recovery of magnesium from seawater, the precipitation of Mg(OH)2 with CaO occurs in the following reaction: Mg2+(aq) + CaO(s) + H2O(l) → Mg(OH)2(s) + Ca2+(aq). What mass of CaO, in grams, is needed to precipitate 1000 lb of Mg(OH)2?

Verified step by step guidance

Convert the mass of Mg(OH)_2 from pounds to grams using the conversion factor: 1 lb = 453.592 grams.

Calculate the molar mass of Mg(OH)_2 by adding the atomic masses of magnesium (Mg), oxygen (O), and hydrogen (H) from the periodic table.

Determine the number of moles of Mg(OH)_2 by dividing the mass in grams by the molar mass of Mg(OH)_2.

Use the stoichiometry of the balanced chemical equation to find the moles of CaO needed. According to the equation, 1 mole of Mg(OH)_2 is produced per mole of CaO.

Calculate the mass of CaO required by multiplying the moles of CaO by its molar mass, which is the sum of the atomic masses of calcium (Ca) and oxygen (O).

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the balanced equation. It allows us to determine the relationships between the amounts of substances involved, enabling us to convert between moles and grams. In this case, understanding the stoichiometric ratios from the reaction is essential to find out how much CaO is needed to precipitate a specific mass of Mg(OH)2.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is crucial for converting between the mass of a substance and the number of moles. To solve the problem, we need to calculate the molar masses of Mg(OH)2 and CaO to convert the mass of Mg(OH)2 into moles and subsequently find the required mass of CaO.

Precipitation Reaction

A precipitation reaction occurs when two soluble salts react in solution to form an insoluble product, known as a precipitate. In this scenario, Mg(OH)2 is the precipitate formed from the reaction of Mg2+ ions with CaO in the presence of water. Understanding this concept helps clarify the process of recovering magnesium from seawater and the significance of the reactants involved.

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