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

A chemical reaction occurs when substances, known as reactants, transform into new substances called products through a process of breaking and forming chemical bonds. The equation representing the reaction showcases the reactants on the left and the products on the right, with an arrow indicating the direction of the transformation.

In our exercise, we have a chemical reaction involving magnesium ions from seawater reacting with calcium oxide (CaO) and water to produce magnesium hydroxide (Mg(OH)₂) and aqueous calcium ions. The balanced chemical equation reflects a one-to-one stoichiometry between magnesium ions and calcium oxide; for each mole of CaO, one mole of Mg(OH)₂ is formed.

Understanding the stoichiometry of the reaction allows for the calculation of how much CaO is needed to completely react with a certain amount of Mg(OH)₂. The balanced equation is fundamental in ensuring that the conservation of mass is respected and all atoms accounted for in the process, which is also an expression of the Law of Conservation of Mass.

Molar mass is a property of a substance defined as the mass of one mole of its particles (atoms, molecules, or formula units) and is expressed in gram per mole (g/mol). It's a bridge between the mass of a sample and the number of moles it contains.

For instance, as calculated in our exercise, the molar mass of magnesium hydroxide, Mg(OH)₂, is approximately 58.319 g/mol, determined by summing the molar masses of individual elements: magnesium, oxygen, and hydrogen. This calculation involves multiplying the atomic mass of each element by the number of atoms of that element in the formula and adding these values together. The same principle applies to calculate CaO's molar mass, ending up with 56.079 g/mol.

Knowing the molar mass is crucial for converting between the mass of a substance and the number of moles. This is important because moles are used in stoichiometry calculations to predict the amounts of reactants and products involved in a chemical reaction.

The conversion from moles to grams and vice versa is a fundamental aspect of stoichiometry in chemistry. It involves using the molar mass of a substance as a conversion factor. To convert from moles to grams, you multiply the number of moles by the molar mass of the substance.

In the context of our exercise, after determining the molar mass of both Mg(OH)₂ and CaO, we first convert the given mass of Mg(OH)₂ in pounds to grams using a unit conversion factor (1 lb = 453.592 g). Then, we use the molar mass of Mg(OH)₂ to find the number of moles. With the balanced chemical equation, we can conclude that the moles of CaO needed are equal to the moles of Mg(OH)₂.

The final step is to convert the moles of CaO back to grams, for which we use CaO's molar mass as the conversion factor. The result tells us the precise mass of CaO required to precipitate 1000 pounds of Mg(OH)₂, completing our stoichiometry calculation and providing the answer to the problem posed.