Hydrogen fluoride is used in the manufacture of Freons (which destroy ozone in the stratosphere) and in the production of aluminum metal. It is prepared by the reaction$$\mathrm{CaF}_{2}+\mathrm{H}_{2} \mathrm{SO}_{4} \longrightarrow \mathrm{CaSO}_{4}+2 \mathrm{HF}$$ In one process, \(6.00 \mathrm{~kg}\) of \(\mathrm{CaF}_{2}\) are treated with an excess of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) and yield \(2.86 \mathrm{~kg}\) of \(\mathrm{HF}\). Calculate the percent yield of HF.

When we talk about stoichiometry, we refer to the branch of chemistry that deals with the quantitative relationships of the substances involved in chemical reactions. Think of it as a recipe for chemistry; you need to know the right amounts of all the ingredients to get the desired product. A balanced chemical equation is the foundation of stoichiometry. It tells you the proportion in which reactants combine and the products form.

For example, in the reaction of calcium fluoride with sulfuric acid to produce hydrogen fluoride, the equation \[\mathrm{CaF}_{2}+\mathrm{H}_{2}\mathrm{SO}_{4}\longrightarrow\mathrm{CaSO}_{4}+2\mathrm{HF}\] illustrates that one mole of calcium fluoride reacts with one mole of sulfuric acid to produce one mole of calcium sulfate and two moles of hydrogen fluoride. To solve problems involving stoichiometry, start by writing a balanced equation, then use the mole concept and molar ratios to calculate how much of a reactant you need or how much product you can expect to be formed.

The theoretical yield is a term used in chemistry to define the maximum amount of product that can be generated from a given amount of reactant, based on stoichiometry and assuming 100% efficiency in the reaction.

However, actual laboratory reactions rarely proceed with perfect efficiency due to various factors like side reactions, incomplete reactions, or purity of reactants. To find the theoretical yield, you apply the stoichiometry of the balanced equation, which often involves converting masses to moles to understand the relative quantities of the reactants and products. In the reaction \[\mathrm{CaF}_{2}+\mathrm{H}_{2}\mathrm{SO}_{4}\longrightarrow\mathrm{CaSO}_{4}+2\mathrm{HF},\] stoichiometry tells us that 1 mole of calcium fluoride theoretically yields 2 moles of hydrogen fluoride. By calculating the moles of calcium fluoride you have, and using the stoichiometric ratios, you can predict the moles, and thus the mass, of hydrogen fluoride that should be produced, which represents the theoretical yield.

The mole concept is a cornerstone of chemistry that provides a bridge between the microscopic world of atoms and molecules and the macroscopic world that we can measure. A mole is defined as the amount of substance that contains as many entities (atoms, ions, or molecules) as there are atoms in 12 grams of carbon-12, which is Avogadro's number \(~6.022\times10^{23}\).

Understanding the mole concept is essential in stoichiometry. For instance, to solve the exercise at hand, you calculate how many moles of calcium fluoride (\(\mathrm{CaF}_{2}\)) you have using its molar mass. From the balanced equation, you use the molar ratio to find the required moles of hydrogen fluoride (\(\mathrm{HF}\)). This process allows us to perform calculations about the amounts of substances involved. Whether you are converting masses to moles or moles to particles, the mole concept is your go-to framework for quantifying and understanding chemical reactions.