The toxic pigment called white lead, \(\mathrm{Pb}_{3}(\mathrm{OH})_{2}\left(\mathrm{CO}_{3}\right)_{2}\), has been replaced in white paints by rutile, TiO_ \(.\) How much rutile (g) can be prepared from 379 g of an ore that contains \(88.3 \%\) ilmenite (FeTiO \(_{3}\) ) by mass? \(2 \mathrm{FeTiO}_{3}+4 \mathrm{HCl}+\mathrm{Cl}_{2} \longrightarrow 2 \mathrm{FeCl}_{3}+2 \mathrm{TiO}_{2}+2 \mathrm{H}_{2} \mathrm{O}\)

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. The basic principle of stoichiometric calculations lies in the law of conservation of mass, which states that matter is neither created nor destroyed in a chemical reaction. Therefore, the amount of reactants consumed will directly affect the amount of products formed.

When focusing on stoichiometric calculations, it's essential to understand the concept of the 'mole,' a unit that measures the amount of substance. These calculations often involve converting grams to moles or vice versa, using the molar mass of the substances involved. As seen in the exercise, the calculation started by determining the amount of pure ilmenite (FeTiO₃) from an ore based on its given purity percentage. This initial step is crucial and sets the foundation for accurate stoichiometric predictions about the resulting compounds.

Another key aspect includes understanding the balanced chemical equation provided in the problem. Each compound's coefficient represents the number of moles that participate in the reaction, which is used to derive the mole ratio needed for further calculations.

The mole ratio is a critical concept in chemistry that denotes the proportion of reactants to products in a balanced chemical equation. It allows chemists to predict the amounts of products formed from a given amount of reactants. In our example, the mole ratio between ilmenite and rutile, as determined from the balanced equation, is 1:1, meaning one mole of ilmenite reacts to form one mole of rutile.

Understanding the mole ratio is vital for stoichiometric calculations because it acts as a conversion factor that equates the number of moles of one substance with another based on the equation. A balanced chemical equation is a prerequisite for establishing accurate mole ratios. Without proper mole ratios, the calculations for how much of one substance is required to react with a given amount of another substance would not be possible. Hence, using the mole ratio and the mass of ilmenite, it is possible to find the corresponding mass of rutile produced.

The molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For stoichiometric problems, the molar mass serves a pivotal role as it allows chemists to interchange between mass and the mole unit, facilitating the various calculations needed in chemical reactions.

In the given exercise, the molar masses of ilmenite and rutile are essential to convert the mass of ilmenite to moles and then to determine the mass of rutile produced from the moles of rutile. The molar mass of a compound can be computed by summing the atomic masses of all the atoms present in the molecule's formula unit. For instance, ilmenite's molar mass was calculated by adding the atomic masses of iron (Fe), titanium (Ti), and three oxygen (O) atoms.

A chemical reaction equation is a symbolic representation that illustrates how reactants transform into products during a chemical reaction. These equations are balanced to obey the law of conservation of mass, ensuring that the number of atoms for each element is the same on both sides of the equation. A balanced equation provides the mole ratio of reactants and products, which is indispensable in stoichiometric calculations.

In the case of our stoichiometry problem, the equation given was already balanced and showed the conversion of ilmenite and additional reactants into rutile and other products. A properly balanced equation is crucial because it dictates the exact stoichiometry of a reaction - how much of each substance is needed and how much will be formed. It acts as a map for chemical conversions, guiding the quantitative analysis to solve stoichiometric problems.