Consider the unbalanced chemical equation \(\mathrm{Cr}+\mathrm{S}_{8} \rightarrow \mathrm{Cr}_{2} \mathrm{~S}_{3}\) If we need to produce \(235.0 \mathrm{~g}\) of \(\mathrm{Cr}_{2} \mathrm{~S}_{3}\) and the reaction has a \(63.80 \%\) yield, how many grams of each reactant do we need?

The process of balancing chemical equations is a foundational skill in chemistry. It involves adjusting the coefficients—the numbers in front of the chemical formulas—to ensure that the number of atoms for each element is the same on both sides of the reaction. This reflects the law of conservation of mass, where mass is neither created nor destroyed in a chemical reaction.

In our exercise, the balanced equation is obtained by ensuring that the number of chromium (Cr) and sulfur (S) atoms are equal in both reactants and products. The technique typically starts by balancing the atoms of elements that appear less frequently and then moving to the more common ones. The balanced equation is:
\(8Cr + 3S_8 \rightarrow 4Cr_2S_3\)
Understanding this step is crucial because stoichiometric calculations are based on a balanced chemical equation.

Stoichiometry is the area of chemistry that pertains to the quantitative relationships between reactants and products in a chemical reaction. It is like a recipe in cooking, dictating the proportions of ingredients needed to create a certain number of servings.

In the exercise, stoichiometry is used to determine how many grams of each reactant are required to produce a desired amount of product, taking into consideration the reaction yield. The balanced equation gives us these proportions; in this case, 8 moles of Cr and 3 moles of S₈ are required to form 4 moles of Cr₂S₃. Understanding the concepts of mole ratios in the balanced equation allows for insights into the relationship between reactants and products, which is the core of stoichiometric calculations.

The mole concept is a fundamental aspect of chemistry that makes it easier to quantify substances. One mole represents Avogadro's number, \(6.022 \times 10^{23}\) entities, whether they're atoms, molecules, ions, or other particles.

In our exercise, moles are the bridge that connects the mass of a substance to the number of particles it contains. We used the molecular weight to convert the given mass of Cr₂S₃ into moles. This conversion is essential because the coefficients in the balanced chemical equation refer to moles, not mass. By calculating the number of moles of the product and using the mole ratios from the balanced equation, we can find out the required moles of reactants. From there, we convert the moles back to mass to determine how much of each reactant is needed in grams. This is what makes the mole concept such a pivotal part of understanding and performing chemical calculations.