How many grams of sulfur (S) are needed to react completely with \(246 \mathrm{~g}\) of mercury (Hg) to form \(\mathrm{HgS} ?\)

Understanding chemical equations is crucial for approaching stoichiometry problems. A chemical equation represents a chemical reaction where the reactants are shown on the left side and the products on the right, typically separated by an arrow symbolizing the direction of the reaction. For instance, the equation provided in the exercise, \(Hg + S \rightarrow HgS\), shows mercury and sulfur as reactants that combine to form mercury(II) sulfide as the product.

For a chemical equation to be balanced, the number of atoms of each element must be the same on both sides of the equation. In our example, both sides have one atom of mercury and sulfur, showing that the equation is already balanced. This balance is necessary because it respects the conservation of mass principle stating that matter cannot be created or destroyed in a chemical reaction. A balanced equation is essential as it provides the stoichiometric ratio needed to perform calculations between reactants and products, laying the groundwork for accurate stoichiometric calculations.

The mole concept is a fundamental principle in chemistry that links the microscopic world of atoms and molecules to the macroscopic world of grams and liters that we can measure. One mole of any substance contains Avogadro's number, \(6.022 \times 10^{23}\), of particles, be they atoms, molecules, ions, or electrons. This large number bridges the gap between an atom's minuscule mass and a substance's observable mass.

When dealing with chemical reactions, chemists use the mole concept to count atoms by weighing. In the given problem, we convert the mass of mercury to moles to use this countable unit in our calculations. Understanding the concept of moles allows us to link the mass of a substance directly to the number of particles it contains, which is a cornerstone of stoichiometric calculations.

Molar mass, often confused with molecular mass, is the mass of one mole of a substance, and it's expressed in grams per mole (g/mol). It is the key to converting between moles and grams—a necessary step in stoichiometry problems. The molar mass of an element is numerically equivalent to its atomic weight listed on the periodic table, and for a compound, it's the sum of the atomic weights of all the atoms in its chemical formula.

For example, sulfur has an atomic weight of 32.07, meaning its molar mass is \(32.07~\text{g/mol}\). This value is used to convert the moles of sulfur needed for the reaction into grams, as seen in the provided solution. Understanding molar mass is vital because it serves as a conversion factor in many stoichiometric calculations, helping to accurately quantify substances involved in chemical reactions.

Stoichiometric calculations are the quantitative aspect of chemistry that involves using balanced chemical equations to find the relationship between the amounts of reactants and products. These calculations often involve converting masses to moles using molar mass, utilizing the mole ratios from a balanced chemical equation, and then converting moles back into grams if necessary.

In the provided example, after finding the moles of mercury, the mole ratio from the balanced chemical equation (1:1:1 for \(Hg : S : HgS\)) is used to find the equal number of moles of sulfur needed. With stoichiometry, it's essential to pay attention to these ratios as they guide the amount of each substance required or produced. The final step in stoichiometric calculations is converting these moles back into grams using the molar mass of the substance of interest, such as sulfur in the problem, yielding the answer in a measurable quantity. This process of conversion is what makes stoichiometric calculations such a powerful tool in predicting the outcomes of chemical reactions and in preparing the correct amounts of reactants.