A quantity of \(4.35 \mathrm{~g}\) of a sample of pyrolusite ore, when heated with conc. HCl, gave chlorine. The chlorine, when passed through potassium iodide solution, liberated \(6.35 \mathrm{~g}\) of iodine. The percentage of pure \(\mathrm{MnO}_{2}\) in the pyrolusite ore is \((\mathrm{Mn}=55, \mathrm{I}=127)\) (a) 40 (b) 50 (c) 60 (d) 70

Stoichiometry is essentially the mathematics behind chemistry. It involves calculating the proportions of elements and compounds involved in chemical reactions. It's based on the principle that matter is conserved in reactions, meaning all atoms in the reactants will be found in the products, just rearranged.

To understand stoichiometry, you first need to grasp the structures of chemical equations, which give you the mole ratios of reactants and products. For example, in the pyrolusite ore problem, for every mole of \textbf{MnO\(_2\)} (manganese(IV) dioxide) that reacts, one mole of \textbf{Cl\(_2\)} (chlorine gas) is produced. This ratio allows us to convert between moles of different substances involved, which then can be used to find the mass of \textbf{MnO\(_2\)} in the sample and its percentage composition.

The mole concept is a way of counting atoms and molecules, which are incredibly tiny and numerous. One mole is Avogadro's number (\textbf{\text{6.022 x 10\(^{23}\)}}) of particles, be it atoms, molecules, electrons, or any other entities.

In the context of the exercise, once the mass of iodine was given, the number of moles of iodine was calculated by dividing the mass of iodine by its molar mass. Understanding the mole concept is crucial here because it provides the link between mass (a physical property) and number of entities (a chemical property) in the sample, enabling the stoichiometric calculations to proceed.

Chemical equations are representations of chemical reactions where reactants are shown on the left and products on the right. Equations must be balanced, meaning they obey the Law of Conservation of Mass—atoms cannot be created or destroyed.

In our chemical equations for the pyrolusite ore reaction, the balanced equations mean that for each mole of \textbf{MnO\(_2\)} that reacts, a certain number of product molecules are formed. Learning to balance these equations is crucial, as it tells you exactly how much of each substance is involved in a reaction, guiding the stoichiometric calculations.

Molar mass is the mass of one mole of a given substance. It's a bridge between the macroscopic world of grams that we can measure and the microscopic world of molecules that we cannot. The molar mass is found by adding up the atomic masses of all atoms in a molecule.

For instance, \textbf{MnO\(_2\)}, crucial to our pyrolusite ore example, has a molar mass of 87 g/mol. Knowing the molar mass allowed us to convert the moles of \textbf{MnO\(_2\)} found using stoichiometry into grams, which then enabled the calculation of the percentage of \textbf{MnO\(_2\)} in the ore, a key step to solving the exercise.