A \(1.100 \mathrm{~g}\) sample of copper ore is dissolved and the \(\mathrm{Cu}^{2+}(\mathrm{aq})\) is treated with excess \(\mathrm{KI}\). The liberated \(\mathrm{I}_{2}\) requires \(12.12 \mathrm{~mL}\) of \(0.10 \mathrm{M} \mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}\) solution for titration. What is \(\%\) copper by mass in the ore?

Stoichiometry is the mathematical relationship between the quantities of reactants and products in a chemical reaction. It is derived from the coefficients of a balanced chemical equation, which indicate the proportions in which chemicals react and are formed. Understanding stoichiometry is critical when conducting an iodometric titration to determine the concentration of a substance, such as copper in an ore sample.

In the given problem, stoichiometry plays a pivotal role in calculating the percentage of copper by mass. First, we define the balanced equation for the redox reaction, which guides us in determining the ratio of the participating compounds. In this case, the reaction shows that two moles of sodium thiosulfate react with one mole of iodine.Therefore, by measuring the amount of sodium thiosulfate required to titrate the liberated iodine, we can back-calculate the amount of iodine, and subsequently the amount of copper, present in the sample.

The mole concept is a fundamental principle in chemistry that provides a bridge between the atomic scale and the macroscopic scale. A mole is defined as the amount of a substance that contains as many elementary entities (atoms, molecules, ions, etc.) as there are atoms in 12 grams of pure carbon-12. One mole corresponds to approximately \(6.022 \times 10^{23}\) entities, known as Avogadro's number.

In the context of an iodometric titration, knowing the mole concept allows us to calculate the number of moles of each reactant and product involved. For instance, after measuring the volume and molarity of sodium thiosulfate used in the titration, we calculate the moles of sodium thiosulfate, and through stoichiometric relationships, can determine the moles of iodine and ultimately the moles of copper in the ore. This quantitative relationship is crucial for determining the percent composition of an element within a compound, as demonstrated in the exercise.

Redox reactions are chemical reactions that involve the transfer of electrons between two species. The term 'redox' is a contraction of 'reduction-oxidation'. In these reactions, one substance is oxidized (loses electrons) while the other is reduced (gains electrons). An understanding of redox reactions is essential when working with iodometric titrations, which are often employed to determine the amount of a reducing agent in a sample.

In the exercise, the redox reaction occurs when the copper ions in the ore sample react with iodide ions to liberate iodine. This iodine is then titrated with sodium thiosulfate, which acts as the reducing agent. The balanced redox equation tells us not only the stoichiometry of the reaction but also the specific oxidation and reduction processes taking place. It is the foundation for calculating the mass and, therefore, the percentage of copper present in the ore sample, highlighting the interconnected nature of redox chemistry, stoichiometry, and the mole concept in quantitative chemical analysis.