For each reaction, calculate how many moles of product form when \(1.75 \mathrm{~mol}\) of the reactant in color completely reacts. Assume there is more than enough of the other reactant. (a) \(\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{HCl}(g)\) (b) \(2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)\) (c) \(2 \mathrm{Na}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{Na}_{2} \mathrm{O}_{2}(s)\) (d) \(2 \mathrm{~S}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)\)

In chemistry, the mole is a fundamental unit that measures the amount of substance. It's part of the International System of Units (SI) and one mole contains exactly 6.02214076×10²³ elementary entities, whether they are atoms, molecules, ions, or electrons. This constant number is known as Avogadro's number.

The importance of the mole concept cannot be overstated as it allows chemists to convert between the mass of a substance and the number of particles it contains. This is crucial for understanding the relationships between elements and compounds in chemical reactions. In our example, knowing the number of moles of reactants helps us to determine the number of moles of products formed.

Chemical reaction stoichiometry deals with the quantitative relationships between the reactants and products in a chemical reaction. The coefficients in a balanced chemical equation tell us the relative proportions of reactants and products. We use these coefficients to calculate how many moles of one chemical are needed to react with another, and how many moles of product will be produced.

For example, consider the reaction where hydrogen reacts with chlorine to form hydrochloric acid: \(\mathrm{H}_{2}(g) + \mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{HCl}(g)\). The coefficients indicate that 1 mole of hydrogen gas reacts with 1 mole of chlorine gas to produce 2 moles of hydrochloric acid gas.

To predict the products of a chemical reaction and the quantities in which they are produced or consumed, one must start with a balanced chemical equation. Each side of the equation must represent the same quantity of each element, thus conserving mass according to the Law of Conservation of Mass.

In our exercise, each chemical equation is balanced before stoichiometric calculations can be made. For instance, the balanced equation \(2 \mathrm{Na}(s) + \mathrm{O}_{2}(g) \longrightarrow \mathrm{Na}_{2}\mathrm{O}_{2}(s)\) tells us that two sodium atoms react with one oxygen molecule to form one molecule of sodium peroxide. This balance is essential for correctly determining the mole ratio used in stoichiometric calculations.

Stoichiometric calculations use the principles of stoichiometry to convert moles of one compound to moles of another using the mole ratio derived from the balanced chemical equation. These calculations are fundamental when trying to determine the amount of reactants to use, or products that will be formed in a chemical reaction.

In the exercise, to find how many moles of hydrochloric acid (HCl) will form when 1.75 moles of hydrogen gas (H₂) completely react, we use the mole ratio of 1:2 from the balanced equation. This simple multiplication gives us the answer (1.75 moles H₂ × 2 = 3.5 moles HCl). Similar calculations allow us to predict the outcomes of the rest of the reactions accurately.