Consider the generic reaction between reactants \(\mathrm{A}\) and \(\mathrm{B}\) : $$ 3 \mathrm{~A}+4 \mathrm{~B} \longrightarrow 2 \mathrm{C} $$ If a reaction vessel initially contains \(9 \mathrm{~mol} \mathrm{~A}\) and \(8 \mathrm{~mol} \mathrm{~B}\), how many moles of \(\mathrm{A}, \mathrm{B}\), and \(\mathrm{C}\) will be in the reaction vessel after the reactants have reacted as much as possible? (Assume \(100 \%\) actual yield.)

Stoichiometry is akin to a recipe for chemical reactions. It involves the calculation of the quantities of reactants and products involved in a chemical reaction. Using the mole concept, which serves as a bridge between the microscopic scale of atoms and molecules and the macroscopic world of grams and liters, we can predict the amounts of substances consumed and produced.

For example, in the given exercise, the stoichiometric coefficients (3, 4, and 2) say that 3 moles of A react with 4 moles of B to produce 2 moles of C. Stoichiometry allows us to figure out that if we start with 9 moles of A and 8 moles of B, B will run out before A, thus limiting the amount of C produced.

Chemical reaction calculations often involve determining which reactant will limit the reaction and how much product will form. This requires a balanced chemical equation, an understanding of the mole concept, and the ability to perform mole-to-mole conversions.

In our exercise, we calculated how many moles of A will be consumed when reacting with the 8 moles of B available. We used the mole ratio between A and B given in the equation (3:4) to do this. Through these calculations, we can predict the amount of remaining reactants and the amount of products formed after the reaction goes to completion, which are fundamental tasks in chemical reaction calculations.

Balanced chemical equations are essential because they ensure the law of conservation of mass is obeyed in a chemical reaction. The numbers in front of the chemical formulas are called stoichiometric coefficients and represent the mole ratios in which substances react and are produced.

The balanced equation for our exercise, \(3 \text{A} + 4 \text{B} \longrightarrow 2 \text{C}\), tells us that for every 3 moles of A that react, 4 moles of B are needed, and 2 moles of C will be produced. Without a balanced equation, it would be impossible to correctly perform stoichiometric calculations and determine the amounts of reactants and products involved.

The mole concept is a central tenet in chemistry that relates the mass of a substance to the number of particles it contains. One mole is defined as the amount of substance that contains as many entities (atoms, molecules, ions, etc.) as there are atoms in 12 grams of carbon-12. This is roughly 6.022 x 10^23 entities, a number known as Avogadro's number.

In stoichiometric calculations, the mole concept is crucial because it allows chemists to count particles by weighing them. This concept was utilized in the exercise to relate the initial moles of reactants A and B with the reaction stoichiometry, in order to determine the remaining amounts of A and B and the amount of C produced after the reaction.