Consider the generic chemical reaction: $$ 2 \mathrm{~A}+3 \mathrm{~B} \longrightarrow 3 \mathrm{C} $$ How many moles of B are required to completely react with: (a) \(6 \mathrm{~mol}\) of \(\mathrm{A}\) (b) \(2 \mathrm{~mol}\) of \(\mathrm{A}\) (c) \(7 \mathrm{~mol}\) of \(\mathrm{A}\) (d) 11 mol of \(\mathrm{A}\)

Chemical reactions are processes where substances, known as reactants, transform into different substances called products. These transformations occur through the breaking and forming of chemical bonds. This is often visualized in a chemical equation, which represents the reactants on the left side and the products on the right.

For instance, in the reaction given by the equation \[2 \mathrm{A}+3 \mathrm{B} \longrightarrow 3 \mathrm{C}\], A and B are the reactants that combine to form the product C. The numbers in front of the chemical symbols are called stoichiometric coefficients. They indicate the proportions in which reactants and products participate in the reaction, reflecting the conservation of mass principle.

In chemistry, the term 'mole' is used to measure the quantity of a substance. One mole is equal to Avogadro's number (\(6.022 \times 10^{23}\)) of atoms, molecules, or other particles. This concept allows chemists to count particles by weighing them, as one mole of any element or compound has a mass that corresponds to its relative molecular (or atomic) mass in grams.

To tie this into our sample reaction, when we say '6 moles of A', we are referring to \(6 \times 6.022 \times 10^{23}\) particles of substance A. The mole concept is fundamental when it comes to quantifying substances in a chemical reaction and is crucial for stoichiometric calculations.

Molar ratios are derived from the coefficients of a balanced chemical equation and they reflect the proportions of the substances involved in the reaction. They are the heart of stoichiometry, as they enable us to convert between moles of different reactants and products.

In our exercise, the molar ratio between A and B is 2:3. This means that, ideally, two moles of A will react with three moles of B. Molar ratios allow us to predict the amount of reactants needed to completely react with a given quantity of another reactant, which is essential for practical applications such as chemical manufacturing.

Stoichiometric calculations use the mole concept and molar ratios to determine the quantitative aspects of chemical reactions. These calculations require a balanced chemical equation as a starting point. The process generally involves converting grams to moles, using the molar ratio to find the number of moles of another substance, and then, if necessary, converting back to grams.

For example, if we start with 6 moles of A, we can find out how many moles of B are required to completely react with A by setting up a proportion using the molar ratio. Our exercise demonstrates this step by step, where knowing that 2 moles of A react with 3 moles of B, we calculate the amount of B needed for different quantities of A. Understanding stoichiometric calculations allows students to predict the outcome of a reaction, a foundational skill in the field of chemistry.