Consider the generic reaction: $$ 2 \mathrm{~A}+3 \mathrm{~B} \longrightarrow \mathrm{C} \Delta H_{\mathrm{rxn}}=-125 \mathrm{~kJ} $$ Determine the amount of heat emitted when each amount of reactant completely reacts (assume that there is more than enough of the other reactant). (a) \(2 \mathrm{~mol} \mathrm{~A}\) (b) \(3 \mathrm{~mol} \mathrm{~A}\) (c) \(3 \mathrm{~mol} \mathrm{~B}\) (d) \(5 \mathrm{~mol} \mathrm{~B}\)

The term heat of reaction, denoted by \( \Delta H_{\mathrm{rxn}} \), is a fundamental concept in thermochemistry. It refers to the amount of heat energy that is either absorbed or released during a chemical reaction. In exothermic reactions, such as the one given in the exercise, heat is emitted and the heat of reaction has a negative value, indicating a release of energy.

Understanding the heat of reaction is crucial for predicting the energy changes in chemical processes. It's also essential in industries where controlling the temperature of reactions is important for safety and product stability. The exercise demonstrates that when 2 moles of A react with B, there is a release of -125 kJ of heat. This is an intrinsic property of the reaction and is independent of the reaction pathway.

To comprehend mole-to-energy calculations, it's imperative to grasp the concept of the mole, which is a unit in chemistry representing an amount of substance. When discussing the energy exchanged in a reaction, we often calculate how much energy is associated with the reaction of one mole of a substance.

This concept is used in the given exercise to convert between the number of moles of reactants A and B and the amount of heat released, as seen in the step by step solution. By setting up a proportion, we can predict the heat released for any given amount of reactants. For example, for 3 moles of A, we calculate the heat emitted based on the given ratio of moles of A to energy, allowing us to scale the reaction's heat emission to different amounts of reactants.

At the heart of predicting the outcomes of chemical reactions is chemical reaction stoichiometry. It involves the quantitative relationship between the reactants and products in a balanced chemical equation. Stoichiometry allows us to deduce the amount of reactants needed to form a certain amount of product, or vice versa.

In the context of our exercise, the stoichiometric coefficients (2 for A and 3 for B) inform us about the ratio in which the reactants combine to form the product C. \( \Delta H_{\mathrm{rxn}} \) is associated with these exact stoichiometric amounts. When performing calculations, correctly applying stoichiometry ensures precise understanding of the reaction's scale. Misinterpreting these ratios can lead to errors in calculating the heat of reaction or in predicting how much product will form.