Determine the amount of heat (in \(\mathrm{kJ}\) ) given off when \(1.26 \times 10^{4} \mathrm{~g}\) of ammonia are produced according to the equation $$ \begin{aligned} \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow & 2 \mathrm{NH}_{3}(g) \\\ \Delta H_{\mathrm{rxn}}^{\circ} &=-92.6 \mathrm{~kJ} / \mathrm{mol} \end{aligned} $$ Assume that the reaction takes place under standardstate conditions at \(25^{\circ} \mathrm{C}\).

The concept of enthalpy change is central to understanding energy transfer during chemical reactions. Enthalpy change, denoted as \( \Delta H \), represents the heat absorbed or released by a chemical reaction under constant pressure. It's a measure of the energy change in a system. While the overall energy of a system can't be measured directly, we can measure changes in energy, which is what \( \Delta H \) represents.

In chemical reactions, when bonds between atoms are broken and formed, energy is either consumed or produced. If the reaction releases heat, it is exothermic, and \( \Delta H \) will be negative, indicating that the system is giving heat to its surroundings. Conversely, if the reaction absorbs heat, it is endothermic, and \( \Delta H \) will be positive.

• An exothermic reaction example involves the formation of ammonia from nitrogen and hydrogen, where heat is released, and \( \Delta H \) is negative.
• An endothermic reaction might involve the decomposition of calcium carbonate, where the system absorbs heat from the surroundings, and \( \Delta H \) is positive.

It's crucial to remember that the given \( \Delta H \) is usually specified per mole of a substance involved in the reaction. This is where stoichiometry and the mole concept come into play to determine the total heat change for the amount of substance actually reacting or being produced.

Stoichiometry is like the recipe for a chemical reaction. It uses the balanced chemical equation to understand the ratio in which reactants combine and products form. This ratio is expressed in moles, allowing chemists to calculate how much of each reactant is needed and how much of each product will be formed.

Here's how it works: each coefficient in a balanced chemical equation represents the number of moles of that substance. For instance, the balanced equation for the formation of ammonia:\[ \mathrm{N}_2(g) + 3 \mathrm{H}_2(g) \longrightarrow 2 \mathrm{NH}_3(g) \]
This equation tells us that one mole of nitrogen gas reacts with three moles of hydrogen gas to produce two moles of ammonia gas.

• If we know the moles of one substance, we can use stoichiometry to find the moles of another.
• Knowing the moles and \( \Delta H \) per mole of a product or reactant, we can calculate the total heat absorbed or released in a reaction.

Essential to solving stoichiometric problems is the concept of the mole, allowing us to use these ratios in practical calculations.

The mole concept is a fundamental bridge between the microscopic world of atoms and molecules and the macroscopic world we live in. A mole is a unit that denotes an amount of a substance that contains as many entities (atoms, molecules, etc.) as there are atoms in 12 grams of carbon-12, which is approximately \(6.022 \times 10^{23}\), also known as Avogadro's number.

Using the mole concept, chemists can relate the mass of a substance to the number of particles it contains and vice versa. In the given exercise, the mass of ammonia (NH3) must be converted to moles to calculate the heat change:

• We use the molar mass of a substance (in this case, ammonia), which tells us how many grams are in one mole of that substance.
• By dividing the given mass of ammonia by its molar mass, we derive the number of moles of ammonia involved in the reaction.

The use of the mole concept thus allows us to apply stoichiometry and enthalpy change to real-world quantities, bridging the gap between the abstract concepts in chemistry and practical, observable phenomena.