Nitroglycerine, \(\mathrm{C}_{3} \mathrm{H}_{5}\left(\mathrm{NO}_{3}\right)_{3}(l)\), is an explosive most often used in mine or quarry blasting. It is a powerful explosive because four gases \(\left(\mathrm{N}_{2}\right)\) \(\mathrm{O}_{2}, \mathrm{CO}_{2}\), and steam) are formed when nitroglycerine is detonated. In addition, \(6.26 \mathrm{~kJ}\) of heat is given off per gram of nitroglycerine detonated. (a) Write a balanced thermochemical equation for the reaction. (b) What is \(\Delta H\) when \(4.65\) mol of products is formed?

The process of balancing chemical equations is akin to solving a puzzle where each side of the equation must have the same number of atoms for each element. In the detonation of nitroglycerine, we deal with a complex molecule that breaks down into simpler gaseous products. To balance the equation, we tally the atoms of each element on both sides, adjusting coefficients—the numbers in front of molecules—accordingly.

It's crucial that no atoms are lost or gained in the reaction; this consistency upholds the law of conservation of mass. After balancing the equation, we can see that for every mole of nitroglycerine decomposed, we get 3 moles of carbon dioxide, a mole of water, 3 moles of nitrogen gas, and 2.5 moles of oxygen gas. These proportions are essential for stoichiometric calculations and enthalpy change computations, providing a roadmap to understanding the reaction's energetics.

Enthalpy change, denoted as \( \Delta H \), measures the heat exchange in a chemical reaction at constant pressure. For exothermic reactions like the detonation of nitroglycerine, \( \Delta H \) is negative, signifying heat release. The calculation of enthalpy change requires knowledge of the reaction's stoichiometry and the amount of heat released or absorbed per mole of reactant or product.

In our example, each mole of nitroglycerine releases 1421 kJ of energy upon detonation—this figure is determined by multiplying the molecular weight of nitroglycerine by the heat given off per gram. When calculating \( \Delta H \) for a given amount of product, it's essential to first establish the stoichiometric relationship between reactants and products—a key concept intertwining stoichiometry and thermochemistry.

Stoichiometry bridges the quantitative relationship between reactants and products in a chemical reaction. It's fundamental in ensuring that calculations for mass, moles, and energy are consistent and accurate. For a given reaction, stoichiometry dictates the exact proportions of each substance involved.

To elucidate this, consider the reaction we are studying. We must first identify the 'limiting reactant' or in this case, utilize the stoichiometric ratios to find out how much nitroglycerine gives rise to 4.65 moles of the product—water, in this scenario. We calculate how much energy is exchanged (\( \Delta H \) value) by applying the stoichiometric principles to relate moles of products back to moles of reactants, essentially showcasing the interconnectedness of reactants, products, and their respective energy changes in a coherent stoichiometric framework.