Calculate the standard enthalpy of reaction for the following reaction using the listed enthalpies of reaction : $$ \begin{aligned} 3 \mathrm{Co}(s)+2 \mathrm{O}_{2}(g) & \longrightarrow \mathrm{Co}_{3} \mathrm{O}_{4}(s) \\ 2 \mathrm{Co}(s)+\mathrm{O}_{2}(g) & \longrightarrow 2 \mathrm{CoO}(s) ; \quad \Delta H_{1}^{\circ}=-475.8 \mathrm{~kJ} \\ 6 \mathrm{CoO}(s)+\mathrm{O}_{2}(g) & \longrightarrow 2 \mathrm{Co}_{3} \mathrm{O}_{4}(s) ; \Delta H_{2}^{\circ}=-355.0 \mathrm{~kJ} \end{aligned} $$ (a) \(-891.2 \mathrm{~kJ}\) (b) \(-120.8 \mathrm{~kJ}\) (c) \(+891.2 \mathrm{~kJ}\) (d) \(-830.8 \mathrm{~kJ}\)

Hess's Law is a fundamental principle applied in thermochemistry which states that the total enthalpy change during the complete course of a chemical reaction is the same regardless of the number of steps in the reaction. This principle is instrumental when the enthalpy change of a reaction is difficult to measure directly.

To apply Hess's Law to a problem, we often need to flip and/or scale certain intermediate reactions to ensure that substances cancel appropriately when added together, eventually enabling us to derive the enthalpy change of the overall reaction. For example, students can manipulate equations by reversing or multiplying them, making sure that the intermediate species cancel out to yield the target reaction of interest.

When working through thermochemistry problems, understanding this law allows you to take known enthalpy changes for individual reactions and algebraically combine them to find the enthalpy change for a more complex reaction.

The standard enthalpy change, symbolized as \( \Delta H^\circ \), is the enthalpy change associated with a chemical reaction taking place under standard conditions, which commonly refers to 1 bar or 1 atm of pressure and a specified temperature, usually 298 K (25 °C).

The importance of defining a standard is that it provides a reference point for thermochemical equations. When we say 'standard' enthalpy change, we're talking about the enthalpy change for the number of moles of substances involved in the equation as written under standard conditions. This is incredibly useful because it allows chemists to tabulate values and form a database of standard enthalpies for various reactions, which can be used to predict the enthalpy changes of other reactions by using Hess's Law.

Thermochemistry problems typically involve exchanges of energy, particularly heat, during chemical reactions. These problems require you to calculate quantities such as heat absorbed or released, changes in temperature, or the standard enthalpy change of a reaction.

To tackle these problems, you need to understand the concepts of heat capacity, calorimetry, and be well-versed with the first law of thermodynamics which relates heat, work, and the internal energy of a system. Problems also often involve conceptualizing the system and the surroundings, and determining the flow of heat based on the nature of the reaction (exothermic or endothermic).

Applying Hess's Law or using enthalpy diagrams are common methods to solve these problems. Mastery of stoichiometry and chemical equilibrium is also crucial, as they often play a role in these calculations.

Chemical reaction stoichiometry deals with the quantitative relationships between the reactants and products in a chemical reaction. It's based on the law of conservation of mass, where the total mass of the reactants equals the total mass of the products. The coefficients in balanced chemical equations represent the stoichiometry of the reaction, telling you the ratios in which reactants combine and products form.

In thermochemical equations, stoichiometry allows for the precise calculation of the enthalpy change for a reaction. For instance, if the stoichiometric coefficients are doubled, the enthalpy change is also doubled. Understanding stoichiometry is vital for predicting the amounts of products formed or reactants needed, as well as for calculating energy changes during reactions using Hess's Law or calorimetry.