The standard enthalpy of formation of \(\mathrm{FeO}\) and \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) is \(-65 \mathrm{kcal}\) \(\mathrm{mol}^{-1}\) and \(-197\) kcal mol \(^{-1}\) respectively. A mixture of two oxides contains \(\mathrm{FeO}\) and \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) in the mole ratio \(2: 1 .\) If by oxidation, it is changed into a \(1: 2\) mole ratio mixture, how much of thermal energy will be released per mol of initial mixture.

Understanding enthalpy change calculations is critical when studying reactions in chemistry. Enthalpy, denoted by the symbol H, is the total heat content of a system. It's a thermodynamic quantity that's difficult to measure directly, but changes in enthalpy can be calculated based on the heat absorbed or released during a chemical reaction at constant pressure.

For the given exercise, we need to calculate the enthalpy change that occurs when a mixture of iron(II) oxide (FeO) and iron(III) oxide (Fe₂O₃) undergoes oxidation, changing its mole ratio. We're provided with the standard enthalpies of formation for both oxides, which represent the enthalpy change when one mole of a compound is formed from its elements in their standard states.

To calculate the enthalpy change for the reaction, we need the enthalpies of the initial and final mixtures. By applying Hess's Law, which states that the total enthalpy change for a reaction is the same, no matter how many steps it involves, we can use the standard enthalpies of formation to find the total enthalpy of the mixture before and after the reaction:

• Initial mixture enthalpy: 2(-65 kcal/mol) + 1(-197 kcal/mol)
• Final mixture enthalpy: 1(-65 kcal/mol) + 2(-197 kcal/mol)

The change in enthalpy (ablaH) is then found by subtracting the final enthalpy from the initial enthalpy.

Chemical thermodynamics deals with the energy changes associated with chemical reactions and the direction in which these reactions occur. The enthalpy change calculation discussed in the previous section is just one aspect of this vast field. Essentially, thermodynamics tells us whether a process is likely to happen and provides insights into how much energy might be involved.

From the thermodynamic perspective, our mixture's oxidation process illustrates an exothermic reaction, where thermal energy is released into the surroundings—indicated by the negative sign in standard enthalpies of formation. This release of energy tends to make the reaction spontaneous, a principle dictated by Gibbs free energy which combines enthalpy, temperature, and entropy to predict the favorability of reactions.

The concept of standard enthalpy of formation, used in the given exercise, is a key concept in thermodynamics that helps us compare the energy required to break bonds in reactants with the energy released upon bond formation in products. These values are critical for scientists and engineers designing processes that take advantage of exothermic reactions, like combustion engines or chemical heaters.

The concept of mole ratio in reactions is foundational in stoichiometry, which is the study of quantitative relationships in chemical reactions. Mole ratio defines the proportional relationship between reactants and products involved in a chemical reaction and is derived from the balanced chemical equation.

In our textbook exercise, the mole ratio changes due to the oxidation process. Initially, the ratio is 2:1 for FeO to Fe₂O₃. After oxidation, the ratio becomes 1:2. This change directly affects the enthalpy calculation, as the number of moles dictates the total enthalpy of each substance, which we use to find the thermal energy released. It's crucial to understand that even without knowing the full balanced chemical equations, the mole ratio can provide us with enough information to calculate the enthalpy changes for the oxidation of the mixture.

With this in mind, students can improve their understanding of this exercise by ensuring they are clear on the concept of mole ratios and how they apply to the conservation of mass and energy within a reaction. It's the link between the microscale (atoms and molecules) and the macroscale (grams and liters) and is central to correctly predicting the outcomes of chemical reactions.