Calculate \(\Delta H_{\mathrm{rxn}}\) for the reaction: $$ \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+3 \mathrm{CO}(g) \longrightarrow 2 \mathrm{Fe}(s)+3 \mathrm{CO}_{2}(g) $$ Use the following reactions and given \(\Delta H^{\prime}\) s: \(2 \mathrm{Fe}(s)+3 / 2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(s) \quad \Delta H=-824.2 \mathrm{~kJ}\) $$\mathrm{CO}(g)+{ }^{1} /{ }_{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g) \quad \Delta H=-282.7\mathrm{~kJ}$$

Chemical thermodynamics is a branch of thermodynamics that focuses on the energy changes, particularly the heat and work associated with chemical reactions. It combines the concepts of heat transfer with the principles of energy conservation, applied specifically to chemical processes. In chemistry, it's essential to predict whether a reaction will be spontaneous or if it requires additional energy to proceed.

One of the primary values we analyze in chemical thermodynamics is enthalpy (H), a measure of the total heat content in a system at constant pressure. The enthalpy change (H) for a reaction indicates the amount of heat absorbed or released during the reaction. A negative H indicates that the reaction is exothermic, releasing heat, while a positive H means the reaction is endothermic, absorbing heat.

To calculate the enthalpy change for a reaction, one might need to consider various pathways or combine multiple reactions, inherently tied to the principles of Hess's law and the laws of stoichiometry.

Hess's Law is a powerful tool in chemical thermodynamics providing simplicity in calculating the enthalpy change of reactions. It states that the total enthalpy change for a chemical reaction is the same irrespective of the number of steps or the route taken during the reaction. This is because enthalpy is a state function, which means its value depends only on the initial and final states, not on the specific path taken.

Using Hess's Law allows us to algebraically add equations to reach a desired reaction. If the equations must be reversed to align with the target reaction, the sign of their H values is also reversed. Multiplication or division of reaction equations requires corresponding multiplication or division of the enthalpy values by the same factor. By systematically adjusting the equations and combining them, we can find the overall enthalpy change for complex reactions that may not be directly measurable in the laboratory.

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It allows chemists to predict the amount of products that can be formed from a given amount of reactants or vice versa. In the context of thermodynamics, stoichiometry helps in balancing chemical equations which is fundamental when applying Hess's Law.

The stoichiometric coefficients indicate the number of moles of each substance involved in the reaction. When we calculate the enthalpy change for a reaction based on constituent reactions, it is crucial to align the stoichiometry precisely. This might include reversing reactions or multiplying them by whole numbers or fractions to ensure that the atoms and molecules on each side balance as per the stoichiometric proportions.

Ensuring Accurate Stoichiometric Calculations

Beyond merely getting the right coefficients, accuracy in stoichiometry is essential for predicting enthalpy changes because it directly affects the computed heat evolution or absorption in a reaction. The total enthalpy change of the reaction is the sum of all enthalpy changes, accounting for each stoichiometric step.