Problem 79 - Chemistry The Science in Context

Question

Explain how the use of \(\Delta H_{f}^{\circ}\) to calculate \(\Delta H_{\mathrm{rxn}}^{\circ}\) is an example of Hess's law.

Step-by-Step Solution

Answer

In summary, the use of standard enthalpy of formation, \(\Delta H_{f}^{\circ}\), to calculate the standard enthalpy of reaction, \(\Delta H_{\mathrm{rxn}}^{\circ}\), serves as an example of Hess's law because it illustrates the principle that the overall enthalpy change for a reaction is independent of the path taken. By considering the formation of individual compounds in the reaction from their constituents as separate reactions, we can calculate the overall enthalpy change by summing up these individual enthalpy changes, which follows the principles of Hess's law.

Step 1: Understanding Hess's law

Hess's law states that the overall enthalpy change of a chemical reaction is independent of the path taken. In other words, if a reaction can be represented by a series of intermediate steps, the total enthalpy change for the overall reaction is equal to the sum of the enthalpy changes for the individual steps.

Step 2: What is standard enthalpy of formation (\(\Delta H_{f}^{\circ}\))?

Standard enthalpy of formation \((\Delta H_{f}^{\circ})\) is the change in enthalpy when one mole of a compound is formed from its constituent elements in their standard state (for example, at 1 atm pressure and \(298 K\) temperature). It serves as a reference point for comparing the stability of different compounds and for calculating the standard enthalpy of reaction.

Step 3: Calculating standard enthalpy of reaction (\(\Delta H_{\mathrm{rxn}}^{\circ}\)) using standard enthalpy of formation

To calculate the standard enthalpy of reaction (\(\Delta H_{\mathrm{rxn}}^{\circ}\)) for a given balanced chemical equation, we use the formula: $$\Delta H_{\mathrm{rxn}}^{\circ} = \sum{(\Delta H_{f(products)}^{\circ})} - \sum{(\Delta H_{f(reactants)}^{\circ})}$$ This equation represents the difference between the sum of the enthalpies of formation of the products and the sum of the enthalpies of formation of the reactants.

Step 4: Applying Hess's law to the calculation of standard enthalpy of reaction

When we calculate \(\Delta H_{\mathrm{rxn}}^{\circ}\) using the enthalpy of formation values for reactants and products, we follow Hess's law: 1. Assume the formation of individual compounds in the reaction from their constituents as separate reactions. 2. Add or subtract the enthalpy changes of these formation reactions according to the stoichiometry, as required. 3. The sum of these enthalpy changes will be equal to the overall \(\Delta H_{\mathrm{rxn}}^{\circ}\). Through this process, we break down the overall reaction into smaller changes in enthalpy - the formation of products and the decomposition of reactants from their standard states. By adding these smaller changes in enthalpy, we achieve the same result as if we considered the overall reaction directly. Thus, the use of \(\Delta H_{f}^{\circ}\) to calculate \(\Delta H_{\mathrm{rxn}}^{\circ}\) is an example of Hess's law, since we manipulate individual enthalpy changes of formation reactions to arrive at the overall enthalpy change of the main reaction.

Key Concepts

Enthalpy Change

Enthalpy change refers to the heat absorbed or released during a chemical reaction at constant pressure. It is a crucial concept in thermodynamics, providing insight into the energy transformation within a chemical system. When the system absorbs heat, the enthalpy change is positive; when it releases heat, the change is negative.
Hess's Law plays a pivotal role here by stating that the total enthalpy change of a chemical reaction is the same, regardless of the route taken from reactants to products. This means we can use individual enthalpy changes from a series of steps to calculate the overall enthalpy change of a reaction.
In practical terms:

• If you have a direct path and an indirect path for a reaction, the sum of enthalpy changes along the indirect path will equal the enthalpy change of the direct path.
• This allows scientists to determine overall enthalpy changes without having to measure each chemical reaction directly.

Standard Enthalpy of Formation

The standard enthalpy of formation, denoted as \(\Delta H_{f}^{\circ}\), plays a central role in understanding how compounds are formed at standard conditions. It is defined as the change in enthalpy when one mole of a compound is formed from its elements, each in their standard states like 1 atmosphere pressure and 298 Kelvin.
This concept is important because:

• It provides a baseline or reference point for thermodynamic calculations, allowing comparisons between different compounds.
• Compounds with highly negative \(\Delta H_{f}^{\circ}\) values are generally more stable since they release more heat during formation.
• This value helps in predicting reaction tendencies, such as whether a reaction will proceed spontaneously under constant pressure.

Knowing the standard enthalpy of formation provides essential data for chemists to calculate the enthalpy of other reactions, using related thermodynamic principles. This becomes instrumental in energy balance equations and process optimizations in chemical engineering.

Enthalpy of Reaction

The enthalpy of reaction, denoted as \(\Delta H_{\mathrm{rxn}}^{\circ}\), is a quantifiable measure of the heat change during a chemical reaction. It helps predict whether a chemical reaction will release heat (exothermic) or absorb heat (endothermic). The calculation of \(\Delta H_{\mathrm{rxn}}^{\circ}\) relies heavily on the standard enthalpies of formation.
The formula used for this calculation is: \[\Delta H_{\mathrm{rxn}}^{\circ} = \sum{(\Delta H_{f(products)}^{\circ})} - \sum{(\Delta H_{f(reactants)}^{\circ})}\] Here's how it works:

• First, calculate the total enthalpy change for forming the products from their elements.
• Then, subtract the total enthalpy change of forming the reactants from their elements.
• The resulting value is the enthalpy change for the reaction, taking into account the stoichiometry of the balanced chemical equation.

By combining standard enthalpy values of reactants and products, this approach applies Hess's Law, ensuring that the calculated reaction enthalpy accurately reflects several possible reaction pathways. Understanding \(\Delta H_{\mathrm{rxn}}^{\circ}\) is essential for chemists to manipulate reaction conditions to favor desired outcomes in both industrial and laboratory settings.