Question

In Section \(10.7,\) two characteristics of enthalpy changes for reactions are listed. What are these characteristics? Explain why these characteristics are true.

Short answer

The two characteristics of enthalpy changes for reactions are: 1. Enthalpy change is a state function: Enthalpy change depends on the initial and final states of the system and not on the path taken between those states. This is because enthalpy is related to the internal energy of the system, which is also a state function, and energy conservation applies. 2. Enthalpy change is directly proportional to the amount of reactants/products: The enthalpy change for a reaction is proportional to the amount of reactants consumed or products formed. This is due to the direct relationship between enthalpy change and heat flow in the reaction, as increasing the amount of reactants will result in more heat being transferred.

Step-by-step solution

Characteristic 1: Enthalpy change is a state function

Enthalpy change is a state function, which means it depends on the initial and final states of the system, but it does not depend on the path taken between those states. The enthalpy change for a reaction is the same regardless of whether the reaction occurs in one step or multiple steps. This property arises due to energy conservation and the fact that enthalpy is related to the internal energy of the system, which is also a state function.

Characteristic 2: Enthalpy change is directly proportional to the amount of reactants/products

Enthalpy change for a reaction is proportional to the amount of reactants consumed or products formed during the reaction. This means that if the amount of reactants doubles, the enthalpy change would also double (assuming constant pressure). This is true because enthalpy change is directly related to the heat flow in the reaction, and as we increase the amount of reactants, more heat will be transferred.

Explaining why these characteristics are true

The first characteristic is true because enthalpy change is derived from internal energy, which is based on the properties of the substances involved and their respective states, rather than the specific path taken in a chemical reaction. The second characteristic is true because the enthalpy change can be considered as heat released/absorbed per mole of reactants or products. If we increase the amount of reactants consumed or products formed, the total heat transferred will increase proportionately, resulting in a directly proportional relationship between the enthalpy change and the amount of reactants/products.

Key concepts

State Function and Its Importance in Enthalpy Change

When discussing the concept of enthalpy change, we must first understand what a state function is. This concept is pivotal to grasping why certain characteristics of enthalpy change hold true for chemical reactions.

A state function is a property of a system that depends only on the current state of the system, not the path by which the system arrived at that state. Examples of state functions include temperature, pressure, volume, and enthalpy. In the context of enthalpy change, this implies that the total enthalpy change is indifferent to the route taken from reactants to products. It is determined solely by the difference in enthalpy between the final and initial states.

This characteristic profoundly simplifies calculations in thermodynamics because we can use reference tables of standard enthalpy values, even if the reaction might occur through multiple steps in practice. Moreover, it underlines a fundamental principle of energy conservation within the confines of a chemical reaction.

Heat Transfer in Reactions

Heat transfer plays an essential role in chemical reactions, and understanding this can help clarify why enthalpy changes behave as they do. During a reaction, energy is either absorbed from or released into the surroundings. This process is intrinsically linked to the concept of enthalpy change.

Heat transfer during a reaction is a manifestation of enthalpy change. If a reaction is exothermic, it releases heat, resulting in a negative enthalpy change. Conversely, for an endothermic reaction, heat is absorbed, and the enthalpy change is positive. This relationship is crucial in fields like calorimetry, where we measure the heat released or absorbed by reactions to calculate enthalpy changes.

Enthalpy change is directly proportional to the number of moles reacting or being produced. Therefore, understanding the relationship between heat transfer and stoichiometric amounts is fundamental. This aspect explains that the more reactants you have, the more heat is either absorbed or released, showing the proportionality of enthalpy change with the quantity of reactants or products.

Stoichiometry and its Role in Determining Enthalpy Change

Stoichiometry is the quantitative aspect of chemistry that involves the calculation of reactants and products in chemical reactions. It's akin to a recipe that signifies how much of each ingredient (reactant) is needed to create a certain number of products.

In terms of enthalpy change, stoichiometry is critical as it lays out the precise proportionality between the amount of reactants or products and the associated enthalpy change. Doubling the number of moles of reactants will double the enthalpy change, given that pressure and other conditions are held constant. This is akin to saying that if you double the ingredients in a recipe, you can expect twice as many cookies—an idea that is straightforward and intuitive.

This proportional relationship is necessary for accurate predictions in chemical engineering, energy management, and a myriad of other applications where energy changes are involved in reactions. Hence, mastering stoichiometric calculations is not only about getting the numbers right but also about understanding the larger energetics of chemical processes.