Question

Hess's law is really just another statement of the first law of thermodynamics. Explain.

Short answer

In conclusion, Hess's Law is a manifestation of the First Law of Thermodynamics, as both laws emphasize the conservation of energy in a chemical system. Hess's Law states that the enthalpy change for a chemical reaction remains constant regardless of the number of steps or intermediates involved, as long as the initial and final states are the same. This concept is consistent with the First Law of Thermodynamics, which dictates that energy cannot be created or destroyed, but only transformed from one form to another. Both laws underscore the constant and independent nature of energy changes in a chemical reaction, ultimately demonstrating the conservation of energy within a system.

Step-by-step solution

1. Define Hess's Law and First Law of Thermodynamics

Hess's Law states that the enthalpy change for a chemical reaction is the same, no matter how many steps or intermediates are involved, as long as the initial and final states are the same. Mathematically, it can be represented as: ΔH_total = Σ(ΔH_i) where ΔH_total is the total enthalpy change, and the summation is over all the individual enthalpy changes (ΔH_i) for each step in the process. The First Law of Thermodynamics states that energy cannot be created or destroyed, only converted from one form to another. It ensures the conservation of energy in a system, which can be represented mathematically as: ΔU = q + w where ΔU is the internal energy change, q is the heat exchanged and w is the work done on or by the system.

2. Relate Hess's Law and First Law of Thermodynamics

In a closed system, the internal energy change (ΔU) is directly related to the enthalpy change (ΔH). More specifically, we know that ΔH = ΔU + PΔV where P is the pressure and ΔV is the change in volume. Now, we can combine the First Law of Thermodynamics and the relationship between internal energy and enthalpy: ΔU = q + w ΔH = ΔU + PΔV Both equations represent energy conservation (enthalpy is a form of energy) in a system. If we focus on a single step in the reaction process, we can see that: ΔH_step = ΔU_step + PΔV_step It's important to note that, as per the First Law of Thermodynamics, the change in internal energy and enthalpy for each individual step would be the same even if we took a different path with different intermediate steps to reach the same initial and final states.

3. Apply Hess's Law to the First Law of Thermodynamics

Considering that the energy (in the form of enthalpy) is conserved through the reaction, we can sum the enthalpy changes for all individual steps in the process: ΔH_total = Σ(ΔH_i) = Σ[ΔU_i + P(ΔV_i)] Applying the First Law of Thermodynamics to each of these individual steps in the process: ΔH_total = Σ(Σ(q_i + w_i) + P(ΔV_i)) Since the energy cannot be created or destroyed, the total enthalpy change will remain constant regardless of the path taken or steps involved in the process, as stated by Hess's Law. In conclusion, Hess's Law is essentially a manifestation of the First Law of Thermodynamics, as it demonstrates the conservation of energy in a chemical system. Both laws are concerned with the flow and transformation of energy within a system, and they emphasize that the energy change is constant and independent of the number of steps or intermediates involved in a chemical reaction.

Key concepts

Enthalpy Change

Enthalpy change is a fundamental concept related to the heat energy within chemical reactions. Simply put, it represents the difference in the amount of heat energy contained in the products compared to the reactants. This value can either be positive, indicating an endothermic reaction that absorbs heat, or negative, for an exothermic reaction that releases heat.

Mathematically, it can be expressed as \( \Delta H = H_{products} - H_{reactants} \) where \( \Delta H \) is the enthalpy change, \( H_{products} \) is the enthalpy of the products, and \( H_{reactants} \) is the enthalpy of the reactants. Understanding enthalpy change is crucial because it helps predict the energy flow and heat exchange that accompanies chemical reactions, essential for applications ranging from industrial processes to biochemical interactions.

Energy Conservation

The principle of energy conservation is a cornerstone of physical sciences, stating that the total energy in an isolated system remains constant—it is conserved. This principle is encapsulated in the First Law of Thermodynamics, which is essentially the law of energy conservation applied to thermodynamic processes.

The First Law relates to the internal energy change within a system as a result of heat exchange with the surroundings and the work done by or on the system, summarized by the equation \( \Delta U = q + w \). Here, \( \Delta U \) represents the change in internal energy, \( q \) is the heat added to the system, and \( w \) is the work done on the system. Understanding this law enables scientists and engineers to calculate the energy requirements and outputs of various processes, which is essential for designing sustainable and efficient systems.

Chemical Reaction

A chemical reaction is a process that involves the transformation of one set of chemical substances into another. Such processes can be depicted through chemical equations that show the reactants converting to products. While these reactions can vary greatly in terms of the substances involved and the conditions under which they occur, they all share a common feature—the rearrangement of atoms.

During chemical reactions, bonds between atoms break and new bonds form. This reorganization of atoms requires energy, potentially absorbed from or released into the surroundings, depending on the nature of the chemicals and the reaction conditions. The study of chemical reactions is fundamental to chemistry, as it can explain not only practical everyday phenomena, such as combustion and corrosion, but also complex biochemical processes that sustain life.