Question

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

Short answer

Hess's law states that the total enthalpy change is conserved in a chemical reaction, regardless of the number of steps, which is essentially a property of state functions. On the other hand, the first law of thermodynamics states that energy is conserved as it is converted from one form to another. The relationship between enthalpy and internal energy, given by H = E + PV, connects the two concepts. At constant pressure, the change in enthalpy (∆H) is equal to the heat transferred (q_p). Since both Hess's law and the first law of thermodynamics dictate conservation of energy, Hess's law can be considered another statement of the first law of thermodynamics.

Step-by-step solution

Define Hess's Law

Hess’s law states that the total enthalpy change for a chemical reaction is the same regardless of whether the process occurs in one step or multiple steps, provided that the initial and final states are the same. In other words, enthalpy is a state function. It can be represented as: ∆H_total = ∑ ∆H_products - ∑ ∆H_reactants where ∆H_total is the total enthalpy change, ∆H_products represents the enthalpy of products, and ∆H_reactants represents the enthalpy of reactants.

Define the First Law of Thermodynamics

The first law of thermodynamics states that energy is conserved as it is converted from one form to another. It can be expressed as: ∆E = q + w where ∆E is the internal energy, q is the heat, and w is the work done on the system. The concept of internal energy conservation is based on the fact that energy cannot be created nor destroyed, but can only be converted from one form to another.

Link Hess's Law and the First Law of Thermodynamics

Since enthalpy (H) is related to the internal energy (E) and the pressure-volume work (PV) in a system, we can write the relationship as: H = E + PV Taking the change in enthalpy (∆H), we can express it as: ∆H = ∆E + ∆(PV) For any system where only pressure-volume work (PV-work) is performed, the first law of thermodynamics can also be written as: ∆E = q_p - P∆V where q_p represents the heat at constant pressure. We can then combine the two equations to represent the change in enthalpy as: ∆H = q_p This equation shows that the change in enthalpy (∆H) for a reaction at constant pressure is equal to the heat (q_p) transferred into or out of the system. Due to the first law of thermodynamics, the energy transferred in the form of heat during a multistep process will be conserved, and since enthalpy change (∆H) is also conserved in a multistep process according to Hess's law, we can conclude that Hess's law is essentially another statement of the first law of thermodynamics.