Problem 61 - Chemistry: The Central Science

Question

What is the connection between Hess's law and the fact that \(H\) is a state function?

Step-by-Step Solution

Answer

The connection between Hess's Law and the fact that enthalpy (H) is a state function lies in their dependence on the initial and final states of a system. As enthalpy is a state function, its change depends only on the initial and final states, regardless of the specific path taken. Hess's Law, which states that the overall enthalpy change for a reaction is equal to the sum of the enthalpy changes for any intermediate reactions connecting the initial and final states, is a direct consequence of this property. Together, they allow us to calculate the enthalpy change of a reaction by summing the enthalpy changes of any set of intermediate reactions connecting the initial and final states.

Step 1: A state function is a property of a system that depends only on its current state, regardless of the path taken to reach that state. Enthalpy (H) is a thermodynamic property of a system and is a state function. This means that the change in enthalpy between two states (initial and final) is the same, irrespective of the specific path taken to reach the final state. #Step 2: Defining Hess's Law#

Hess's Law states that the enthalpy change for a chemical reaction is equal to the sum of the enthalpy changes for all intermediate reactions involved in the process. In other words, the overall enthalpy change of a reaction is the sum of the enthalpy changes of the individual steps, regardless of the specific pathway. #Step 3: Connecting enthalpy as a state function with Hess's Law#

Step 2: Since enthalpy is a state function, the total change in enthalpy depends only on the initial and final states and not on the pathway taken to reach the final state. This means that if we can find a series of intermediate reactions that lead from the initial state to the final state, the sum of the enthalpy changes for each of these intermediate steps will be equal to the overall enthalpy change for the complete reaction. This is precisely what Hess's Law states: the overall enthalpy change for a reaction is equal to the sum of the enthalpy changes for any intermediate reactions that can be used to connect the initial and final states of the system. #Step 4: Conclusion#

Hess's Law is a direct consequence of the fact that enthalpy is a state function. Because enthalpy changes depend only on the initial and final states of a system and not on the specific path taken to reach those states, we can use Hess's Law to calculate the enthalpy change of a reaction by summing the enthalpy changes of any set of intermediate reactions that connect the initial and final states.