Problem 59 - 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 enthalpy being a state function lies in the fact that both concepts emphasize the significance of the initial and final states of a system. Hess's Law states that the total enthalpy change of a chemical reaction is independent of the pathway taken, as long as the initial and final states are the same. Since enthalpy (H) is a state function, its value depends only on the initial and final states, and not on the specific process or pathway. This connection allows us to understand and predict the enthalpy changes of chemical reactions, regardless of the specific processes or pathways involved.

Step 1: Define Hess's Law and state function

Hess's Law states that the total enthalpy change of a chemical reaction is independent of the pathway taken, as long as the initial and final states are the same. A state function, such as enthalpy (H), is a property of a system that depends only on its current state and not on the history or path taken to reach that state.

Step 2: Describe the connection between Hess's Law and enthalpy being a state function

The connection between Hess's Law and enthalpy being a state function is that both concepts emphasize the significance of the initial and final states of a system. Since enthalpy is a state function, its value only depends on the initial and final states, and not on the pathway taken to reach those states. Similarly, Hess's Law states that the total enthalpy change of a chemical reaction depends only on the initial and final states, and not on the specific process or pathway.

Step 3: Illustrate the connection with an example

Consider the following reaction sequence: (1) \(A \rightarrow B\) with enthalpy change \(\Delta H_1\) (2) \(B \rightarrow C\) with enthalpy change \(\Delta H_2\) According to Hess's Law, the overall enthalpy change for the reaction \(A \rightarrow C\) is simply the sum of the individual enthalpy changes: \[\Delta H = \Delta H_1 + \Delta H_2\] Even if there were multiple pathways between A and C, as long as the initial state is A and the final state is C, the overall enthalpy change remains the same. This demonstrates the intrinsic connection between Hess's Law and the enthalpy being a state function. In conclusion, the connection between Hess's Law and enthalpy being a state function lies in the fact that both concepts emphasize the significance of the initial and final states of a system. This connection allows us to understand and predict the enthalpy changes of chemical reactions, regardless of the specific processes or pathways involved.