Can you use an approach similar to Hess's law to calculate the change in internal energy, \(\Delta E,\) for an overall reaction by summing the \(\Delta E\) values of individual reactions that add up to give the desired overall reaction?

Enthalpy (\(\Delta H\)) is the heat content of a system at constant pressure. It is a state function, which means its value depends only on the current state of the system and not on the path taken to reach that state. Given this property, we can use Hess's law to find the change in enthalpy for a reaction by summing the changes in enthalpy for individual reactions that add up to the overall reaction. However, internal energy (\(\Delta E\)) is not a solely state function. It also depends on the path taken by the system during a reaction due to the presence of work done on or by the system. This means that internal energy is influenced by factors such as pressure, volume, and temperature changes in addition to the heat content of the system.

Since internal energy is a path-dependent quantity and influenced by factors other than heat content, we must consider whether an approach similar to Hess's law can be used for finding the change in internal energy for an overall reaction. In situations where the work done on or by the system is negligible, the internal energy change can be considered as a state function. This generally occurs when there are no significant pressure, volume, or temperature changes during the reaction. In such cases, we can adopt an approach similar to Hess's law and calculate the change in internal energy for an overall reaction by summing the internal energy changes of individual reactions. However, in situations where the work done on or by the system cannot be neglected and leads to significant pressure, volume, or temperature changes, we cannot use an approach analogous to Hess's law for calculating the change in internal energy for an overall reaction.

An approach similar to Hess's law can be used to calculate the change in internal energy, \(\Delta E\), for an overall reaction by summing the internal energy values of individual reactions ONLY in cases when the work done on or by the system is negligible and there are no significant pressure, volume, or temperature changes during the reaction. In situations where the work done on or by the system is significant, we cannot use such an approach, as internal energy is influenced by the specific path taken during the reaction.