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?

The relationship between internal energy (\(E\)) and enthalpy (\(H\)) is given by the following equation: \[H = E + PV,\] where \(P\) is pressure, and \(V\) is volume. Both internal energy and enthalpy are state functions, which means their values depend on the initial and final states of the system and not on the path taken to reach those states.

Internal energy (\(\Delta E\)) is path-independent, and its value depends on the initial and final states of the system. During a reaction, the internal energy can undergo changes due to heat and work exchanges with the surroundings. Similarly, the change in enthalpy (\(\Delta H\)) is also path-independent. Under constant pressure, the change in enthalpy is equal to the heat exchange between the system and its surroundings. Because both internal energy and enthalpy are path-independent, their changes remain constant, regardless of the intermediate steps taken in a reaction. If a reaction occurs in multiple steps, the sum of the changes in internal energy or enthalpy of each step will result in the same change in internal energy or enthalpy for the overall reaction. Therefore, the additive nature of \(\Delta H\) described in Hess's law also applies to \(\Delta E\).

In summary, since both internal energy (\(\Delta E\)) and enthalpy (\(\Delta H\)) are state functions and path-independent, an approach similar to Hess's law can be used to calculate the change in internal energy for an overall reaction by summing the \(\Delta E\) values of individual reactions that add up to give the desired overall reaction.