Why is enthalpy a state function?

Enthalpy is a state function because its value depends only on the current state of the system, not the path taken to reach that state.

In thermodynamics, a state function, or state quantity, is a property of a system that depends only on the current equilibrium state of the system, not on the way in which the system acquired that state. Enthalpy is one such state function. It is a measure of the total energy of a thermodynamic system. It includes the internal energy, which is the energy required to create a system, and the amount of energy required to make room for it by displacing its environment and establishing its volume and pressure.

The reason why enthalpy is a state function lies in its definition. Enthalpy (H) of a system is defined as the sum of its internal energy (U) and the product of its pressure (P) and volume (V), i.e., H = U + PV. Both internal energy, pressure and volume are state functions, and the sum or difference of state functions is also a state function. Therefore, enthalpy, being the sum of state functions, is also a state function.

This property of enthalpy is particularly useful in chemistry, especially in the study of chemical reactions. For example, when we talk about the enthalpy change in a chemical reaction, we are only interested in the initial and final states of the reaction, not the specific steps or path the reaction took to get from the initial to the final state. This simplifies the analysis of energy changes in chemical reactions, as we don't need to know the details of the process, just the initial and final states.

In conclusion, enthalpy is a state function because it depends only on the current state of the system, not on the path taken to reach that state. This property makes it a very useful concept in the study of energy changes in chemical reactions.