State functions are properties of a system that depend only on the current state of the system, not on the path used to get to that state. They are intrinsic properties of the system and include properties like pressure, temperature, volume, internal energy, enthalpy, entropy, and Gibbs free energy.

Option A: Internal Energy

Internal energy, denoted as $$U$$, is a state function. It is the total energy contained within the system, including kinetic and potential energy at the molecular level. Internal energy changes in a system only depend on the initial and final states of the system, regardless of the process or path taken to achieve these states. Therefore, it fits the criteria of a state function.

Option B: Irreversible Expansion Work

Irreversible expansion work is not a state function. Work, in general, is a path function because it depends on the path taken during a process. Whether the path involves irreversible or reversible processes, work includes energy transfer that depends significantly on how that transfer is carried out. Therefore, irreversible expansion work depends on the specific details of the process and is not solely determined by the initial and final states of the system.

Option C: Reversible Expansion Work

Similarly to irreversible expansion work, reversible expansion work is also a path function and not a state function. Even though reversible processes are ideal and involve quasi-static changes that maintain the system in near equilibrium throughout, the work done (or reversible expansion work) during such processes still depends on the specific path taken. This includes how slowly the process is carried out and the intermediate steps, distinguishing it from a state function.

Option D: Molar Enthalpy

Molar enthalpy, denoted as $$H$$, is a state function. It is defined as the sum of the internal energy $$U$$ of a system plus the product of the pressure $$P$$ and volume $$V$$ of the system, multiplied by the number of moles $$n$$, expressed as:

$H = U + PV$

Since $$U$$, $$P$$, and $$V$$ are all state functions, their combination into enthalpy continues to be dependent solely on the state of the system, not on the path taken to reach that state.

Conclusion:

Among the given options, Internal energy (Option A) and Molar enthalpy (Option D) are state functions, while both Irreversible expansion work (Option B) and Reversible expansion work (Option C) are not state functions. They are path functions.