Is delta H a state function?

My teacher says $H$ is a state function but $\Delta H$ is not. But I think both of them should be state function. Is he correct?




$\Delta H$ is a function of two states, the initial state and the final state.


For a given final state, there can be infinite $\Delta H$ values depending upon what the inital state was. 


For a given inital state, there can be infinite $\Delta H$ values depending upon what the final state is.


Therefore, $\Delta H$ is not a state function.


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I generally agree with DavePhD's answer but I also want to give the opposite view (!). Everyone agrees $H$ is a state function, but energy (and thus enthalpy) has no built in zero-scale. So really even in defining $H$, there is some built-in standard state that you are comparing the state of interest to. For example, the standard state might be all electrons and all nuclei infinitely separated from each other (this standard is commonly used in quantum chemistry). 


But we could also specify other standard states. We could say the standard state is one where all electrons and all protons and neutrons are infinitely separated...but that's possibly only useful for nuclear chemistry. We could also a standard state where all the atoms in a sample are separated into pure chemical elements. So to compute "the" enthalpy $H$ of say $\ce{CH4}$ using this standard state, we first separate its atoms to $\ce{C}$ and $\ce{2H2}$, our standard state, and then see how much the enthalpy changes.


Regardless of how we definite the standard state, enthalpy is a state function. But "the" enthalpy $H$ that we compute from the last standard state is the same as the enthalphy *change* of formation, $\Delta H\_{form}$! So if those two things are equal, and one of them is a state function, then the other one must be a state function too! So $\Delta H$ is also a state function.


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A state function is a **property of a single state** of the system. 


A change in a state function is associated with a **process that involves two states** of a system. 


You may be thinking that the change in enthalpy will be a state function because you can take any path you like between the initial and final states and still get the same enthalpy change. But that's beside the point; the enthalpy change isn't a property of a single state of the system, so it isn't a state function.


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