A state function is a term used quite a bit in chemistry, especially when talking about thermodynamics, and sometimes it’s confusing as to what it really is. It’s not an equation or anything, but a way to describe a property of something. Here’s the easy definition, and a way to remember it.
A state function is a property of something (like the change of energy), that only depends on the current state, not how it got there. Just a helpful note; if a state function returns to it’s initial conditions, the overall change is zero since it’s value depends only on where it is now. Read the following example and it will definitely clear this up.
[Easy way to remember what a state function is]
To remember what a state function is, imagine you’re going to take a trip across the United States from New York to California. You leave New York and arrive in California after awhile. You’re having so much fun on the road trip that it really doesn’t matter how long it takes you to get to California, the point is that you are there! You crossed a few states on the way, but who even cares? For all anyone knows, you could have driven through 30 states first, but it doesn’t even matter.
In this case, your position is a state function. All that matters is your total change in position, that is the distance between where you left in New York to where you are in California.
[Easy way to remember reversibility of a state function]
Now, imagine you’re in California and decide to go back to New York. After crossing through some states and a little time later you end up back in New York, right where you started. Your total position change is zero since you left from New York and came right back to New York. Same goes for a state function when it’s reversed and brought back to where it started.
Some chemistry related examples of a state function include change in energy or enthalpy (think Hess’s Law).
Hope this helps! I know I had a hard time figuring it out when I was in Chemistry; there are so many types of functions that it’s so easy to get them mixed up.