Incorporate the compressibility factor of air at 250F
Read this and return here if you don't understand how to do it.
https://en.wikipedia.org/wiki/Compressibility_fact...

I need some help solving for pressure.

Say the initial conditions are:
Temperate= 291 K
Pressure= .1 mPa (atmosphere)
Air Volume= 45 ml

Final conditions:
System heated to 374 K
Oil expands and compresses air volume to 35 ml

What is the pressure?
Thanks

Most of us here do not usually provide answers to such problems. It's kind of like doing your homework for you. What would you learn from that. We try to teach you enough about your specific problem so that you can go away and solve it yourself, thereby earning your own money.

Well, from your link I see a look up table for Z, but it is dependent on pressure which is what I am trying to solve for.

Also, there is no mansion of humid air, which I think would play a large role.

It does say that the ideal gas law is probably a good approximation below 2 atm, I think I am below 2 atm, so ideal gas law it is?

If the final pressure is less than 5 atmospheres I would ignore compressibility.

Calculate the pressure using the reduced gas volume due to the expanded oil volume and also assuming the gas has reached the oil's temperature. Then using the ideal gas equation, calculate the pressure. If both assumed and calculated pressures are nearly equal, the pressure value you assumed was a good one. Leave it at that, or do another iteration.

Your gas is probably in contact with oil, not water, so if anything it has oil vapor in it, not water. Worry about that later. If you have a gas mixed with other vapors, compressibility becomes much more complicated. Hire a chem E if the answer is that critical.