Pressure vessel ideal gas calculation

Hello all,

As part of a research project, I am trying to calculate the amount of water/dry ice I would need to put in a cylindrical pressure vessel to obtain an internal pressure of ~100 psi at 200C (from room temperature, ~23C).

I haven't had to do a calculation like this in awhile, but here are my thoughts so far:
I will know the volume of water, dry ice, and air at room temperature (and consequently the amount of moles). I can then use the PV/T=constant relation to calculate the final pressure. I would use the internal volume of the pressure vessel minus the volume of the water/dry ice cube as the initial volume and the internal volume of the pressure vessel as the final volume. Also, T1=23C, T2=200C, P1~1 atm.
I would then check that the partial pressure of water (from P2 and moles of water) is below the saturation pressure of water, but at 200C this is likely the case.
Do you see anything wrong with this calculation? Is ideal gas law still reasonably applicable at ~100 psi? 5-10% accuracy is reasonable for my application.

I feel like there should be a way to do this calculation more accurately using steam and CO2 properties tables.

Thanks in advance for your help.