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I have a sealed container with a volume of 1 liter. I want to go from an initial pressure of $P_{1}=1\ \mathrm{atm}$ and an initial temperature of $T_{1}=298\ \mathrm{K}$ to a final pressure of $P_{2}=9.95\ \mathrm{atm}$ and a final temperature of $T_{2}=453\ \mathrm{K}$..

I want to use water to create the pressure. But I do not know how to determine the amount of water. How would I do that?

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As I understand your question, you are limited to a total volume of $\pu{1L}$ and you can only add water (which I assume should remain liquid) and heat to the system, and are able to monitor it's pressure and temperature.

Your limitation is the vapor pressure of water at the desired temperature.

At $\pu{453K}$, the vapor pressure of water is $\pu{9.88 atm}$. At $\pu{9.95 atm}$, water boils at $\pu{456K}$. So, if you heat the water to $\pu{453K}$, you will have the desired temperature and be very close to your desired pressure. Or, you could heat the water to $\pu{456K}$, and you would have the desired pressure. Or you could heat the water to a temperature between $\pu{453K}$ and $\pu{456K}$ to get some trade off of being even closer to the desired temperature and pressure, but with neither of them being exactly what you want.

Again,this trade-off is a limitation arising from the constraint of using water to control the pressure. If you selected a liquid with a higher boiling point at $\pu{9.95 atm}$, then you could select a temperature at which the vapor pressure of the liquid would be equal to your desired pressure.

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  • $\begingroup$ But at 298 K the vapor pressure of water is nowhere near 1 atmosphere. $\endgroup$ – MaxW Feb 14 '17 at 5:14
  • $\begingroup$ But at 373K the vapor pressure of water is 1 atmosphere, and at 456K it is 9.95 atm; I'm not sure I follow your point...have I dropped the ball somewhere? $\endgroup$ – airhuff Feb 14 '17 at 5:24
  • $\begingroup$ "I want to go from an initial pressure of P1=1 atm and an initial temperature of T1=298 K"...// He can't start from there. $\endgroup$ – MaxW Feb 14 '17 at 7:02
  • $\begingroup$ Yea, I guess that's a bit ambiguous, as the OP doesn't say 1 atm of what. You're right in that it can't be 1 atm of water vapor at at T=298K. If that's what he meant then question and answer are bunk, but I don't think that's what he meant. $\endgroup$ – airhuff Feb 14 '17 at 7:16

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