# Pressure of supercritical water inside a vessel

## Homework Statement

I'm trying to revive an old project a previous grad student had been toying with. Essentially, the reaction requires a sealed quartz tube (with a dilute acid) to be placed ("free-floating") inside a thick walled-autoclave capable of well over 40,000 PSI. The reaction is run at 500C. I'm trying to figure out how to appropriately equate the two pressures such that the pressure around the free floating quartz tube is the same that is inside the tube, so the tube will not burst. What is the best way to go about this, assuming I know the temperature and pressure I wish to run the reaction?

## Homework Equations

Previously, I thought the ideal gas law would work. Obviously, this was not a good approximate since we're dealing with water, which isn't an ideal gas even in gas form... I then used steam tables to find the density of water, which I then multiplied the amount of volume I was wanting to fill at that pressure, and used that mass as the basis of water I needed to add. This did not work.

## The Attempt at a Solution

Above.

Chestermiller
Mentor
Why didn't it work? Show us some numbers.

Chet

I found that the density of the critical steam at my desired Temp/Pressure of 500C/4,500 psi would be 120 kg/m^3. I then multiplied this by the (volume of autoclave-volume occupied by floating, sealed quarts tube) which was 24.1ml. From this, I said that I needed 2.904ml of water inside the autoclave (assuming water is 1g/ml and I just said that i needed 2.904g of steam which = the amount of water), and .17ml inside the sealed quartz tube (which had a volume of 1.3ml). The pressure never built inside the autoclave above 500psi- probably because the quartz tube broke and increased the volume of the autoclave. This is why I believe I'm not accurately estimating the pressures based off steam tables. Am I right in assuming that I can just use the mass of the steam and say that (mass of steam from density@volume)=(Mass of water needed)?

Chestermiller
Mentor
I found that the density of the critical steam at my desired Temp/Pressure of 500C/4,500 psi would be 120 kg/m^3. I then multiplied this by the (volume of autoclave-volume occupied by floating, sealed quarts tube) which was 24.1ml. From this, I said that I needed 2.904ml of water inside the autoclave (assuming water is 1g/ml and I just said that i needed 2.904g of steam which = the amount of water), and .17ml inside the sealed quartz tube (which had a volume of 1.3ml). The pressure never built inside the autoclave above 500psi- probably because the quartz tube broke and increased the volume of the autoclave. This is why I believe I'm not accurately estimating the pressures based off steam tables. Am I right in assuming that I can just use the mass of the steam and say that (mass of steam from density@volume)=(Mass of water needed)?
It looks like you did it correctly. The 120 kg/l looks OK. But, even if the quartz tube broke, shouldn't the volume not have changed? Have you tried the experiment without the quartz tube? It is very puzzling that the pressure never built up above 500 psi. What do you think the reason for this is (not the quartz tube breaking)?

chet