# Pressure of supercritical water inside a vessel

• Manoffew
In summary: 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... In summary, the ideal gas law does not work well for water because it is not an ideal gas.
Manoffew

## 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.

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)?

Manoffew said:
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

## 1. What is supercritical water and how does it differ from regular water?

Supercritical water refers to water that is heated and pressurized to a state where it has properties of both a liquid and a gas. This state is achieved at temperatures above 374 degrees Celsius and pressures above 218 atmospheres, making it significantly different from regular water that we encounter in our daily lives.

## 2. What are the applications of using supercritical water inside a vessel?

Supercritical water has many industrial and scientific applications, including in the production of clean fuels, waste treatment, and extraction of valuable compounds from natural sources. It can also be used as a solvent in chemical reactions and in the synthesis of new materials.

## 3. How does the pressure of supercritical water inside a vessel affect its properties?

The pressure of supercritical water inside a vessel has a significant impact on its properties, such as density, viscosity, and solubility. As the pressure increases, the density of the water decreases, and it becomes more compressible. The viscosity also decreases with increasing pressure, making it easier for substances to dissolve in supercritical water.

## 4. What are the safety concerns when working with supercritical water inside a vessel?

Working with supercritical water can be dangerous due to its high temperature and pressure. The vessel containing the water must be able to withstand these extreme conditions to prevent explosions or leaks. There is also a risk of corrosion from the highly reactive nature of supercritical water, so proper material selection is crucial.

## 5. How is the pressure of supercritical water inside a vessel controlled and measured?

The pressure of supercritical water inside a vessel can be controlled and measured using various techniques such as pressure relief valves, pressure sensors, and flow restriction devices. These instruments can help maintain a safe and stable pressure within the vessel, allowing for efficient and accurate experimentation with supercritical water.

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