If you know the boiling temperature of the liquid, then you can calculate the pressure in the system. If you know a "general" temperature - for example, of the pot / chamber, then the pressure is more difficult to infer as you cannot be sure of the precise boiling temperature of the liquid.

With a few data points that you can look up you can plot the curve. Boiling point of water at various pressures:

6mbar = 0°C

8mbar = 4°C

112mbar = 50°C

1000mbar = 100°C

1956mbar = 121°C

Similar can be plotted for other solvents.

Kind regards,

Rob

Rob Darrington Thank you for your answer. Still, it is interesting whether degree of filling affects pressure or not.

Ilia Martakov degree of filling has no effect (so long as there is water present). The controlling factor is the pressure - so if the pressure is regulated up, temperature goes up.

The short answer is that the pressure is determined by the temperature and filling factor FF, there are several tables and graphs that can be found on the internet of P(T,FF) (see attached). However, I had the same question on how to calculate the pressure and I have solved the problem analytically, can provide a Python code if interested. If you want to work on the problem follow the next steps:

Assuming no chemical reactions are taking place, the pressure can be calculated according to Dalton's law as the sum of partial pressures:

a) vapor pressure of the liquid at T

b) pressure due to gas escaping from the liquid

c) pressure from the gas initially filling the head space

Here is how to calculate each:

• As long as liquid and gas coexist in the autoclave (generally true for filling factors below 70%), the vapor pressure depends solely on T, is the line dividing gas/liquid phases in the phase diagram of your solvent, can also be calculated as a function of T from Antoine's equation.
• The solubility of gases in a liquid decreases with T, therefore as T increases gas is released to the head space volume which increases the pressure. The pressure increase due to gas escaping from the liquid depends on the change in solubility with T, and can be calculated from Henry's law. Keep in mind that your gas may be composed of different constituents with different solubilities. It is easy to prove that this pressure increases with T and FF (the more liquid, the more gas is released in less volume). As a reference, at standard conditions, the mass of air dissolved in water is ~23 mg for each Kg of water, even assuming that all the dissolved air escapes (which really is just about half of it), this just result in 1-3% increase to the air mass already in the head space. So in the water/air scenario, neglecting this pressure can be a valid approximation, specially at low FF.
• The pressure of the gas filling the chamber raises as the T increases and the gas volume decreases. In general, the resistant to compression (i.e. bulk modulus) of liquids is several orders of magnitude larger than in gases, so as T increases, the liquid expands and the gas volume decreases. This pressure depend on T and FF. A first approximation of this pressure is to assume that the gas volume stays the same and use Gay-Lussac's law to calculate gas pressure or you can follow the next steps to include the calculation of V_2:

Basic assumptions are that the container is rigid, the contribution of the escaping gas is negligible, the gas is an ideal gas and the head space is always at equilibrium with the liquid medium (P_vapor is always known).

Article Subcritical Solvothermal Synthesis of Condensed Inorganic Materials

Raul Montes thank you for the great answer. In the spirit of oversimplification though, I would like to ask a question (more of a true / false statement):

When using a solvothermal autoclave in an oven where the external temperature is set (e.g. to 150 deg C) and the solution in the autoclave is filled to 60%, the pressure within the autoclave will facilitate the solvothermal reaction, but the actual internal temperature of the solution inside the autoclave should not exceed 150 deg C due to the lack of additional energy sources. So the vapour pressure cannot actually increase the solution temperature? As an example, if a 5% PVA solution (PVA in water) is autoclaved at 150 deg C, could the solution reach its degradation point (200 deg C) even though the vapour pressure is increased? Sorry for my slow comprehension on this topic, I have read your attached article and failed to formulate an answer myself.

Troy Warry At thermodynamic equilibrium all objects in the system have the same temperature. Out of equilibrium there are a variety of things that can happen and I am not sure which one plays the main role. But considering that water is almost incompressible, the pressure built in the head space will not exert work on water and thus will not change its temperature, if that pressure is higher than the vapor pressure, vapor will simply condense. I believe your question rather than a true/false statement about the grounds of thermodynamics out of equilibrium is more a question about how to make sure the temperature inside the autoclave matches the set temperature. In this case the answer is to use a low heating rate (< 5ºC/min) so that you allow enough time for the autoclave to reach thermal equilibrium.