# How much liquid water do I need to get a relative humidity of 10%?

Rub3y
I need to calculate how much liquid (mass) could cause a relative humidity of 10% in a pipeline. The pressure in the pipeline is 38 barg and the temperature is 105 °C. I calculated the partial pressure of the water which would be 3,74 bar (with formula relative humidity and antoine coëfficiënts), but couldn't get further to get to the mass of liquid in this situation. Any suggestions are welcome! :)

Side question: I wanted to use Raoult's law to get the fraction in liquid phase but the formula is the same as the one for relative humidity. Why is this? Am I missing something?

Mentor
The vapor pressure of water at 105 C is about 1.2 bars, so, for a relative humidity of 10%, the partial pressure would have to be about 0.12 bars.

Rub3y
The vapor pressure of water at 105 C is about 1.2 bars, so, for a relative humidity of 10%, the partial pressure would have to be about 0.12 bars.
Thanks for the reply! Shouldn't you take the vapor pressure of water at 38 bar (boiling point would be 249 °C at 38 bar -> with Antoine coëfficiënts I can calculate the equilibrium vapor pressure)? The vapor pressure would then be 37,4 bar so the partial pressure of the water (10%) would 3,74 bar. But I still don't know how much liquid needs to go though the pipeline to get this water partial pressure of 3,74 bar. But please correct me if I'm wrong.

Mentor
Thanks for the reply! Shouldn't you take the vapor pressure of water at 38 bar (boiling point would be 249 °C at 38 bar -> with Antoine coëfficiënts I can calculate the equilibrium vapor pressure)?
No way. You evaluate it at the actual gas temperature. The boiling point at 38 bars has nothing to do with this.

But I still don't know how much liquid needs to go though the pipeline to get this water partial pressure of 3,74 bar. But please correct me if I'm wrong.
Let's agree on the partial pressure first.

Rub3y
No way. You evaluate it at the actual gas temperature. The boiling point at 38 bars has nothing to do with this.

Let's agree on the partial pressure first.
I see what I did wrong. Got it, So partial pressure is 0,12 bar. So what do I do next? Use Raoult's law to get the the mole fraction in the liquid? I thought about using this but it's the same formula as relative humidity (never noticed it until now) so it confused me.

Btw I used the other site because it's a little time sensitive, it has nothing to do with you ;)

Mentor
Raoult's law does not apply because there is no liquid phase. Assuming for now that the gas phase behaves like an ideal gas, what is the molar volume of an ideal gas at 39 bars absolute and 378 K?

Rub3y
Raoult's law does not apply because there is no liquid phase. Assuming for now that the gas phase behaves like an ideal gas, what is the molar volume of an ideal gas at 39 bars absolute and 378 K?
Why would there be no liquid phase? A part of the liquid phase would evaporate, causing a partial pressure of water? And I need to know how much liquid goes through the pipe, which will cause a relative humidity of 10%.

Last edited:
Mentor
Why would there be no liquid phase? A part of the liquid phase would evaporate, causing a partial pressure of water? And I need to know how much liquid goes through the pipe, which will cause a relative humidity of 10%.
Sorry. I misread the vapor pressure data on benzene. At 105C and 39 bars, benzene is a compressed liquid. So you should have all liquid phase, and no vapor.

Rub3y
Sorry. I misread the vapor pressure data on benzene. At 105C and 39 bars, benzene is a compressed liquid. So you should have all liquid phase, and no vapor.
Okay, that I did know. But there still is water in liquid phase right? So how do I determine how much is in liquid phase, which will cause a relative humidity of 10%?

And the extra information, if you need it: The flow is 60 m3/h. There is mainly benzene (around 60 %), but also H2S, NH3 and some hydrocarbons in the pipeline.

Mentor
Okay, that I did know. But there still is water in liquid phase right? So how do I determine how much is in liquid phase, which will cause a relative humidity of 10%?

And the extra information, if you need it: The flow is 60 m3/h. There is mainly benzene (around 60 %), but also H2S, NH3 and some hydrocarbons in the pipeline.
I see. This is going to be a non-ideal liquid solution, in contact with a somewhat non-ideal gas phase. Is there any VLE data on this system. If not, I guess you can try some of the non-ideal liquid models like uniquak.

• Rub3y