Complicated liquid to vapor conversion problem

[JamesBone]

I had a question about the volume of vapor produced from an amount of liquid after increasing the pressure inside a container containing the liquid, then rapidly decreasing it back to the original pressure.

Say you have an amount of water, say 1mL (or another liquid, not sure what descriptors you would need to know, possibly boiling point?) in a closed container, let's say 2L. you pressurize the container (initial pressure 1atm/14.69psi) to a pressure, let's say 100 psi. Now if you immediately decrease the pressure back to 1atm (instantly in less than 1 second), causing the liquid to vaporize, how could you calculate the volume of the now vaporized water in the bottle? in other words, if all of the water in the bottle is not vaporized, how could you calculate the volume that was? If you included other factors such as temperature of the air, water, exact amount of time spent depressurizing the container, physical properties of the liquid, etc. I also know the easiest way to solve this would be to remove the vapor then re-measure the amount of liquid remaining in the bottle, but that shortcut isn't allowed in this problem.

Could someone create a blueprint equation of this problem and solve it using made up amounts? I was trying to figure it out using PV=nRT but I haven't taken chem in a while and couldn't go much further than that. I appreciate any help!

 

[Yanick]

I doubt anyone will sit around and solve your problems for you but we will try and aid you in your search.

You can check out:

1. Phase Diagrams for a pure 1 component-2 phase system.
2. The Clausius-Clayperon Equation can be used.

I'm not sure what you are trying to accomplish by "quickly" lowering the pressure. For Thermodynamics to be applicable you need to system to reach equilibrium.

 

[Borek]

Just depressurizing the container is not a reason for the water to evaporate. And the volume is limited by the container, you are always going to have 2 L of the water vapor.

Something doesn't add up.

 

[256bits]

How are you pressurizing and depressurizing - adding more moles to the container and then removing, using a piston to change the volume, adding and removing heat?

Your problem needs to be defined a bit more streniously, otherwise it is all assumptions.

 

[LudusRex]

I would approach this problem by first considering the physical properties of the liquid in question. The most important factor here would be the boiling point of the liquid. This is the temperature at which the liquid will vaporize at a given pressure.

Using the ideal gas law (PV = nRT), we can calculate the volume of vapor produced from an amount of liquid by first determining the number of moles of the liquid (n) and the initial and final pressures (P1 and P2) at which the vaporization occurs. We would also need to know the temperature (T) at which the liquid and vapor exist.

To calculate the number of moles of the liquid, we can use the density (ρ) of the liquid and the volume (V) of the liquid given in the problem. The number of moles can be calculated using the equation n = m/ρ, where m is the mass of the liquid.

Once we have the number of moles of the liquid, we can use the ideal gas law to calculate the volume of the vapor produced. The equation would be V2 = (nRT2)/P2, where V2 is the volume of the vapor, T2 is the temperature of the vapor, and P2 is the final pressure.

To determine the temperature of the vapor (T2), we can use the Clausius-Clapeyron equation, which relates the vapor pressure (Pvap) of a substance to its temperature (T) and enthalpy of vaporization (ΔHvap). The equation is ln(Pvap2/Pvap1) = (-ΔHvap/R)(1/T2 - 1/T1), where Pvap1 is the vapor pressure at the initial temperature (T1).

In this problem, we would need to know the enthalpy of vaporization for the specific liquid in question. We would also need to consider the temperature of the air and the water, as well as the exact amount of time spent depressurizing the container, as these factors can affect the final temperature of the vapor.

To summarize, the blueprint equation for this problem would be:
V2 = (m/ρ)(RT2/P2) = (m/ρ)(RT2/P1)(Pvap2/Pvap1) = (m/ρ)(RT2/P1)e^(-ΔHvap/R)(1/T2 -