Phase Equilibria, Condense Phases

[Alchai]

Homework Statement

I'm given vapor pressures of an assumed ideal gas:
(Clausius Clapeyron.. ln(p) = -A/T-BlnT+C)
I am given A, B, C for liquid and solid.
And given T,melt.

I am to find what the first condense phase is, and at what temperature, given isothermal compression from T>Tmelt and P < Patm

Homework Equations

Clausius Clapeyron.. ln(p) = -A/T-BlnT+C
dG(gas)/dP = Vg = RT/P

The Attempt at a Solution

At first glance, I assumed I would just have to find the P values in the Clausius Clapeyron for the temperature given...assuming that when the pressure on the system = pressure from the liquid or solid phase, (as given in the above eq), the condense phase would be the lowest pressure...
Am I assuming this to be too easy?
I have no examples, and no notes on isothermal compression's effect on vapor pressures...

 

[Jhero]

Thank you for your post. It seems like you are on the right track in using the Clausius Clapeyron equation to solve this problem. However, it is important to note that this equation is typically used for phase changes between two different phases, rather than for isothermal compression. Additionally, the equation you have provided is for an ideal gas, which may not accurately represent the behavior of the substance you are studying.

To determine the first condense phase and its temperature, you will need to use the given values of A, B, and C for the liquid and solid phases and the temperature at which the substance melts (Tmelt). From there, you can use the Clausius Clapeyron equation to calculate the vapor pressure at Tmelt for both the liquid and solid phases. The phase with the lower vapor pressure at Tmelt will be the first phase to condense.

It is also important to consider the pressure of the system (P) and the atmospheric pressure (Patm). If P is less than Patm, then the substance will not be able to condense at all, as the atmospheric pressure is greater than the pressure at which the substance can condense. However, if P is greater than Patm, then the substance can condense at a lower pressure.

In summary, to solve this problem, you will need to use the given values of A, B, and C for the liquid and solid phases, the temperature at which the substance melts (Tmelt), and the pressure of the system (P) to determine the first condense phase and its temperature. I hope this helps guide you towards the correct solution. Best of luck with your calculations!