I have a system in vapor-liquid equilibrium which also has some gas inside (let's say that the VLE system is Water and the gas is Air). The system looks like this:
There is some heat applied to it and therefore more water will vaporize and the Saturation Pressure of the vapor will increase. Since it is a closed system, I the amount of gas stays the same, while the amount of vapor increases. I would like to calculate the pressure of this system and I'm not sure 100% that my approach is correct.
I was thinking that the total pressure of the system is:
$P_{tot} = P_{sat} + P_{gas}$
So the Saturation Pressure can be calculated using the Antoine equation or taken from tables. I'm fine with that. Here Question 1 arises: how can one check if the VLE condition still applies once heat is applied? Compare Antoine with Ideal Gas?
Now the main question is... what to do with the gas? If I assume that it is ideal gas, it can be written as:
$P_{gas} = \frac{n_{gas} R T}{V_{gas}}$
And here is where I get confused. Question 2: Is $V_{gas}$ the volume of the gas phase only or it is considered together with the vapor like in the figure ($V_{gas}=V_{vap}$)? And if it is considered together with the vapor, then obviously it should be a variable, i.e. $V_{gas} = m_{vap} \rho_{vap}$. Another question arises with this: Question 3: If I don't know the amount of gas, how do I find it? (I know that one can find the amount at the initial state of the system or STP conditions $n_{gas} = \frac{(P_{init}-P_{sat})V}{RT}$, but there are two unknowns: $n_{gas}$ and $V$, unless the V is known). So basically the volume is the one that confuses me and I am thinking of using Raoult's law to get the fractions between the gas and the vapor, but I'm not sure this is the right approach. Can anyone advice me on this?
Thank you!
Paul