Vapor composition in storage tank 1

[GK12345BM]

Hi All,

I have an ethanol storage tank with nitrogen blanketing and I would like to determine the vapor composition in the tank.
However I am a bit stuck on the calculation.

Tank volume = 100m3.
Tank level = 50%
Tank head space = 50m3
Liquid = ethanol (100% assumption but in real life 96%)
Tank temperature = 293 K
Vapor pressure ethanol = 7343 Pa
Vapor pressure nitrogen = unknown
P(ambient) = 1 atm = 101325 Pa


Raoult's law: Ptotal = sum(Vp,1 * n,1 + Vp,2 * n,2 ... ect.)
Vp = vapor pressure
n = mol fraction

Ideal gas law: PV = nRT
P = Pa
V = m3
n = mol
R = 8,3145
T = K

My calculation thought process:

101325 (total pressure) = (7343(vapor pressure ethanol) * 1(molfraction ethanol))+ (another gas)

This is where I am stuck:
1) The equation above would apply if the system is closed. The liquid composition mol fraction = the gas mol fraction. Since the vapor pressure is lower than atm. another gas must be
present otherwise the tank would implode (nitrogen of course since nitrogen blanketing is used.

If another gas is present the mol fraction of ethanol can not be equal to 1.

2) I don't know the vapor pressure of nitrogen. I can approximate it by using clausius-clapeyron but since I can't find the value in literature I don't think this is the correct way, is
it?
3) If the assumption is made that the whole vapor space is nitrogen which would mean that the mol fraction is 1 the tank would explode since the vapor pressure of nitrogen is extremely
high. So this can also not be true.
4) My best guess would than be:
((101325 - 7343)* 50m3) / 8,3145 * 293 K ) = mol Nitrogen
((7343)* 50m3) / 8,3145 * 293 K ) = mol Ethanol

I have the feeling that I am either making somewhere a fundamental mistake or I can't calculate it without knowing the the concentration in the vapor space.
Where am I making a mistake??

Thanks in advance.

 

[Compositepro]

The vapor pressure of nitrogen is not relevant, there is no liquid nitrogen present. The total pressure is equal to the partial pressure of ethanol plus partial pressure of other gases (nitrogen). Total pressure is known (ambient) and the partial pressure of ethanol will be the vapor pressure.

 

[GK12345BM]

So a fundamental mistake it is.

Thanks for you're reply.

 

[georgeverghese]

At this end of the liquid phase composition, Henry's Law applies to nitrogen ( since the operating T>Tc for N2)

Pt = x1. H1 + x2.P2sat under ideal conditons, where 1 refers to N2 and 2 refers to EtOH. Since x2 is very nearly 1.0, the partial pressure of EtOH in the vapor space, which is y2.Pt cannot exceed the 2nd term. If you must have some idea of N2 concentration in the liquid phase, which would be very small, look up tables for Henry's Law constants for N2 in EtOH at your operating temp. There are values for H in water for many gases in Perry Chem Engg Handbook.