Finding Max Volume for evaporation

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SUMMARY

The discussion focuses on calculating the maximum volume of 70% isopropyl alcohol that can evaporate in a closed 2L woosh bottle. The user employs the ideal gas law and Raoult's law to analyze the system, noting the initial conditions of pressure (1 atm), temperature (298 K), and the composition of air (21% O2 and 79% N2). Despite formulating several equations, the user encounters a challenge due to having more unknowns than equations, indicating a need for additional information or clarification on the application of Raoult's law in this context.

PREREQUISITES
  • Understanding of the ideal gas law (PV=nRT)
  • Familiarity with Raoult's law and its application in vapor pressure calculations
  • Knowledge of stoichiometry and mole fractions in gas mixtures
  • Basic thermodynamics concepts related to evaporation and equilibrium
NEXT STEPS
  • Research the application of Raoult's law in mixtures, specifically for isopropyl alcohol and water
  • Study the behavior of vapor-liquid equilibrium in closed systems
  • Explore advanced thermodynamic concepts related to evaporation rates
  • Learn about the effects of temperature and pressure on the evaporation of volatile substances
USEFUL FOR

Chemical engineers, physical chemists, and anyone involved in experimental design or safety assessments of flammable liquids in closed systems.

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So this is the problem that I am working on. It is a woosh bottle where I am inputting 70% isopropyl alcohol, closing the top and waiting for the alcohol to evaporate. This mixture is then ignited to generate a flame. My job for this project is to calculate the maximum volume of 70% isopropyl alcohol where all of the alcohol evaporates.
Here hows I attempted to solve the problem
Knowns
P*(init)=1atm
V=2L
T=298k
Then I just started writing up equations
V=Vliq+Vgasinit %I am saying that the inital amount of gas in my 2L bottle plus the volume of the alchol is equal to the total volume in the container.
Pinit*Vgasinit=n(init)*R*T %Perfect gas law for the container originally
n(init)=n(O2)+n(N2) %The has is just oxygen and nitrogen as first (air)
.21n(init)=n(O2)
.79n(init)=n(N2)
n(final)-n(water)-n(alcohol)=n(init) %The number of moles after the fuel has evaporated and come to equilibrium with air
P(final)*V=n(final)*R*T
n(final)=n(alcohol)+n(H2O)+n(O2)+n(N2) %The n alcohol is the 70% of the isopropyl and 30% is water which is where I got the n(H20)
I been looking at this problem for hours and can seem to figure out where to go. With the amount of equations I have made up, I have way morre unknowns than equations. Is there something to do with raoults law that I can do or this problem just not possible with the amount of information that I know.
Any help would really be appreciated.
 
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