Find the amount of ethanol (70 degC) in gas phase in a tank at atm

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SUMMARY

The discussion focuses on calculating the amount of ethanol in the gas phase at 70 degrees Celsius using Antoine coefficients and the ideal gas law. The partial pressure of ethanol was determined to be 0.7 bar, leading to the calculation of 307 moles of ethanol in a 1500-liter volume. This results in a mass of 14,130 grams of ethanol, yielding a concentration of 9.42 g/liter in the vapor phase. The calculation indicates that if 500 liters are released, approximately 4.7 kg of ethanol is emitted, raising concerns about the accuracy of the initial assumptions regarding partial pressures.

PREREQUISITES
  • Understanding of Antoine coefficients for vapor pressure calculations
  • Familiarity with the ideal gas law (PV=nRT)
  • Knowledge of unit conversions between liters and cubic meters
  • Basic chemistry concepts, including molecular weight calculations
NEXT STEPS
  • Review Antoine equation applications for various substances
  • Study the ideal gas law in detail, including unit conversions
  • Explore vapor-liquid equilibrium concepts in thermodynamics
  • Investigate methods for calculating gas concentrations in different phases
USEFUL FOR

Chemical engineers, process engineers, and anyone involved in vapor phase calculations or ethanol production will benefit from this discussion.

warliooo
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Homework Statement
Question: Find the amount of ethanol in gas phase in a tank blanketed by N2 at atmospheric pressure.

An empty tank of 2000 litres at atmospheric pressure and 20 degC is being used to store ethanol waste. The tank is blanketed with nitrogen, and is kept at atmospheric pressure by venting (to atmosphere).

500 litres of ethanol at 70 degrees is added to the tank. By adding 500 litres of ethanol, 500 litres of nitrogen leaves through the vent (atmospheric pressure remained).

Assuming that the ethanol in the tank reaches equilibrium in the new tank and stays at 70 degC, 1) how much ethanol will be in the gas phase within the tank? 2) if another 500 litres of ethanol is added, how much ethanol is vented to the atmosphere?
Relevant Equations
Raoults Law
I first found the partial pressure of ethanol at 70 degrees using Antoine coefficients:

Coefficients:
A
7.68117​
B
1332.04​
C
199.2​

Equation:

241016


And found a partial pressure of 0.7 bar.

This is the pressure exerted by the vapour on the liquid.

I then found the moles of ethanol at this pressure using the volume of the vessel (2000l-500l):

PV=nRT

n=PV/RT= (0.7*101325)*1500/(8.3143*(273+70))

n=307 moles

Molecular weight of ethanol = 46g/mol

1)

Mass (g) of ethanol in the vapour phase= (307*46)=14130 g

2)

Concentration of ethanol in gas phase:14130/1500=9.42 g/liter vapour

if 500 litres released: 9.42*500/1000 = 4.7 kg released.
 
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This all looks correct. Is there a question here?
 
The amount released seemed a bit high when I calculated it so I assumed I had made a mistake/misunderstood partial pressures. Does this seem ok to you?
 
In the ideal gas law, you should be using m^3, not liters.