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

In summary, the conversation discussed the calculation of the partial pressure of ethanol at 70 degrees using Antoine coefficients and the volume of the vessel. It was found that the partial pressure was 0.7 bar and the moles of ethanol at this pressure were 307. The molecular weight of ethanol was also considered, resulting in a mass of 14130 g in the vapor phase and a concentration of 9.42 g/liter in the gas phase. A question was raised about the accuracy of the amount released, which was calculated to be 4.7 kg.
  • #1
warliooo
2
0
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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  • #2
This all looks correct. Is there a question here?
 
  • #3
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?
 
  • #4
In the ideal gas law, you should be using m^3, not liters.
 

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

1. How do you calculate the amount of ethanol in gas phase in a tank at 70 degC and atmospheric pressure?

The amount of ethanol in gas phase in a tank can be calculated using the ideal gas law, which states that the pressure (P), volume (V), and temperature (T) of a gas are related by the equation PV = nRT, where n is the number of moles of the gas and R is the ideal gas constant. By rearranging this equation to solve for n, we can find the number of moles of ethanol in the tank. From there, we can convert to mass or volume using the molar mass and density of ethanol at the given temperature and pressure.

2. What is the ideal gas constant and how is it used in the calculation?

The ideal gas constant (R) is a proportionality constant that relates the properties of an ideal gas. It has a value of 8.314 J/mol*K and is used in the ideal gas law equation (PV = nRT) to calculate the number of moles of a gas under given conditions of pressure, volume, and temperature.

3. How does temperature affect the amount of ethanol in gas phase in a tank?

According to the ideal gas law, temperature is directly proportional to the amount of gas in a tank. This means that as the temperature increases, the amount of ethanol in gas phase in the tank will also increase. This is because the gas molecules will have more kinetic energy and move around more, resulting in a larger volume and therefore more moles of gas.

4. Can the amount of ethanol in gas phase in a tank change over time?

Yes, the amount of ethanol in gas phase in a tank can change over time. This can happen due to factors such as changes in temperature, pressure, or volume of the tank. Additionally, if the tank is not completely sealed, the ethanol may evaporate or escape, resulting in a decrease in the amount of gas in the tank.

5. Are there any safety concerns when dealing with ethanol in gas phase in a tank at high temperatures?

Yes, there are safety concerns when dealing with ethanol in gas phase in a tank at high temperatures. Ethanol is flammable and can ignite at temperatures above 13 degC. It is important to handle and store ethanol safely, following proper storage and handling guidelines to prevent accidents and fires.

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