Calculate the equilibrium concentration of CO2 in beer in grams/liter

In summary, the conversation discussed the calculation of absolute pressure by adding atmospheric pressure and gauge pressure, the use of Henry's law to calculate the concentration of CO2, and the steps to calculate it using the mole fraction and the amount of liquid present. The final result was a concentration of 6.104 g/L.
  • #1
sci0x
83
5
Homework Statement
At end of fermentation, beer is cooled to 2 degrees C. Height of beer in vessel is 20m, top pressure of 0.1 bar g of co2 is applied. Calculate the equilibrium conc of co2 in the beer in g/l assuming that a reasonable estimate of its average conc can be obtained by considerimg the prevailing pressure at the mid-point of beer in the vessel

Data:
Henrys constant at 2 degrees C = 84.1 x 106Pa (mole fraction) -1
Beer density = 1008kg m-3
Acc due to grav = 9.81 m s-2
Mol weight CO2 = 44
Mol mass beer = 18
Atm pressure = 1.013 bar 1 bar = 105 Pa
Relevant Equations
P1 = P0 + qgh
Absolute pressure = Gauge press + Atmos press
Atmos press = 105 Pa
Co2 press = 0.1 bar g = 10000Pa
Abs press = 10,105 Pa

Hydrostatic pressure = absolute press + (density)(grav)(height at midpoint)
= 10,105 + (1008)(9.81)(10)
10,8989.8 Pa

Calc CO2 conc by henrys law
P=KHC
C=P/KH
= 108989.8/84.1x10^6Pa
= 1.29 x 10^-3
Ans x 44 = 0.056 g/l

Can i get some help please:
Have i calculated absolute pressure correctly.
Atmos pressure CO2 should be used in calc of absolute pressure from gauge pressure
Hydrostatic pressure is added for the pressure at the mid-point, calculated by multiplying density x acceleration due to grav x liquid height (10m)

Calc of Co2 conc is by henry's law
Mole fraction is converted to g/L
Answer should be 6.1 g/L
 
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  • #2
I think absolute atmospheric pressure can be taken as 100000 Pa, so the absolute pressure of CO2 at the top is 110000 Pa.
 
  • #3
Is it chemistry or physics problem?
 
  • #4
bagasme said:
Is it chemistry or physics problem?
What is your motivation for asking this question?
 
  • #5
Chestermiller said:
I think absolute atmospheric pressure can be taken as 100000 Pa, so the absolute pressure of CO2 at the top is 110000 Pa.
Yes i think the question says atmos pressure is 105 Pa, think it means 10^5

So absolute pressure is 110,000 Pa
Then i add hrdrostatic pressure for pressure at the mid point
Is 110,000 + (1008)(9.81)(10)
Is 208884.8 Pa

If this is right i should be able to calc CO2 conc by henrys law
P=KHC
This P refers to partial pressure, can i calc this from absolute pressure
 
  • #6
sci0x said:
Yes i think the question says atmos pressure is 105 Pa, think it means 10^5

So absolute pressure is 110,000 Pa
Then i add hrdrostatic pressure for pressure at the mid point
Is 110,000 + (1008)(9.81)(10)
Is 208884.8 Pa

If this is right i should be able to calc CO2 conc by henrys law
P=KHC
This P refers to partial pressure, can i calc this from absolute pressure
It’s not the partial pressure. This is pure CO2.
 
  • #7
So P = KHC
208884.8 Pa = 84.1 x 10^6 Pa (C)
C= 2.48 x 10^-3 moles / L

44g CO2 in 1 mole
0.109 g in 2.48x10^-3 mole

Am i on the right track?
 
  • #8
sci0x said:
So P = KHC
208884.8 Pa = 84.1 x 10^6 Pa (C)
C= 2.48 x 10^-3 moles / L

44g CO2 in 1 mole
0.109 g in 2.48x10^-3 mole

Am i on the right track?
Not quite. The henry's law constant is in Pa/(mole fraction). So what you calculated was the mole fraction of CO2. Do you know how to calculate the concentration of CO2 from this?
 
  • #9
No would really appreciate if you could show me
 
  • #10
sci0x said:
No would really appreciate if you could show me
In 1 liter of beer, you have 1008 gm of liquid. Assuming it is essentially water, the number of moles of water is 1008/18. If the mole fraction of CO2 is the value you have calculated, how many moles of CO2 does this represent?
 
  • #11
Chestermiller said:
What is your motivation for asking this question?
I think this problem falls into either physics or chem
 
  • #12
bagasme said:
I think this problem falls into either physics or chem
Relative to the solution to this problem, your point is?
 
  • #13
Okay so 0.109 g in 2.48x10^-3 mole is the mole fraction of co2

1008/18 is 56 moles in 1L water

Concentration CO2 is 56 x 0.109 is 6.104 g/l

Many thanks
 

Related to Calculate the equilibrium concentration of CO2 in beer in grams/liter

1. How do you calculate the equilibrium concentration of CO2 in beer?

The equilibrium concentration of CO2 in beer can be calculated using the Henry's Law equation, which states that the concentration of a gas dissolved in a liquid is directly proportional to the partial pressure of the gas above the liquid. This means that the equilibrium concentration of CO2 in beer is dependent on the partial pressure of CO2 in the atmosphere and the solubility of CO2 in beer.

2. What is the significance of calculating the equilibrium concentration of CO2 in beer?

The equilibrium concentration of CO2 in beer is important for determining the carbonation level and taste of the beer. It can also impact the stability and shelf life of the beer, as well as the foam characteristics.

3. What factors can affect the equilibrium concentration of CO2 in beer?

The equilibrium concentration of CO2 in beer can be affected by temperature, pressure, and the composition of the beer (such as alcohol content and pH level). Additionally, the type of container and the amount of headspace in the beer can also impact the equilibrium concentration.

4. Can the equilibrium concentration of CO2 in beer be controlled?

Yes, the equilibrium concentration of CO2 in beer can be controlled by adjusting the temperature, pressure, and composition of the beer. Brewers can also use carbonation techniques and equipment to control the carbonation level in the beer.

5. How can the equilibrium concentration of CO2 in beer be measured?

The equilibrium concentration of CO2 in beer can be measured using various methods such as gas chromatography, pressure gauge readings, and carbonation testers. These methods allow for accurate and precise measurements of the CO2 concentration in beer.

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