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

[sci0x]

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

 

[Chestermiller]

I think absolute atmospheric pressure can be taken as 100000 Pa, so the absolute pressure of CO2 at the top is 110000 Pa.

 

[bagasme]

Is it chemistry or physics problem?

 

[Chestermiller]

Is it chemistry or physics problem?

What is your motivation for asking this question?

 

[sci0x]

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

 

[Chestermiller]

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.

 

[sci0x]

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?

 

[Chestermiller]

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?

 

[sci0x]

No would really appreciate if you could show me

 

[Chestermiller]

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?

 

[bagasme]

What is your motivation for asking this question?

I think this problem falls into either physics or chem

 

[Chestermiller]

I think this problem falls into either physics or chem

Relative to the solution to this problem, your point is?

 

[sci0x]

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