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Chemistry Forums for Students => Undergraduate General Chemistry Forum => Topic started by: sci0x on February 10, 2020, 10:41:55 AM

Title: Calculate the equilibrium concentration of CO2 in beer
Post by: sci0x on February 10, 2020, 10:41:55 AM
Question
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

My workings:
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, its from a past exam paper
Notes to help solve:
Atmos pressure co2 should be used in calc of absolute pressure from gauge pressure
Hydrostatic pressure should 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
Title: Re: Calculate the equilibrium concentration of CO2 in beer
Post by: mjc123 on February 10, 2020, 01:04:21 PM
Atmospheric pressure is not 105 Pa. Did the question say 105 Pa?
Title: Re: Calculate the equilibrium concentration of CO2 in beer
Post by: sci0x on February 10, 2020, 01:34:27 PM
It says 105 Pa, maybe supposed to be 10^5 Pa

Add atmospheric pressure of co2 is 110000

Add hydrostatic pressure for pressure at midpoint
Is 110,000 + (1008)(9.81)(10)
Is 208884.8
This should be the absolute pressure

If this is right i should be able to calc co2 conc by henrys law

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?