Equilibrium concentration of co2 in beer

[sci0x]

Homework Statement

Beer keg, stored at 10 deg C, is pressurized by gas 70% vol/vol CO2 : 30% N2. If the top pressure of the mixed gas is 1.29 bar guage, calculate the equilibrium conc of CO2 in beer (gl-1) assuming that the hydrostatic effect of pressure on CO2 conc of the beer in the keg can ben neglected and the beer has the same density of water

Henrys constant for CO2 at 10 deg C is 116 x 10^3 Pa mole fraction-1
Atm pressure is 1.01 bar absolute
1 bar = 10^5 Pa
Density of water at 10 deg C = 1000kgm-3
Relative mol weight of CO2 and H2O are 44 and 18 respectively

Relevant Equations

Henrys law P=KhC

Absolute pressure is gauge pressure + atmos press

Guage press = 1.29 bar G
1 bar = 10^5 Pa
1.29 bar = 129,000 Pa

Atmos Pres = 1.01x10^5 Pa

Absolute pressure = 230,000 Pa

Henrys law: P=KhC
230000Pa = (116x10^3Pa)C
1.98 mole fraction =C
70% CO2 = 1.387 mole fraction

44g Co2 in 1 mole
61.07g in 1.89mole

1L beer = 1000kgm-3 ÷ 18 = 55.5g

55.5g x 61.07g CO2
= 3389.33 g/L

Please confirm if this is correct

 

[Chestermiller]

Do you really think the mole fraction of CO2 is greater than 1? The Henry's law constant is not 116 x 10^3 Pa. It is 116 x 10^6 Pa.

 

[sci0x]

Updating henrys law constant:

Henrys law: P=KhC
230000Pa = (116x10^6Pa)C
0.0019 mole fraction =C
70% CO2 = 1.33x10^-3 mole fraction

44g Co2 in 1 mole
0.05852g CO2 in 1.33x10^-3 mole

1L beer = 1000kgm-3 ÷ 18 = 55.5g

55.5g x 0.05852g CO2
= 3.247 g/L

 

[Chestermiller]

That should be 55.5 moles of beer in a liter, not grams. Moles CO2 in a liter = 0.00133 x 55.5 = 0.0738 moles/liter

0.0738 moles/liter x 44 g/mole = 3.25 g/l

 

[sci0x]

Thanks Chester