4. Suppose the total pressure in a bottle of soda water before it is opened is 3

Question

4. Suppose the total pressure in a bottle of soda water before it is opened is 35 psig and that the gas mixture is 75% CO2 and 25% other gases. The temperature is 5°C. The Henry's Law constant for CO2 is 29.4 atm.L/mol. a. If the system is in equilibrium, what is the saturated mass concentration of CO2 dissolved in the soda? Answer: about 3790 mg/L b. Calculate the new equilibrium concentration when the bottle is opened. The volumetric fraction of CO2 in the normal atmosphere is 400 ppmv. Knowing this, explain why the CO2 acts as it does when the bottle is opened. Partial answer: 0.6 mg/L

Explanation / Answer

Henry’s law constant , H= P/C

C= concentration of CO2 in water and P= partial pressure of CO2

P= partial pressure of CO2= mole fraction* total pressure

Total pressure = 35Psig= 35+14.7 psia= 49.7 psia

14.7 psia= 1 atm, 49,7 psia= 49.7/14.7= 3.38 atm

P= 0.75*3.38 atm=2.5 atm

C= P/H= 2.5/(29.4 ) mol/L=0.085 moles/L

Molar mass of CO2= 44 g/mole, C in terms of mass =0.085*44 g/L=3.74 g/L

1gm= 1000mg, concentration = 3.74*1000 mg/L= 3740 mg/L

2. When the bottle is opened, CO2 gas diffuses out

Partial pressure = mole fraction* atmospheric pressure = 400/106

C= 400/106/29.4 = 13.6*10-6 moles/L = 13.6*44*10-6 gm/L= 13.6*44*1000*10-6 mg/L=0.6 mg/L

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