Chapter 14 MASS TRANSFER

Chapter 14 Mass Transfer14-41 A carbonated drink in a bottle is considered. Assuming the gas space above the liquid consists of asaturated mixture of CO 2 and water vapor and treating the drink as a water, determine the mole fraction ofthe water vapor in the CO 2 gas and the mass of dissolved CO 2 in a 200 ml drink are to be determined whenthe water and the CO 2 gas are in thermal and phase equilibrium.Assumptions 1 The liquid drink can be treated as water. 2 Both the CO 2 and the water vapor are idealgases. 3 The CO 2 gas and water vapor in the bottle from a saturated mixture. 4 The CO 2 is weakly solublein water and thus Henry’s law is applicable.Properties The saturation pressure of water at 27C is 3.60 kPa (Table A-9). Henry’s constant for CO 2dissolved in water at 27ºC (300 K) is given in Table 14-6 to be H = 1710 bar. Molar masses of CO 2 andwater are 44 and 18 kg/kmol, respectively (Table A-1).Analysis (a) Noting that the CO 2 gas in the bottle is saturated, the partial pressure of water vapor in the airwill simply be the saturation pressure of water at 27C,P vapor P sat @ 27º C 360 . kPaAssuming both CO 2 and vapor to be ideal gases, the mole fraction of water vapor in the CO 2 gas becomesyvaporPvapor360 . kPa 0.0277P 130 kPa(b) Noting that the total pressure is 130 kPa, the partial pressure of CO 2 isP CO gas P P vapor 130 360 . 126.4 kPa = 1.264 bar2From Henry’s law, the mole fraction of CO 2 in the drink is determined to beyCO ,liquid side2PCO ,gas side 1264 . bar2 7.39 10 4H 1710barThen the mole fraction of water in the drink becomesywater, liquid side 1 y 1 7. 39 10 0.9993CO 2 , liquid side4CO 2H 2 O27ºC130 kPaThe mass and mole fractions of a mixture are related to each other bymiNiMiwyM i im N M Mmmmimwhere the apparent molar mass of the drink (liquid water - CO 2 mixture) ism i i liquid water water CO COM y M y M y M 09993 . 18. 0 ( 7. 39 10 ) 18. 0 18.02 kg / kmol2 2Then the mass fraction of dissolved CO 2 gas in liquid water becomeswCO , liquidside2 2MCO2444 yCO , liquidside ( 0) 7.39 10 0.0018018.02M mTherefore, the mass of dissolved CO 2 in a 200 ml 200 g drink ism CO w CO m m 0. 00180( 200 g) 0.360g2 2414-18